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Chapter 1

In this chapter let us see how we use airthmetic in our day-to-day life directly or indirectly.

1.1 Introduction

Some information about Ishwarya and Krithika are given below :

S.No. Information Ishwarya krithika

1. Age 17 years 15 years

2. Height 136 cm 123 cm

3. Weight 31 kg 29 kg

4. Quantity of drinking water 5 litres 3 litres

5. Studying Time 4 hours 3 hours

6. Playing Time 2 hours 2 hours

7. No. of note books used 13 14

8. Speed of cycling 10 km/hr 15 km/hr

From the above table we can compare their information easily. Ratio is used to compare two quantities of the same kind.

From the above table we can easily fi nd out1. Ratio of their ages 17:152. Ratio of their Height 136 : 123

3. Ratio of their Weight 31 : 29

4. Ratio of their Quantity of drinking water 5 : 3

5. Ratio of their Studying Time 4 : 3

6. Ratio of their Playing Time 2 : 2

7. Ratio of their No. of note books used 13 : 14

8. Ratio of their Speed of cycling 10 : 15

1. EVERYDAY ARITHMETICRatio, Proportion and Direct Variation

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Everyday Arithmetic

1.2 Ratio - Ratio is a comparison of two quantities of same units. - The ratio of two quantities a and b is written as a : b. It is read as “ a is to b” - The symbol “:” is read as “is to” - The ratio of b and a is written as b : a. - It is understood that a : b is different from b : a. - When compared the units of a and b must be the same. - The units of a and b are always positive.For Example : If 1m and 90 cm are given, we can compare only after converting them into same units. (i.e.) after converting 1 m as 100 cm, we compare it with 90 cm and write the ratio as 100 : 90. Comparison of bigger number may be diffi cult. It is necessary to reduce them into their lowest terms. We write the ratios as fractions and reduce them into their lowest terms.

S.No. Quantity Ratio form Fractional form

Reduced form

1. Ratio of 15 men and 10 women 15 : 101015 3 : 2

2. Ratio of 500 gm and 1 kg 500 : 10001000500 1 : 2

3. Ratio of 1 m 25 cm and 2m 125 : 200200125 5 : 8

1. A student has 11 note books and 7 textbooks. Find the ratio of the notebooks to that of the text books.

Solution : Number of note books = 11 Number of text books = 7 Ratio of the notebooks to the text books = 11 : 7

The cost of a pen is Rs.8 and the cost of a pencil is Rs.2.50 Find (1) The ratio of the cost of a pen to that of a pencil (2) The ratio of the cost of a pencil to that of a pen. Solution : The Cost of a pen = Rs.8.00 = 8.00x100 = 800 paise The Cost of a pencil = Rs.2.50 = 2.50x100 = 250 paise

Example : 1

Example : 2

Example : 3

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Chapter 1

Example : 4

S.No. Quantity Ratio form Fractional form

Reduced form

1. Ratio of the cost of a pen to that of a pencil 800 : 250

250800 16 : 5

2. Ratio of the cost of pencil to that of a pen 250 : 800

800250 5 : 16

In a Village of 10,000 people, 4,000 are Government Employees and the remaining are self-employed. Find the ratio of i) Government employees to people of the village. ii) Self employed to people of the village. iii) Government employees to self employees.Solution : Number of people in the village = 10,000 Number of Government employees = 4,000 ` Self employed = 10,000 – 4,000 = 6,000

S.No. Quantity Ratio form Fractional form

Lowest form of

the Ratio

1. Government employees to people of the village. 4000 : 10000

100004000 2 : 5

2. Self employed to people of the village. 6000 : 10000

100006000 3 : 5

3. Government employees to self employed. 4000 : 6000

60004000 2 : 3

1. Express the following ratios in the lowest form: (i) 3:5 (ii) 15:25 (iii) 22:55 (iv) 24:48

2. Express the following ratios in the lowest form: (i) 1kg to 500g (ii) 24cm to 4m (iii) 250ml to 3litres (iv) 45min to 2hrs (v) 30paise to 3Rs (vi) 70students to 2teachers

3. Sundar is 50 years old, his son is 10 years old. Write down the ratio between their ages.

(i) 5 years ago (ii) At present (iii) After 5 years

Do These

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Everyday Arithmetic

4. Match the following equivalent ratios: Column A Column B 3:4 5:15 1:3 9:12 4:5 20:30 2:7 14:49 2:3 12:15

1.3 Equivalent Ratios Let us divide an apple into eight equal parts and share it among two people in the ratio 6 : 2

6 : 2 can be simplifi ed as 3 : 1 So, 6 : 2 and 3 : 1 are equal.

Hence like equivalent fractions we can say this as equivalent ratios.

So, in the ratio a : b if the terms ‘a’ and ‘b’ are multiplied by the same non zero number, we get equivalent ratios.

Write any 5 equivalent ratios for 5 : 7Solution :Given ratio = 5 : 7

The ratio in fractional form = 75

The equivalent fractions of 75 are , , , ,

1410

2115

2820

3525

7755

` The equivalent ratios of 5 : 7 are 10 : 14, 15 : 21, 20 : 28, 25 : 35 and 55 : 77

Exercise : 1.11) Say whether the following are true or false i) The ratios of 4 pens to 6 pens is 4 : 6 ii) In a class of 50 students, the ratio between 30 girls and 20 boys is 20 : 30 iii) 3 : 2 and 2 : 3 are equivalent ratios iv) 10 : 14 is a equivalent ratio of 5 : 2

2) Choose the correct answer : i) The fractional form of 3 : 4 is ________

(1) 34 (2)

43 (3)

31 (4) 3.4

ii) The equivalent ratio of 7 : 8 is ________ (1) 14 : 16 (2) 8 : 9 (3) 6 : 7 (4) 8 : 7

Example : 5

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Chapter 1

Example : 6

iii) Simplifi ed form of 16 : 32 ________ (1)

3216 (2)

1632 (3) 1:2 (4) 2:1

iv) If 2 : 3, 4 : _ are equivalent ratios, then the missing term is (1) 2 (2) 3 (3) 4 (4) 6 v) The ratio of 1 cm to 2mm is (1) 1:20 (2) 20:1 (3) 10:2 (4) 2:103) Simplify the following ratios : (i) 20:45 (ii) 100:180 (iii) 144:2164) Write 4 equivalent ratios for the following : (i) 3:5 (ii) 3:7 (iii) 5:95) Write the ratio of the following and simplify : (i) The ratio of 81 to 108 (ii) The ratio of 30 minutes to 1 hour and 30 minutes (iii) The ratio of 60 cm to 1.2 m.6) Seema’s monthly income is Rs.20,000 and her savings is Rs.500. Find the ratio of i) the monthly income to the savings ii) the monthly income to the expenses iii) savings to the expenses.7) Out of 50 students in a class, 30 are boys. Find the ratio of i) Boys to the total number of students ii) Girls to the total number of students iii) Boys to the Girls8) From the given fi gure, fi nd the ratio of i) Number of triangles to Number of circles ii) Number of circles to Number of squares iii) Number of triangles to Number of squares iv) Number of circles to total number of fi gures v) Number of triangles to total number of fi gures vi) Number of squares to total number of fi gures

1.4 Comparison of RatiosTwo ratios can be compared. To compare the ratios, convert the given ratios

into fractions with the same denominator.

Compare 3:5 and 4:7 We have to compare

53 and

74

The L.C.M of denominator 5 and 7 is 35.

53

53

77

3521

#= = 74

74

55

3520

#= =

3521 is greater than

3520

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Everyday Arithmetic

Example : 7

Example : 8

Example : 9

53` is greater than

74

Hence 3:5 is greater than 4:7

Divide Rs. 280 in the ratio 3:5 3:5 means the fi rst quantity is 3 parts and the second quantity in 5 parts. The Total number of parts = 3 + 5 = 8 8 parts = Rs.280 ` 1part =

8280 =35

`3 parts = 3 35 105Rs.# =

and 5 parts = 355# =Rs.175

The length and breadth of a rectangle are in the ratio 4:7. If the breadth is 77cm, fi nd the length?

Breadth = 77cmThe ratio of length to breadth is 4:7

Breadth = 7 parts 7parts = 77cm 1part =

777 cm = 11cm

length = 4 parts 4parts = 4 # 11 cm = 44cm ` Length of the rectangle = 44cm.

In a village of 1,21,000 people, the ratio of men to women is 6 : 5Find the number of men and women?

Solution : Number of people in the village = 1,21,000 Ratio of men to women = 6 : 5 Total number of parts = 6 + 5 = 11 11 parts = 1,21,000

` 1 part = , ,,

111 21 000

11 000=

` Number of men in the village = 6 # 11,000 = 66,000

` Number of women in the village = 5 # 11,000 = 55,000

Parts No. of people 11 1210006 ?5 ?

Parts Amount8 2803 ?5 ?

Parts Measurements7 771 ?4 ?

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Chapter 1

Example : 10

Exercise 1.21. Which is greater (i) 2:3 (or) 3:4 (ii) 4:5 (or) 5:72. Which is smaller (i) 3:4 (or) 4:5 (ii) 3:7 (or) 7:9

3. (i) Divide Rs. 400 in the ratio 3:5 (ii) Divide 5kg 500gm in the ratio 5:6 (iii) Divide 2m 25cm in the ratio 5:4 (iv) Divide 5hours in the ratio 1:54. If Rs.6,600 is divided between Arun and Anand in the ratio 6:5, who will

get more and how much more?5. The length and breadth of a rectangle are in the ratio 7:2. If the length is

49cm. Find the breadth?6. The ratio of expenditure and savings in a family is 5:3. If the expenditure

is Rs3,500. What is the savings?7. Rahim and Bhashir decides to share the gift money of competition in the

ratio 7 : 8. If they receive Rs.7,500. Find the share of each.8. There are 1,00,000 voters in the city. If the ratio of male to female voters is

11 : 9, fi nd the number of men and women voters in the city.

1.5 Proportion If the simplifi ed form of two ratios are equal, they form a proportion. We use “=” or “::” to denote a proportion. If a, b, c, d are proportion, then a:b = c : d or a : b :: c : d

1. Show that the ratios (i) 2 : 3, 8 : 12, (ii) 25 : 45, 35 : 63 are in proportion.

Solution : Ratio form Fractional form Simplifi ed form

i) 2:3 32 2:3

8:12 128

32= 2:3

` 2:3, 8:12 are in proportion

ii) 25:45 4525

95= 5:9

35:63 6335

95= 5:9

` 25:45, 35:63 are in proportion

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Example : 11

Do These

Example : 12

Note : In the above example (ii), multiply 45 by 35 and 25 by 63 We get 25 # 63 = 45 # 35 = 1575

If a : b and c : d are in proportion then a # d = b # c The proportion is written as a : b :: c : d

In a proportion, the product of extremes is equal to the product of means.

Show that 12 : 9, 4 : 3 are in proportion. Solution : The product of the extremes = 12 # 3 = 36 The product of the means = 9 # 4 = 36 ` 12 : 9, 4 : 3 are in proportion (i.e.) 12 : 9 :: 4 : 3

Find the missing term in 3 : 4 = 12 : ____

Solution :

The product of the extremes = The product of the means

Therefore 3 # ____ = 4 # 12 ; By dividing both sides by 3

we get the missing term = 3

4 12# = 16

Using 3 and 12 as means, write any two proportions. Given 3 and 12 are means So, __:3 = 12 : __ The product of the means 3 # 12 = 36 The product of Extremes must be 36 36 can be written as 2 # 18 or 4 # 9 etc, ` 2:3=12:18 4:3=12:19 Two proportions are 2:3::12:18 and 4:3::12:9

1. Using 4 and 20 as means, write two proportions.

2. Using 6 and 15 as means, write two proportions.

Example : 13

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Example : 14

If the cost of a book is Rs.12, fi nd the ratio of 2, 5, 7 books to their cost. What do you observe from this?

No. of books Total Cost Ratio Fractional

formSimplifi ed

form

2 2 # 12 = 24 2 : 24242 1 : 12

5 5 # 12 = 60 5 : 60605 1 : 12

7 7 # 12 = 84 7 : 84847 1 : 12

From the above table, we fi nd that the ratio of the number of books to the cost of books are in proportion.

1.6 Direct Variation

Two quantities are said to be in direct variation if an increase (or decrease) in one quantity results in increase (or decrease) in the other quantity. (i.e.) If two quantities vary always in the same ratio then they are in direct variation.

Shabhana takes 2 hours to travel 35 km. How much distance she will travel in 6 hours? Solution : When time increases the distance also increases. Therefore, they are in direct variation

2 : 6 = 35 : missing term =

26 35 105# =

Shabana has travelled 105 km in 6 hours.

The cost of uniforms for twelve students is Rs.3,000. How many students can get uniform for Rs.1250.Solution :

No. of students Cost of the uniformRs.

12 3,000? 1,250

Example : 15

Example : 16

Time (hrs) Distance (km)2 356 ?

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Everyday Arithmetic

Example : 17

When money spent decreases the number of uniform also drecreases. They are in direct variation

12 : = 3000 : 1250

Missing Term = 3000

12 1250 5# =

5 students can be given uniform for Rs.1,250.

Verify whether the following represents direct variation.

Numbers of books 10 8 20 4Cost (in Rs.) 25 20 50 10

Arrange the data in ascending order.

Numbers of books 4 8 10 20Cost (in Rs.) 10 20 25 50

Here the ratios are , , ,104

52

208

52

2510

52

5020

52= = = =

104

208

2510

2520` = = =

Here all the ratios are equal. ` They are in direct variation.

Exercise : 1.31) State whether the following ratios are in proportion. i) 1:5 and 3:15 (Yes / No) ii) 2:7 and 14:4 (Yes / No) iii) 2:9 and 18:81 (Yes / No) iv) 15:45 and 25:5 (Yes / No) v) 30:40 and 45:60 (Yes / No)

2) Choose the correct answer :

i) Which of the following pair of ratios form a proportion.

(1) 3:4, 6:8 (2) 3:4, 8:6 (3) 4:3, 6:8 (4) 4:8, 6:3

ii) Find the missing term if 2:5 = ___ : 50

(1) 10 (2) 20 (3) 30 (4) 40

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Chapter 1

iii) If the cost of 6 balls is Rs.30 then the cost of 4 balls is (1) Rs.5 (2) Rs.10 (3) Rs.15 (4) Rs.20 iv) If 5,6,10 _____ form a proportion (in the same order), the missing term is (1) 60 (2) 50 (3) 30 (4) 12 v) When you divdide 100 in the ratio 3 : 2, we get _____ (1) 30, 20 (2) 60, 40 (3) 20, 30 (4) 40, 60

3) Verify whether the following represent direct variation or not.

i) Time (in hrs) 2 5 4 3Distance (in kms) 80 200 160 120

ii) Age (in yrs) 2 6 4 8Weight (in kg) 3.5 10.75 15 23

iii) Principal (in Rs) 300 450 250 600Interest (in Rs) 18 27 15 36

4) Complete the table if they are in direct variation.i) 8 10 15 4 2

16 - - - -

ii) 5 - 12 15 10- 28 48 - -

iii) - 20 - 15 1045 - 60 - 15

5) Sarath buys 9 cricket bats for Rs.1,350. How much will Manoj spend to buy 13 cricket bats at the same rate.

6) If a person reads 20 pages from a book in 2 hours, how many pages will he read in 8 hours at the same speed?

7) If 15 people can repair a road of length 150 metres, how many people are needed to repair a road of length 420 metres.

8) The rent for a room for 2 months is Rs. 9200 what will be the rent for one year for that room.

9) The cost of 15 chairs is Rs. 7500. Find the numbers of such chairs that can be purchased for Rs.12,000?

10) The cost of 10 k.g. rice is Rs.400. Find the cost of 3 k.g. rice? 11) A car needs 12 litres of petrol to cover a distance of 156 k.m.

How much petrol will be required for the car to cover a distance of 1300 k.m?

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Everyday Arithmetic

Example : 18

1.7 Proportion - Application. If we want to draw a plan of a home, it is not possible to draw the plan in actual dimensions (size). Let the ratio between drawn length and actual length be a : b

1.If a is less than b,we get a reduced fi gure. 2.If a = b, we get equal scale fi gure (same size fi gure). 3.If a is greater than b, we get an enlarged fi gure.For Example, 1. A house plan map - a reduced fi gure. 2. Geometrical fi gure drawn in note book - equal scale fi gure. 3. Bacteria seen through microscope - enlarged fi gure.

A map is drawn to the scale of 1cm to 200km.

(i) What is the representive fraction.

(ii) If the distance between Nellai and Chennai are 3cm on this map, what is the actual distance between the two places?

Note the drawn length and the actual length are not in the same unit. Therefore convert them into the same unit. Now 200 km = 200 # 100000 cm [a 1km = 100000cm] = 2,00,00,000cm (i) The representive fraction =

200000001

(ii) The distance between Nellai and Chennai (in map) = 3 cm The actual distance between Nellai and Chennai = 3 # 200 = 600 km

Discuss:Look at the India map showing railway routes.

Note the scale on the map and fi nd the actual distance between 1. Chennai and Calcutta 2. Chennai and Mumbai 3. Chennai and Delhi

Exercise 1.4

1. A map is drawn in the scale 1cm to 1000km a) Express this as a representive fraction. b) What is the actual distance represented by 3.5cm in the map? c) What distance on the map will represent an actual distance of 2100km?

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Chapter 1

Points to remember

• The comparison of two quantities of the same unit is called ratio.

• When the terms of ratio are multiplied by the same number, we get equivalent ratios.

• The equality of two ratios is called a proportion.

• In a proportion, the product of extremes = product of means.

• If two quantities vary in the same ratio, then they are in direct variation.

2. A scale used in a map is 1cm to 500m. i) Express as a representive fraction. ii) What is the actual distance represented by 5.5cm on the map? iii)What distance on the map will represent an actual length of 2500m?

3. Fill in the blanks .Scale Actual Length Drawn Length

i) 1 c.m. = 200m 4cmii) 1 c.m. = 250m 1750miii) 1 c.m. =_____m 3700m 5cm

4. The scale of a graph is 1 cm = 200 km. (The distance 1 cm in the graph denotes 200 km in actual length). What would be the length of 3600 km on the graph?

Activity Draw a rough sketch of a rectangular fi eld of length 400m and breadth 250m

by taking a suitable scale.

Project Write the simplest form of ratios in between the total number of boys and

girls in your class and the school.

Find out the ratio for any of your two friends with the help of their height, weight, study hours and playing times.

Make each student to listout the height and weight of his / her fi ve friends and fi nd out the ratio using it.

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Algebra

2.1 IntroductionYou would have played many games eagerly and enthusiastically. Now, shall

we play with numbers?Divide the students in the class into small groups. Each group should think of

a two digit number. Then ask them to do the following calculations.

Step 1 : Multiply the two digit number by 2.

Step 2 : Add 4 to the result.

Step 3 : Muliply the result by 5.

Step 4 : Finally subtract it by 20

From the fi nal answer the number selected by a group can be found. The result obtained by dividing the fi nal answer by 10 is the original number. This is applicable for all the groups.

For example ;If the fi nal answer is 380, now divide 380 by 10.Therefore, the selected number is 38.How do we fi nd this? Let us list the answers for the different

number taken by the group. Observe the pattern formed.For example :Selected number = 23; 23 # 2 = 46; 46 + 4 = 50; 50 # 5 = 250; 250 – 20 = 230If the selected number is 23 the result is 230.Let us verify this with a few more examples.

Selected number = 25, Result obtained = 250Selected number = 40, Result obtained = 400Selected number = 37, Result obtained = 370

Now, we are able to see the relation between the selected number and its result. Note : The algebraic explanation for the above is given at the end of the chapter.

Do it Yourself Try the above game with three and four digit numbers. Create and solve a few more mathematical games.

Check1. 38#2=762. 76+4=803. 80#5=4004. 400–20=380

2. ALGEBRAConstants, Variables and Expressions

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Chapter 2

Exercise : 2.11) Find the missing number in the sequence. 5, 10, 15, _, 25, 30. (i) 20 (ii) 2 (iii) 22 (iv) 232) Choose the next three shapes from the pattern

(i) (ii) (iii)

(iv)

3.

First number 1 2 3 4 5 6Second number 10 20 30 40 50 60

What is the pattern obtained from the table?(i) Second number = 10 + fi rst number. (ii) Second number = 10 – fi rst number.(iii) Second number = 10 ' fi rst number. (iv) Second number = 10 # fi rst number.

2.2 Introduction of constants and variables through patterns

Latha made the following triangular patterns with the match sticks she had.

1. 2. 3. 4.

To fi nd out the total match sticks used for the above formation she prepared the following table.

Numbers of triangles 1 2 3 4 ....

Number of match sticks used.

3 6 9 12 ....

3#1 3#2 3#3 3#4 ....

From the above table she found a relation between the number of triangles and the number of match sticks used. That is

Number of match sticks used = 3 # number of triangles

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Algebra

Example : 1

Here according to the number of triangles formed there is a change in the number of match sticks used. We fi nd that the number of match sticks used to form a triangle is always the same. Likewise a quantity which takes a fi xed numerical value is called a constant. But number of triangles keep changing. Therefore we denote number of triangles by the letter x. Therefore number of match sticks used = 3 # x = 3x The above reduced law can be taken as “Laws of patterns”. A quantity which takes different numerical values is called a variable. Usually variables are denoted by small letters.a,b,c, ...., x,y,z, ,....

Let us see the fomation of letter E with the help of match sticks. We need 5 match sticks to form letter E

1. 2. 3.

4. 5.

Number of E formation 1 2 3 4 5 ....

Number of match sticks used

5 10 15 20 25 ....

5 # 1 5 # 2 5 # 3 5 # 4 5 # 5

Law obtained from the above table.

Number of match sticks used = 5 # (Number of E formation)

Number of E formation is denoted as the variable x.

Therefore, number of match sticks used = 5 # x = 5 x

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Chapter 2

Example : 2

Look at the pattern of the Asoka tree given. The base is always formed with two match sticks. The top portion of the tree differs in multiples of 3.

1 2 3 4 5

Number of top portions 1 2 3 4 5 ....

Number of match sticks needed for the top portion

3 6 9 12 15 ....

3#1 3#2 3#3 3#4 3#5 ....

Number of match sticks needed for the base

2 2 2 2 2

Total num-ber of match sticks used

3#1+2 3#2+2 3#3+2 3#4+2 3#5+2 ....

Law obtained from the above table,Number of match sticks used = ( 3 # Number of top portions) + (Number of

match sticks used for the base)If the number of triangular formations is denoted as the variable x,Number of match sticks used = 3 # x + 2 = 3x + 2

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Algebra

Exercise 2.2 1. Choose the correct answer:

a)First

number 16 26 36 46 56 66

Second number 10 20 30 40 50 60

Choose the law in which the above pairs are based on?1) Second number = fi rst number + 6ii) Second number = fi rst number – 6iii) Second number = fi rst number ' 6

iv) Second number = fi rst number # 6

b)

First number 1 2 3 4 5

Second number 9 10 11 12 13

Choose the law in which the above pairs are based on? i) Second number = fi rst number ' 8 ii) Second number = fi rst number -8 iii) Second number = fi rst number + 8 iv) Second number = fi rst number # 8

2. If a box contains 40 apples, the total number of apples depends on the number of boxes given. Form an algebraic term (Consider the number of boxes as ‘x’).

3. If there are 12 pencils in a bundle, the total number of pencils depends

on the number of boxes given . Form an algebraic term (Consider the number of bundles as ‘b’).

4. From the following patterns given below, form an algebraic term. i)

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Chapter 2

Project Make one square, two squares, three squares ... ten squares using match sticks

and listout how many match sticks are required for each squares.

Note : Algebraic explanation for the group gameAlgebraic explanation for the group game is given in the beginning of the chap-ter.Let the number selected by the friend be ‘x’ multiply the selected number by 2, 2x; and 4(2x+4); Multiply by 5(5x (2x + 4) = 10x + 20)Subtract 20 (10x + 20 – 20 = 10x)Now the number selected can be found by dividing 10x by 10. Finally we get the number selected.

Points to remember

• Variable has no constant value. It takes various values according to the given situation.

• Variables are denoted by small letters a, b, c, ... x, y, z...

• Expressions can be related using variables.

• In arithmetic and geometry, formulae are obtained using variables.

ii)

iii)

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Measurements

Introduction

Let us observe our activities from morning to evening .

We fi x certain timings for morning routines, going to school, studying, playing etc., Our ancestors used to calculate time by just looking at the sun, to perform their duties.But that would not be possible during cloudy days and rainy seasons.

In olden days,they used many different clock instruments to fi nd time. Egyptians used shadow clock, Britishers used candle clock, Chinese used rope clock, Europeans used oil clock and Indians used water clock. Sand clock was used by many other countries.

Shadow Clock Candle Clock Rope Clock Water Clock Sand Clock

In course of time mechanized clock were introduced by rectifying the faults in these clocks. As time is very imporatant in our life, it is necessary to learn about time.

3.1 Units of time Seconds, minute, hour, day, week, month and year are the units of time. Let us learn about these units now:

Convert 120 Seconds into minutes Solution:120 seconds = 120 #

601 =

60120 = 2 minutes

120 seconds = 2 minutes

60 seconds = 1 minute1 sec =

601 minute

60 minutes = 1 hour1 minute =

601 hour

1 minute = 60 seconds1 hour = 60 minutes = 60 # 60 seconds = 3600 seconds1 day = 24 hours = 1440 minutes (24 # 60)

= 86,400 seconds (24 # 60 # 60)

Example : 1

a 60 seconds = 1 minute 1 second =

601 minute

3. MEASUREMENTS Measures of Time

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Chapter 3

Convert 360 minutes into hoursSolution :360 minutes = 360 #

601 = 360/60 = 6 hours

360 minutes = 6 hours.

Convert 3 hours 45 minutes into minutesSolution : 1 hour = 60 minutes 3 hours = 3 # 60 = 180 minutes 3 hours and 45 minutes = 180 minutes + 45 minutes = 225 minutes.

Convert 5400 seconds into hoursSolution : 5400 Seconds = 5400 #

36001 hour

= 69 =

23 = 1

21 hours.

5400 seconds = 1 21 hours.

Do it yourself1) Convert the duration of the lunch break into seconds.2) Convert play time in the evening into hours.

Convert 2 hours 30 minutes 15 seconds into seconds.Solution : 1 hour = 3600 seconds & 2 hours = 2 # 3600 = 7200 seconds1 minute = 60 seconds & 30 minutes = 30 # 60 = 1800 seconds 2 hours 3 minutes 15 seconds = 7200 + 1800 +15 = 9015 seconds.We normally denote time from 12 mid-night to 12 noon as a.m. (Ante meridiem) and the time from 12 noon to 12 mid-night is noted as p.m. (post meridiem).Note : We denote 4 hours and 30 minutes as 4 : 30 (or) 4 . 30. Even though we are using the decimal point it is not a usual decimal number.

Example : 2

Example : 3

Example : 4

Example : 5

60 minutes = 1 hour` 1 minute =

601 hour

3600 seconds = 1 hour` 1 second =

36001 hour

9.00 hours in the morning is denoted as 9.00 a.m. and 4.30 hours in the evening is denoted as 4.30 p.m.

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Measurements

Exercise 3.11. Fill in the blanks i) 1 hour = -----------------minutes ii) 24 hours = -----------------day iii) 1 minute = -----------------seconds iv) 7 hours and 15 minutes in the morning is denoted as------------------------- v) 3 hours and 45 minutes in the evening is denoted as--------------------------

2. Convert into seconds i) 15 minutes ii) 30 minutes 12 seconds iii) 3 hours 10 minutes 5 seconds iv) 45 minutes 20 seconds

3. Convert into minutes i) 8 hours ii) 11 hours 50 minutes iii) 9 hours 35 minutes iv) 2 hours 55 minutes

4. Convert into hours i) 525 minutes ii) 7200 seconds iii) 11880 seconds iv) 3600 seconds

3.2 Railway time Observe the following table : Have you seen a table like this anywhere else?

Sl.No. TrainNumber

Name of theTrain

Place ofDeparture Destination Departure

TimeArrivalTime

1. 2633 Kanyakumari Express Egmore Kanyakumari 17.25 hrs. 6.30 hrs.

2. 2693 MuthunagarExpress Egmore Tuticorin 19.45 hrs. 6.15 hrs.

3. 6123 Nellai Express Egmore Nellai 19.00 hrs. 8.10 hrs.

4. 2637 Pandian Express Egmore Madurai

Junction 21.30 hrs. 6.15 hrs.

5. 6177 Rock Fort Express Egmore Trichirappalli 22.30 hrs. 5.25 hrs.

6. 2635 Vaigai Express Egmore Madurai 12.25 hrs. 20.10 hrs.

7. 2605 Pallavan Express Egmore Trichirappalli 15.30 hrs. 20.50 hrs.

24

Chapter 3

Observe the timing given in the above table. How many hours are there in a day? Ans. 24 hours.

We generally call 24 hour clock time as railway time. Railway timings are not expressed in a.m. and p.m. All timings are expressed as just hours. In the above table, departure time and arrival time of some express are more than 12.00 hours. While converting these hours into ordinary timings we should subtract 12 from the hours column.

Shall we learn to convert timings?

1. Convert into railway timings(i) 8.00 a.m. (ii) 10.25 a.m. (iii) 12 noon (i) 8.00 a.m. = 8.00 hours (ii) 10.25 p.m. = 10.25 + 12.00 ---------- = 22.25 hours ---------- (iii) 12.00 noon = 12.00 hours

2. Express in ordinary timings (i) 23.10 hours (ii) 24 hours (iii) 9.20 hoursSolution : i) 23.10 hours = 23.10 -12.00 = 11.10 p.m. ii) 24 hours = 24.00 = 12.00 midnight iii) 9.20 hours = 9.20 a.m.

Example : 6

Example : 7

Exercise 3.2

1. Express in railway timings. (i) 6.30 a.m. (ii) 12.00 midnight (iii) 9.15 p.m. (iv) 1.10 p.m.

2. Express in ordinary timings. (i) 10.30 hours (ii) 12.00 hours (iii) 00.00 hours (iv) 23.35 hours

3.3 Calculating time intervalDeepa said to her friend Jancy that she studied for 3 hours from 8.00 a.m. to11.00 a.m. How did Deepa calculate the duration of time as 3 hours?

Find the duration of time from 4.00 a.m. to 4.00 p.m.Solution : 4.00 p.m. = 4 hrs. 00 min + 12 hrs. 00 min. = 16 hrs. 00 min = 16 hrs. ` duration of time = 4.00 p.m. - 4.00 a.m. = 16.00 hrs - 4.00 hrs. = 12 hours.

Do it yourself

List your daily routines in railway timings and convert them into ordinary timings.

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Measurements

Example : 8

Example : 9

Cheran Express departs from Chennai at 22.10 hours and reaches Salem at 02.50 hours the next day. Find the jouney time.Solution : Arrival at Salem = 02.50 hrs. Departure time form Chennai = 22.10 hrs. (previous day) Journey time = (24.00 – 22.10) + 2.50 = 1.50 + 2.50 = 4.40 ` Journey time = 4 hours 40 minutes.

A boy went to school at 9.00 a.m. After school, he went to his friend’s house and played. If he reached back home at 5.30 p.m. fi nd the duration of time he spent out of his house.Solution : Starting time from home = 9.00 a.m. Duration between starting time and 12.00 noon = 12.00 – 9.00 = 3.00 hours Reaching time (home) = 5.30 p.m ` Duration of time he spent out of his house = 3.00 + 5.30 = 8.30 hours.

Exercise 3.31. Calculate the duration of time (i) from 3.30 a.m to 2.15 p.m. (ii) from 6.45 a.m. to 5.30 p.m.

2. Nellai Express departs from Tirunelvelli at 18.30 hours and reaches Chennai Egmore at 06.10 hours. Find the running time of the train.

3. Sangavi starts from her uncle’s house at 10.00 hours and reaches her house at 1.15 p.m. What is the duration of time to reach her house?

3.4 Leap Year

Rama was celebrating his birth day happily. His friend Dilip was sitting aloof at a corner. Rama asked Dilip “why are you sad?”. Dilip replied “I can’t invite you every year for my birthday”. When Rama asked ‘why’, Dilip said “I can celebrate my birth day only once in 4 years”. Rama exclaimed “why is that so?”

“Because my birthday falls on 29th February” replied Dilip.

26

Chapter 3

Example : 10

Satish asked “29” February! what are you talking Dilip? But February has only 28 days”. “Yes Satish, generally it is 28 days. But once in 4 years February has 29 days. We call that year as a leap year. There are 366 days in a leap year and 365 days in an ordinary year” Dilip said. “Why do we have an extra day in a leap year?” “I don’t know. Let us ask our teacher” replied Dilip. Both went to meet their teacher and expressed their doubt. The teacher explained the reason as follows: You know that the earth takes one year to make one complete revolution around the sun and 365 days make 1 year. But in fact the earth takes 365.25 days to make one revolution. So this extra 0.25 day is added to every February and it amounts to one day in 4 years (0.25 # 4 = 1). Such a year is known as leap year. So February has 29 days in a leap year.

Know yourself1. Which century are we in?2. Which is a millennium year?

1day = 24 hours1 week = 7 days1 year = 12 months1 year = 365 days1 leap year = 366 days10 years = 1 decade100 years = 1 century1000 years = 1 millennium

How will you identify a leap year? A year which is exactly divisible by 4 is a leap year.

But the years which are multiples of 100, should be exactly divisible by 400 to be a leap year. The years 1900, 1800, 1700, 1500 are not leap years why? Because, these numbers leave remainders when we divide by 400.

But 1200, 1600, 2000, 2400 are all leap years as they leave no remainder when divided by 400.

Which of the following are leap years? (i) 1400 (ii) 1993 (iii) 2800 (iv) 2008solution : (i) Divide 1400 by 400 1400 ' 400 gives Quotient 3, Remainder 200 ` 1400 is not a leap year

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Example : 11

Example : 12

Example : 13

(ii) Divide 1993 by 4 1993 ' 4 gives Quotient 498 remainder 1 ` 1993 is not a leap year.

(iii) Divide 2800 by 400 2800 ' 400 gives Quotient = 7, Remainder = 0 ` 2800 is leap year.

(iv) Divide 2008 by 4 2008 ' 4 gives Quotient = 502, Remainder = 0 ` 2008 is leap year.

Find the number of days from 15th August to 27th October.Solution : There are 31 days in August. Number of days in August = 31 – 14 = 17 days Number of days in September = 30 days Number of days in October = 27 days Total = 74 days

Convert 298 days into weeks.Solution : 298 days =

7298 weeks

` 298 days = 42 weeks and 4 days.

Find the number of days between 12th January 2004 and 7th March 2004.Solution : Find whether the given year is a leap year or not. 2004 ' 4 Quotient = 501, remainder = 0. ` 2004 is a leap year and has 29 days in February.

Note :Since it is given from 15th August Substract 14 days (Prior to 15th) from 31 (The total number of days of the month)

1 week = 7 days.1 day =

71 week.

28

Chapter 3

Example : 14

Number of days in January = 31–12 = 19 daysNumber of days in February = 29 daysNumber of days in March = 6 days Total Number of days = 54 days` Number of days between 12th January 2004 and 7th March 2004 are 54 days.

Exercise 3.41. Fill in the blanks. (i) 1 week = _________ days. (ii) In a leap year, February has _________days. (iii) 3 days = _________ hours. (iv) 1 year = _________ months. (v) 1 hour = _________ seconds.2. Which of the following are leap years? (i) 1992 (ii) 1978 (iii) 2003 (iv) 1200 (v) 19973. Find the number of days from 4th January 1996 to 8th April 1996.4. Convert into weeks. (i) 328 days (ii) 175 days

An offi ce functions from 10 in the morning till 5:45 in the evening with a lunch break in the afternoon from 12:45 to 1:30. If an offi ce works for 6 days in a week. Find the total duration of working hours in a week.

Solution : hrs. min. The closing time of the offi ce = 17 45 The opening time of the offi ce = 10 00 ----------- Time in between = 07 45 Lunch break [13:30-12:45] = 00 45 ----------- Working hours for 1 day = 07 00 -----------

` Total working hours for 6 days = 7#6 hrs. = 42 hrs. ` Total duration of working hours in a week = 42 hrs.

5.45 p.m. = 17.45 hrs1.30 p.m. = 13.30 hrs.

Hrs. Min. 12 90 13 30 12 45 0 45

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Measurements

Example : 15 A clock is fast by 5 seconds per hour fi nd the time that it will show at 4 p.m.

if it was adjusted to correct time at 6 a.m.Solution :

4 p.m. = 16.00 hrs. 6 a.m . = 06.00 hrs. ----------- Duration of time = 10.00 hrs. -----------

In 1 hr, the clock runs fast by 5sec.

In 10 hrs, it runs fast by 10#5sec. = 50sec.

Hence, the clock will show 50sec more than the correct time at 4 p.m. (i.e.) at 4 p.m., the clock will show 4 hrs 00 Min 50 sec in the afternoon.

Try these 1. A bank functions from 9 in the morning till 3:30 in the afternoon with a

lunch break in the afternoon from 12:30 to 1:15. If the bank works for 6 days in a week, fi nd the total duration of working hours in a week.

2. A clock is slow by 6 seconds. per hour. If it was adjusted to correct time at 5.a.m. fi nd the time the clock will show at 3.00.p.m.

ActivityDivide the class into different groups. Ask them to compare their ages and fi nd out the eldest. Compare all the groups and fi nd the eldest and youngest in the class.

Project Make them to fi nd out the leap years between 1980 to 2012.

Go to the nearest railway station and prepare a project using the destination, departure time, arrival time and distance of different trains.

Find out the years of your birthday and family members as ordinary year or a leap year.

30

Chapter 3

Points to remember

• Seconds, minutes, hours, day, week, month and year are the units of time.

• 12.00 midnight to 12.00 noon is forenoon.

• 12.00 noon to 12.00 midnight is afternoon.

• 12 hours in forenoon and 12 hours in afternoon together gives 24 hours of

railway timings.

• An ordinary year has 365 days. But a leap year has 366 days.

1. Convert the following into seconds: i) 2 minutes = sec ii) 5 minutes 7 seconds = sec iii) 2.5 minutes = sec iv) 3.5 hrs = sec

2. Convert the following into minutes i) 30 seconds = min. ii) 2.4 hrs = min. iii) 1 hr. 16 min. = min. iv) 2 days 1 hr. = min.

3. Convert the following into hours. i) 90 minutes = hrs. ii) 2.25 days = hrs. iii) 2 days 14 hrs = hrs. iv) 1 week 2days = hrs.

4. Calculate the time interval for the following i) 4.45 p.m. to 9.50 p.m. Ans : hrs. mins. ii) 7.15 a.m. to 7.25 p.m. Ans : hrs. mins. iii) 2.05 p.m. to 6.45 a.m. the next day. Ans : hrs. mins. iv) 5.36 a.m. yesterday to 9.38 p.m. today. Ans : hrs. mins.

Try These

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Geometry

4.1 Introduction

Mark a point ‘O’ on a sheet of paper. From ‘O’ draw two rays ,OA OB as shown in the fi gure.

In this fi gure both the rays start from a single point ‘O’. An angle is formed at ‘O’. Two rays ,OA OB are called as arms (or sides) of the angle. The common point ‘O’ is called as the ‘vertex’ of the angle. The angle is represented by a small curve as shown in the fi gure 1.

So, an angle is formed when two rays are drawn from a common point.

The angle shown in fi g. 1 is represented as AOB+ or BOA+ . We read it as angle AOB or angle BOA. Vertex of the angle is always written in the middle. Sometimes the angle is represented as O+ .

Observe the adjacent fi gure (fi g.2)

We know that rays are named by two points - one at its start and one on the remaining portion. So, ,OA OB represent the same ray. Likewise ,OC OD also represent the same ray. Therefore, the angles can be represented by the following ways.

O, COA, DOA, COB, DOB, AOC, AOD, BOC, BOD+ + + + + + + + +

In fi g.3, with ‘O’ as the centre, OA rotates in the anticlockwise direction and reaches OB .

The rotation made by the ray is called the measure of that angle.

fi g.2

fi g.3

4. GEOMETRYAngles

32

Chapter 4

Rigth angle

Fold a piece of paper as shown in the

fi gure and unfold it. We get two intersecting

line segments. Name these as AB and CD.

These line segments make four angles at

the point of intersection ‘O’. We see that

the four angles

AOC, BOC, DOB, AOD+ + + + are equal.

Each of them is called a right angle.

Right angle measures 90o. In the fi g. XOY+ is a right angle

Straight angle

An angle whose measure is 180o is called a striaght angle.

Acute angle

An angle whose measure is greater than 0o but less than 90o is called an acute angle Example : 2o, 10o, 37o, 80o, 89o.

The measure of the angle at 3 o’ clock.

Measure of the angle at 6 o’ clock.

Measure of the angle at 11.55.

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Geometry

Obtuse angle

An angle whose measure is greater than 90o and less than 180o is called an obtuse angle

Example : 91o, 96o, 142o, 160o, 178o.

Zero angle

If both the rays coincide, the angle formed is 0o.

Exercise 4.1

1. State whether the given angles are acute, right or obtuse angle.

(i) 45o (ii) 138o (iii) 100o (iv) 175o

2. What is the measure of the angle formed by the hour hand and minute hand of a clock for the following timings?

(i) 12.10 (ii) 4.00 (iii) 9.00 (iv) 7.45

3. Name the angles and write its kind.

(i) (ii)

Measure of the angle at 8 o’ clock.

Measure of the angle at 12 o’ clock.

34

Chapter 4

Example : 1

Activity 1. Through how many degrees does the minute - hand turn in 15 minutes? 2. Through how many degrees does the minute-hand turn in 30 minutes? 3. Through how many degrees does the minute-hand turn in 1 hour? 4. Through how many degrees does the hour-hand turn in 3 hours? 5. Through how many degrees does the hour-hand turn in 6 hours?

6. Give some examples for right angle from your environment?

4.2 Complementary angles and Supplementary angles

Complementary angles

In the fi gure given AOB 90+ = c, we know that it is a right angle. The other angles are

AOC 30 , COB 60+ += =c c. Sum of AOC+ and COB+ is 90o.

(i.e) 30o + 60o = 90o 30o and 60o are complementary angles.If the sum of the measures of two angles is 90o then they are called complementary angles.

For Example :When a ladder is leaning on a wall, the angles made by the ladder with the fl oor and the wall are always complementary.

The complement of 40o = 90o – 40o = 50o

The complement of 66o = 90o – 66o = 24o

The complement of 35o = 90o – 35o = 55o

Supplementary angles

In the given fi gure the angle formed by AB with ‘O’ is a straight angle (ie) 180o.Here AOC 50 , COB 130+ += =c c.Moreover the sum of these two is 180o.(i.e.) 130o + 50o = 180o

130o and 50o are supplementary angles.

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Geometry

If the sum of measures of two angles is 180o then they are called supplementary angles.

Example : The angles formed at the centre point of a see-saw are always supplementary angles.

supplement of 40o = 180o – 40o = 140o supplement of 78o = 180o – 78o = 102o

supplement of 110o = 180o – 110o = 70o supplement of 66o = 180o – 66o = 114o

Exercise 4.21. Find the complementary angles for the following. (i) 37o (ii) 42o (iii) 88o (iv) 0o (iv) 16o

2. Find the supplementary angles for the following. (i) 6o (ii) 27o (iii) 88o (iv) 104o (v) 116o (vi) 146o (vii) 58o (viii) 179o

3. Find the measures of the angle from the fi gure. BOC+ = ______4. State whether true or false.

(i) Measure of a striaght angle is 180o. (ii) If the sum of the measure of two angles is 90o, then they are called

complementary angles. (iii) Complement of 26o is 84o. (iv) If the sum of the measures of two angles is 180o, then it is called a right

angle. (v) The Complement of an acute angle is an acute angle. (vi) The supplement of 110o is 70o.5. State whether the given angles are complementary or supplementary (i) 25o, 65o (ii) 120o, 60o (iii) 45o, 45o (iv) 100o, 80o

6. (i) Find the angle which is equal to its complement? (ii) Find the angle which is equal to its supplement?7. Fill in the blanks (i) Supplement of a right angle is ................ (ii) Supplement of a acute angle is ................ (iii) Supplement of a obtuse angle is ................ (iv) Complement of an acute angle is ................

36

Chapter 4

Project List the measure of angles using the paper folding.

Colour the complementary angles and supplementary angles using papers.

Prepare a model clock and draw the pictures of acute, obtuse and right angles.

Collect and paste the pictures which represents acute, obtuse and right angles.

List ten places where angles are being produced which we see in our day today life.

1. State the type of angle (acute, right, obtuse or straight) for the following: i) 45o Type of angle : ii) 62o Type of angle : iii) 90o Type of angle : iv) 105o Type of angle : v) 180o Type of angle : vi) 32o Type of angle : vii) 155o Type of angle : viii) 162o Type of angle :

2. Calculate the complementary angles for i) 15o complementary angle = degrees ii) 79o complementary angle = degrees iii) 56o complementary angle = degrees

3. a and b are complementary angles. If a = b fi nd the value of a. a = degrees

4. x and y are complementary angles. If x = 2y fi nd the values of x and y. x = degrees, y = degrees

5. Calculate the supplementary angles for i) 56o supplementary angle = degrees ii) 92o supplementary angle = degrees iii) 105o supplementary angle = degrees

6. a and b are supplementary angles. If a = 2b fi nd the values of a and b. a = degrees, b = degrees

7. x and y are supplementary angles. If x = 5y fi nd the values of x and y. x = degrees, y = degrees

Try These

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Practical Geometry

5. PRACTICAL GEOMETRYConstructing and Measuring Angles

5.1 Constructing and Measuring Angles We have studied the concept of an angle and the different kinds of angle in the previous chapter. We shall now learn how to measure and draw the given angle. The unit for measurement of an angle is degree and an angle is measured with the help of the protractor. Construct an acute angle of 60o.Sept 1 : Draw a line segment PA.Sept 2 : (i) Place the protractor on the line

segment PA (ii) Place the mid point of the protractor

at point P as shown in the fi gure.Sept 3 : (i) On PA from the right start counting

from 0o in the ascending order (anticlock wise direction and fi nally mark a point Q using a sharp pencil at the point showing 60o on the semi-circular edge of the protractor.

(ii) Remove the protractor and join PQ (iii) We get the required angle m APQ 60+ = c

Construct an obtuse angle 125o

Follow the procedure given in example 1 for step 1 and step 2Sept 3 : (i) On PA from the right start counting from

0o in the ascending order (anticlock wise direction ) and fi nally mark a point Q using a sharp pencil at the point between 120o and 130o showing 120o on the semi-circular edge of the protractor.

(ii) Remove the protractor and join PQ (iii) We get the required angle m 125APQ+ = c

Example : 1

Example : 2

38

Chapter 5

Exercise 5.11. Draw and name the following angles.

(i) 65o (ii) 35o (iii) 110o (iv) 155o (v) 69o

2. Draw and measure the angles made by the hour hand a minute hand of a clock when it shows 9 o’ clock, 4 o’ clock and 12 o’ clock respectively.

3. Measure and name the angles for the following fi gures.

4. From the given fi gure measure and write m ABC, m BCD, m CDE+ + +

5. Measure the following six angles in the fi gure given below.

.

.

.

.

.

.

m AOB

m AOC

m AOD

m BOC

m BOD

m COD

1

2

3

4

5

6

+

+

+

+

+

+

6. Measure and name the angles in the following fi gure.

1. Draw different angles and measure them.2. Draw angles for different measures as you like.

Do These

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Exercise 1.11. (i) True (ii) False (iii) False (iv) False2. (i) 2 (ii) 1 (iii) 3 (iv) 4 (v) 33. (i) 4 : 9 (ii) 5 : 9 (iii) 2 : 3 4. (i) 6 : 10, 9 : 15, 12 : 20, 24 : 40 (ii) 6 : 14, 12 : 28, 15 : 35, 30 : 70 (iii) 10 : 18, 15 : 27, 30 : 54, 40 : 725. (i) 3 : 4 (ii) 1 : 3 (iii) 1 : 2 6. (i) 40 : 1 (ii) 40 : 39 (iii) 1 : 397. (i) 3 : 5 (ii) 2 : 5 (iii) 3 : 28. (i) 1 : 2 (ii) 4 : 3 (iii) 2 : 3 (iv) 4 : 9 (v) 2 : 9 (vi) 1 : 3

Exercise 1.21. (i) 3 : 4 (ii) 4 : 5 2. (i) 3 : 4 (ii) 3 : 73. (i) 150, 250 (ii) 2k.g 500g, 3kg. (iii) 1m 25c.m, 1m. (iv) 50 min, 6hr 10min.4. Arun got Rs. 600 more than Anand5. 14c.m, 6. Rs. 2,100 7. Rs. 3,500, Rs. 4,0008. 55,000, 45,000

Exercise 1.31) (i) yes (ii) No (iii) Yes (iv) No (v) Yes2) (i) 1 (ii) 2 (iii) 4 (iv) 4 (v) 23) (i) yes (ii) No (iii) No4) (i) 20, 30, 8, 4 (ii) 20, 7, 60, 40 (iii) 30, 30, 40, 22.55) Rs. 1950 6) 80 7) 42 8) Rs. 55,200 9) 24 10) 120 11) 100

Exercise 1.41) (i)

, , ,10 00 00 0001 (ii) 3,500 k.m. (iii) 2.1 c.m.

2) (i) ,50 0001 (ii) 2,750 k.m. (iii) 5 c.m.

3) (i) 800 m. (ii) 7 c.m. (iii) 740 m 4) 18 c.m.

Exercise 2.1

1) (i) 20 2) (ii) 3) (iv) Second number = 10 x First number

ANSWERS

40

Exercise 2.21) a) (ii) b) (iii) 2) 40x 3) 12b 4) (i) 6x (ii) 6y (iii) 7z

Exercise 3.11) (i) 60 (ii) 1 (iii) 60 (iv) 07.15 a.m. (v) 3.45 p.m.2) (i) 900 seconds (ii) 1812 seconds (iii) 11,405 seconds (iv) 2720 seconds3) (i) 480 minutes (ii) 710 minutes (iii) 575 minutes (iv) 175 minutes4) (i) 8 hours 45 minutes (ii) 2 hours (iii) 3 hours 18 minutes (iv) 1 hour

Exercise 3.21) (i) 6.30 hours (ii) 0 hour (iii) 21.15 hours (iv) 13.10 hours2) (i) 10.30 a.m. (ii) 12 noon (iii) Midnight 12 (iv) 11.35 p.m.

Exercise 3.31) (i) 10 hours 45 minutes (ii) 10 hours 45 minutes 2) 11 hours 40 minutes 3) 3 hours 15 minutes

Exercise 3.41) (i) 7 (ii) 29 (iii) 72 (iv) 12 (v) 36002) (i), (iv) 3) 96 4) (i) 46 weeks and 6 days (ii) 25 weeks

Exercise 4.11. (i) Acute angle (ii) Obtuse angle (iii) Obtuse angle (iv) Obtuse angle2. (i) Acute angle (ii) Obtuse angle (iii) Right angle (iv) Acute angle3. (i) +AOB Straight angle +DOB Obtuse angle +BOA Straight angle +AOD Acute angle +DOC Acute angle +AOC Right angle (ii) +AOB Acute angle +AOC Acute angle +AOD Right angle +BOC Acute angle +COD Acute angle

Exercise 4.21) (i) 53o (ii) 48o (iii) 2o (iv) 90o (v) 74o

2) (i) 174o (ii) 153o (iii) 92o (iv) 76o (v) 64o

(vi) 34o (vii) 122o (viii) 1o 3) 50o

4) (i) True (ii) True (iii) False (iv) False (v) True (vi) True5) (i) Complementary (ii) Supplementary (iii) Complementary (iv) Supplementary6) (i) 45o (ii) 90o

7) (i) Right angle (ii) Obtuse angle (iii) Acute angle (iv) Acute angle

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Textbook TeamAuthors

S.Shameem, Senior Lecturer, DIET, Triplicane, Chennai.R.Sivagama Sundari. DEEO, Chennai. V.Balamurugan. P.G.Teacher, Dr. Radhakrishnan GHSS (B), Tiruttani, Thiruvallur Dist.H.Jayala Irince, P.G.Teacher, GHSS, Maduravoyal, Thiruvallur Dist.M.Shanthi, P.G.Teacher, Sri Vidhyalaya Mat.HSS, Gobichettipalayam, Erode Dist.M.Srivellingiri, H.M, P.U.M.School, Pongaliyur, K.M.Pattinam, Pollachi. Coimbatore Dist.N.Saravanan, B.T.Asst, Govt. High School, Kuppichipalayam, Erode Dist.S.Jayapriya, B.T.Asst,P.U.M.S, Kattumalayanur, Thiruvannamalai Dist. P.Devarajan, BRTE, Zone-2, Royapuram, Chennai. T.S.Sarasvathi, B.T.Asst, Municipal Hr.Sec.School, Jameen Royapetrtai, Kanchipuram Dist. A.Julia Mary, BRTE, Villivakkam Block, Thiruvallur District.

TranslatorsB.Ilangovan, Asst Head Master, Karnataka Sanga Hr. Sec. School, T.Nagar, Chennai.S.Thapasi, P.G.Asst, Wesley Hr. Sec. School, Royapettah, Chennai.R.Soundarapandian, P.G.Asst, Sir.M.Ct.M. Hr. Sec. School, Purasawalkam, Chennai.R.Madhumidha, P.G.Asst, Wesley Hr. Sec. School, Royapettah, Chennai.E.Sampath Kumar, B.T.Asst, Jg.V.V.Mat.Hr. Sec. School, Anna Nagar, Chennai.G.Angelin Ruby, T.G.T.Zion Mat Hr. Sec. School, Selaiyur,Tambaram, Kanchipuram District. Josephine Rosalind Eugene, B.T.Asst, St.Joseph A.I.Hr.Sec.School, Perambur, Chennai. P.Preetha, M.G.B.T.Asst., St.Joseph A.I. Hr. Sec.School.Perambur,Chennai.S.Usha, T. G .T., S.B.O.A Mat. Hr. Sec. School, Anna Nagar, Chennai.

IllustrationA.Kasiviswanathan, Art Master, Govt. Hr. Sec.School, Udayapatti, Salem District.M.Chinnasamy, Art Master, Govt. Hr. Sec.School, Kottur, Coimbatore District.

Laser Typeset & Book layout: K.Sivakumar, M.S.Nagarajan, J.Sankaran

ScienceStandard Six

Term II

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Note to the teacher…

As we present this revised edition of the Science Textbook, we would like to express our deepest gratitude to the learners and the teaching community for their enthusiastic responses.

In science some concepts could be subject to change from time to time as new theories and principles are constantly being evolved.

We have tried to present facts and concepts of science (both concrete and abstract) in a visually appealing manner without detracting from the content.

Activity based learning is now accepted as the basis of science education. These activities should be regarded as a means for open-ended investigation rather than for verifi cation of principles/content given in the textbook are has been designed to facilitate low cost activities and experiments using locally available materials. With a view to streamlining the activities, we have now segregated them into three groups:

I Do - activities to be done by an individual learner. We Do - activities to be done by a group of learners. and We Observe - activities to be demonstrated by the teacher.

The third group of activities have a higher degree of diffi culty or require careful handling as it may involve dealing with chemicals, electricity etc.,

The “More to know” snippets in the text represents some unusual and interesting facts or information in which the students need not be examined.

The evaluation section is nothing but another space for learning in a different manner. As the focus is on understanding, rote learning is to be discouraged thoroughly. Application of learnt ideas, problem solving skills and critical thinking is to be encouraged. There could be scope for more than one answer to a question, which should be acknowledged always.

To facilitate further reference, books and websites have been suggested at the end of each lesson. Suggestions and constructive criticism are most welcome. Valuable suggestions will be duly incorporated.

- Authors

sciencetextbook@gmail.com

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Cell Structure 1

wall of a building

cells of an onion peel

When we see the cells in an onion peel and those on the wall, we fi nd that they are similar in structure.

What is a building made up of?

What is our human body made up of?

Just as a building is made up of many bricks, the human body is also made up of several small units called cells. Cell is the basic structural and functional unit of all living organisms.

Can you see a cell with naked eyes? No, cells are very minute and cannot be seen with our naked eyes. They can be observed only through a scientifi c instrument called microscope

Compound microscope

Adjustmentknob

If there is a microscope in your school laboratory, observe the cells of an onion peel under it with the help of your teacher.

Do you know who saw the cell fi rst? It was Robert Hooke, an optic seller. In those days glass bottles were closed with lids made of cork. He made thin sections of the cork and observed them through his hand-made lens and saw many small identical hexagonal chambers. In Latin the word 'cellula' means "a small chamber". So Robert Hooke named this chamber as cell in 1665. He became a famous scientist by showing the cell magic through his lens.

ArmStage

Mirror

Objective lens

Eyepiece lens

Base

To show the parts of a compound microscope.

Activity 1

We Observe

Activity 2

We Observe

Not only human beings, but other organisms like plants and animals are also made up of cells.

44

Can we see the inner part of the cell?

The same thought arose in the mind of Robert Hooke. Following him, Robert Brown, a school teacher, invented an advanced microscope through which the inner parts of a cell can be observed. He discovered the nucleus.He found that there is a different world within a cell.

He understood that the cell is a small factory with nearly twelve to thirteen cell organelles which are involved in a heavy task.

Classifi cation of cells :

Cells of plants and animals are not similar. Bacteria and some algae are made up of a single cell. They lack membrane bound organelles.

A cell that does not contain membrane bound organelles and

a well defi ned nucleus is called Prokaryotic cell. i.e., simple cell.e.g: Bacteria.

A cell that contains a well-defi ned nucleus, nuclear membrane and membrane bound cell organelles is called Eukaryotic cell, i.e., complete cell. e.g., cells of plants and animals.

Structure of an Animal cell

Plasma membrane

Mitochondrion

CentrioleEndoplasmic reticulumNucleolus

Nucleus

Ribosome

Lysosome

Cytoplasm

Vacuole

Golgi bodies

As discussed earlier, even cells of plants and animals are not alike.Though they vary in their size and structure according to their function, they are similar in their basic organisation.

Now, let us observe an animal cell.

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Pla

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46

Cell is a small factory. Let us learn the specifi c function of each component of an animal cell.

Shall we enter the cell factory and view it?

I can hear someone calling me........

Plasma membrane :"Hi! Animal cell welcomes you.

I am the plasma membrane, enveloping the cell. I give shape to the cell.I check the entry and exit of the cell and act as a guard.Come on my friends, come one after another and introduce yourselves".

"Get inside. Protoplasm is waiting for you."

Protoplasm: "I am a colloid, found inside

the plasma membrane. I have two components namely cytoplasm

and nucleus of the cell. My name is protoplasm".

J.E. Purkinjee coined the term protoplasm. 'Proto' means 'fi rst' and 'plasma' means 'colloid'.

Cytoplasm :"Hello! I am cytoplasm, found in

between the plasma membrane and the nucleus. I include organelles, proteins,carbohydrates and lipids.

Nucleus : "I am the controlling centre of the

cell. But I need not be present at the centre.

I am called nucleus. I am spherical in shape. I have nucleoplasm, nucleolus and chromatin reticulum and am enclosed by the nuclear membrane. I carry the genetic characters from generation to generation.

Neuron

Fat cell

White Blood cell

Ostrich’s eggMuscle cell

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Mitochondria- singular : Mitochondrion :

"We are involved in cell respiration. We help in the oxidation of food materials that you eat and provide energy. We do not rest. We are also known as Power houses of the cell".

Golgi bodies:“"Hi, come on! We are tubular

structures, involved in the secretion of digestive enzymes and formation of lysosomes.We separate proteins from the ingested food and give strength to the cells and the body. In plant cells we are known as Dictyosomes"

Chromatin reticulum

Nuclear membrane

Nucleus

Nuclear sap

Nucleolus

Endoplasmic reticulum :"Hello! I am the endoplasmic

reticulum. I help in transportation of materials from one part of the cell to another".

Mitochondrion

Outer membrane

Inner membrane

Cristae

Golgi bodies

Endoplasmic reticulum

Ribosomes :"Come, Look at us! We are

granular structures. We are called Protein factories of the cell. We help in protein synthesis".

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centrosome

Lysosomes :"Are you interested looking at us?

We are spherical yellow coloured bodies. We help in cell protection. We destroy the pathogens entering into the cell. We are called Suicidal bags of the cell. In addition to this we also help in cell digestion".

Lysosome

Vacuoles : "Wait! Don't neglect us. We

are light blue in colour and appear like bubbles. We store cell sap. We maintain intracellular pressure. Oh! this work is very diffi cult. Plasma, my friend, good bye to all".

Did you meet the workers of the animal cell factory? Now, let us know about the plant cell.

Plant cell : Have you ever wondered about

the different features of a plant cell structure? Centrosome is absent in plant cells. Before listing

Centrosome :"Let me introduce myself. I am

centrosome.I'm found only in the animal cell. I appear as microtubule and am stick like. I am near the nucleus. I have centrioles in me.. Cell division is my function i.e., formation of new cells."

Cell Wall

Plasma membrane

Endoplasmic reticulum

Chloroplast

lysosome

Nucleus

Ribosome

Mitochondrion

Vacuole

Structure of a plant cell

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the differences between a plant cell and an animal cell, let us know the reason for herbs, climbers and trees being rigid in nature.

Plants are more rigid than animals due to the presence of the cell wall.Cell wall :

It is an outer layer which gives shape to the cell. It is made up of cellulose. Its function is to protect the inner organelles and to give shape to the cell. Plastids :

These organelles are found only in plant cells. They contain pigments. Based on the pigments, they are classifi ed into three types.

Type Pigment FunctionsChloroplast Chlorophyll - green pigment gives green colour to

the stem and leavesChromoplast Carotene - orange pigment

Xanthophyll - yellow pigmentgives colour to the fl owers and fruits

Leucoplast - found in roots and underground stems

We divide ourselves as various components of the cell factory and enact their functions.

Activity :3Activity 3 We Do

Let us now list out the differences between a plant cell and an animal cell.

Sl.No. Plant cell Animal Cell1. Presence of cell wall Absence of cell wall2. Presence of plastids Absence of plastids 3. Centrosome is absent Centrosome is present4. Vacuoles are larger in size Vacuoles are smaller in size

All activities like eating, drinking of water, jumping, playing, and breathing, thinking and even sleeping are due to the functioning of the cells. Each cell is a small factory. The brain has several millions of cells.

When the cells, the so called small factories are affected and injured, diseases are caused and we visit a physician.

e.g. cancer, hereditary diseases, diabetes, etc.

50

Making a cell model

We divide ourselves into groups and make the structure of a plant cell using the easily available materials.

We build the model of a cell and learn about the cell organelles.Materials required :

A thick cardboard from any old note book, a white sheet, paste, broom sticks, coloured thread, sand, bangle pieces, bindhi, groundnut shells, green gram, cow peas, broken chick peas, pepper, peas, mustard, cardamom, colour papers.

Method we follow: We take a thick card board and paste a white sheet over it. We draw the outline of the plant cell from the text book on the white sheet.

We draw the nucleus at the centre of the plant cell. We make the organelles by pasting the materials as listed below.

Organelles Materials we useNucleolus bindhi Chromatin reticulum coloured threadNuclear membrane bangle piecesCytoplasm paste, sandEndoplasmic reticulum coloured threadRibosome mustardLysosome broken chick peasGolgi bodies (dictyosomes) bangle pieces, pepperMitochondria groundnut shellsPlastids green gram/peas/cardamomVacuoles bits of paperPlasma membrane threadCell wall broom stick

By sticking black threads, We label the parts one below the other.

We have learnt

We have understood the structure of a plant cell.

Activity 4 We Do

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Having the learnt various components of the cell, shall we now learn their functions too?

Cell organelles and their functions

S.No

Cell components Functions

1. Plasma membrane

It gives shape to the cell It selects the substances required by the cell and transports them in and out

It gives protection to the cell2. Cytoplasm It distributes the nutrients within the cell

3. Nucleus It controls all the activities of the cell It carries the hereditary characters from one generation to another

4. Mitochondria They provide energy to the cell

5. Golgi bodies They secrete enzymes and hormones They store protein They help in formation of Lysosome

6. Endoplasmic reticulum

It helps in transportation within the cell It helps in protein synthesis

7. Ribosomes They synthesize protein

8. Lysosome It destroys the germs that enter into the cell It helps in intra and extra cellular digestion

9. Centrosome It helps in cell division

10. Vacuoles They control the intra cellular pressure They store cell sap

11. Plastids They help in photosynthesis They give colour to fl owers and fruits

12. Cell wall It gives shape and protection to the plant cell

We divide ourselves into groups. We discuss and present the structure and function of the cell components and their names with the help of the model made by us.

Activity :5Activity 5 We Do

52

Facts at a glance1. There are about 6,50,00,000 cells in the human body.

2. Bones are made up of special type of dry cells.

3. Anton Van Leeuwenhoek (1675) discovered that blood contains RBC (Red Blood Cells).

4. Nerve cell is the longest cell in animal cells.

5. Bone cell is the toughest cell in animal cells.

6. Mature Red Blood Cells of mammals do not contain nucleus.

EVALUATION I. Choose the correct answer

1. Structural and functional unit of living organisms is ________.

a) nucleus b) cell c) mitochondria d) ribosome

2.The instrument used to magnify the things placed on the slide is______.

a) telescope b) microscope c) binocular d) periscope

3.Select the prokaryotic cell from the given cells.

4.Power house of the cell is known as

a) mitochondria b) ribosome c) lysosome d) nucleus

5.The organelle which is known as ‘suicidal bag’ is ________.

a) dictyosome b) ribosome c) centrosome d) lysosome

(a) (b) (c) (d)

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6.The spherical organelle which controls the activities of the cell is ________.

a) golgi bodies b) ribosome c) nucleus d) lysosome

7. The organelle that involves in destroying the germs which enters into the cell is ______.

a) dictyosome b) ribosome c) centrosome d) lysosome.

8. The organelle which is found only in animal cell is _______.

a) mitochondria b) centrosome c) plasma membrane d) chloroplast

9. The cell which contains a large vacuole is __________.

a)cell of onion peel b) bacteria c) nerve cell d) cell of muscle

10. The longest cell is ________.

a)bone cell b)nerve cell c) cell of a muscle d) blood cell

II. Who am I?

1. I'm a tiny organelle. Cell respiration occurs in me. I'm otherwise called "Power house of the cell". Who am I?

2. I help in Photosynthesis. I am found only in plants. Who am I?

3. I give shape and protection to the plants. I'm made up of cellulose. I'm found only in plants. Who am I?

4. I help in cell division. I'm seen only in animal cell. Who am I?

5. I’m a colloid, found inbetween the plasma membrane and the nucleus. I distribute the nutrients within the cell. Who am I ?

III. Pick the odd one out

1. nucleus, nucleolus, chromatin reticulum, plasma membrane

2. Robert Hooke, Anton Van Leeuwenhoek, Schleiden and Schwann, Newton

3. lysosome, centrosome, ribosome, chromosome

4. cell wall, chloroplast, larger vacuole, centrosome

54

IV. Match:

Cell Organelle Other names FunctionsMitochondria “Suicidal bag” protein synthesisRibosome “Power house of the cell” transfer of hereditary

characterLysosome “Controlling centre of the

cell”production of energy

Nucleus “Protein factory of the cell” cell destruction

V. Draw and label:

1.Nucleus(nuclear membrane, chromatin reticulum, nuclear sap, nucleolus )2. Mitochondria (outer membrane , cristae, inner membrane)

VI.Colour the following diagram of the animal cell and label the parts

VIII. Explore and answer1. The leaves appear green due to the presence of green pigment chlorophyll.

A ripened mango appears yellow. Give reason.2. Nucleus is known as the controlling centre of the cell. Give reason in

your own words.

VII. Answer the following questions from the diagram given below:

1. Name the organelle given here.2. How is this organelle known in a plant cell?3. What is the function of this organelle?

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Cell structure

Websites :

www.enchanted learning.comwww.biology4 kids.comwww.teacher vision.fen.comwww.diffen .comwww.wiki.answers.com

Further reference

Plant cell

Nucleus

Nuclear membrane

Cytoplasm

Vacuole

Lysosome

IX. Fill in

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Separation of Substances 2Ibrahim is very much interested in science. Last week, he won the

fi rst prize at a science talent search competition . The competition was very interesting and challenging. Each participant was provided with (i) an empty bucket (ii) a bucket full of water (iii) a bag of sand and (iv) gravels.

Participants were asked to fi ll the empty bucket with water, sand and gravels. They had to use every material and see that water did not overfl ow.

Some of them poured water into the empty bucket fi rst and then dropped the gravels. Immediately the water over fl owed.

Some put the sand fi rst and then poured water. The bucket became full and gravels could not be put in to it.

Do you want to know what Ibrahim did?

First he put the gravels in the bucket, and then he put the sand gently on it and poured water slowly over it. The bucket was full. Everyone appreciated him and there was a loud applause. Then, Ibrahim was asked to separate the mixture. How did Ibrahim separate the mixture? First he poured out the water slowly from the bucket, and spread the wet sand and gravel mixture on a newspaper and dried it. Later he picked up the gravels using his hands. Thus he separated the three components.

In the above competition Ibrahim used the methods of separation like hand picking and fi ltration.

We drink water after fi ltering and boiling it. We know that before cooking rice, it is cleaned with water. While preparing tea, we separate tea dust by fi ltration. We purify rava and wheat fl our by sieving, and rice and pulses by winnowing. Do you know why we do so?

_________________________

_________________________

What do we understand from this?

We need to use different methods of separation

to remove the unwanted substances

to remove substances which are harmful to our body

to obtain the substances which are useful to us in a pure state

Let us learn about the different methods of separation we use in our daily life.

_________________________

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Separation of Substances

Methods used to separate mixture of solids:Solid mixtures can be separated using methods like hand picking, winnowing,

sieving and magnetic separation.

HandpickingHow do we separate vegetables at home? We

separate them into its kinds like tomato, chilly etc. by using our hands. Separation is easier as they differ in size, colour and shape.

The method of separating the substances based on size, colour and shape using hands, is called handpicking.

1. By which method does the woman in the given picture separate the substances?

2. Mention some substances which can be separated by this method.

..............................................................................................................

..............................................................................................................

...............................................................................................................

Hand picking method can be applied only when the quantity is small.

WinnowingFarmers allow the mixture of grain and husk to fall from a height when wind

blows. Grains, being heavier fall down and form a heap. Husk, being lighter is carried away by wind and forms a separate heap.

The method of separating lighter particles from heavier particles with the help of wind is called winnowing.

Lighter particles present in a mixure can be separated by winnowing.

..............................................................................................................

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Sieving:We can separate the impurities

like bran, husk, stone, worms, stalk and tiny insects from fl our by sieving. It allows the fi ne particles to pass through the pores while the coarser particles remain on the sieve .

Magnetic separation :Insert a magnet into a heap of

sand and take it out. If iron particles are present in the heap of sand, we can see them clinging to the ends of the magnet.

Magnetic separation is used to separate mixtures containing components which are attracted by magnet.

Components of a mixture can be separated by the method of sieving only when they differ in their size.

At construction sites, you would have seen the separation of pebbles and stones from sand by sieving using a sieve.

Can we separate iron substances from water using a magnet?

Activity 1 I Do

I need : Beaker, water, bell pins and a magnet

I take a beaker and fi ll half of it with water.

I drop some pins into it.

I hold a magnet over the surface of water or by the side of the beaker.My inference:

______________________________

______________________________

______________________________

______________________________

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Shall we complete the table?

Mixture Method of separation

States of components (Solid, Liquid, Gas)

Paddy and chaff

Ragi and pulses

Sand and stone

Rava and Iron particlessedimentation. The clear liquid above the sediment is called super natant liquid.

e.g. a mixture of sand and water

DecantationTransferring the clear liquid

(super natant liquid) into another container using a glass rod is called decantation.

Methods of separation of insoluble solids from liquids

Can we separate a mixture of sand and water by using methods like hand picking, sieving, winnowing or by magnetic separation? No we can not separate them. why? Since water is in liquid state, the methods used to separate solid mixtures cannot be used here. The method of separation depends on the nature of the substances to be separated.

Hence we can separate insoluble solids from liquids by using the method of decantation, sedimentation and fi ltration.

SedimentationThe mixture of insoluble solids

and liquid is taken in a beaker and the solid subtances are allowed to settle down as sediments. This is known as

Sedimentation

water

sand

Decantation

glass rod

beaker

(super natant liquid)

(sediment)

FiltrationObserve the liquid obtained by

decantation and see whether it contains suspended impurities. Try to fi lter the impurities using a clean cotton cloth. As there are tiny pores in the cloth(like the pores in a sieve), the clear water passes through the pores and the suspended impurities

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like sand remain on the cloth. In the laboratory we use a fi lter paper instead of a cloth to purify water. There are tiny pores in the fi lter paper also.

Let us fi lter the mixture in the laboratory using a fi lter paper.

Take a fi lter paper and fold it like a cone. Fix it inside a glass funnel. Fix the funnel in a stand and place a beaker below it. Pour the impure liquid containing suspended impurities into the funnel. Liquid drains through pores of the fi lter paper. The clear liquid that is collected in the beaker is known as fi ltrate. The dust particles which remain on the fi lter paper are called "residue".

Activity 2 We Observe

Take a small amount of salt solution in a beaker and place it over a wire gauze on a tripod stand. Heat the solution well. After the complete evaporation of water, see what is left in the beaker.Our observation and inference:

______________________________

______________________________

Methods of separation of solid substances dissolved in liquidsEvaporation and condensation processes are used to separate solid substances dissolved in liquids.

fi ltrate

stand

fi lter paper

fi rst fold

cone fi lter paper cone in the funnel

second-fold

Evaporation

Thus we have separated salt from water by evaporation method.

Evaporation is a process in which a liquid changes into its vapour on heating. Evaporation method is used to separate the dissolved solids from the liquids.

Do you know?One litre of sea water contains about 3.5 grams of salt. Sea water contains not only common salt but also more than 50 other mineral salts. These salts are industrially important.

Salt pan

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Separation of Substances

CondensationTake a mixture of sand and salt in

a beaker. Add water to this mixture and stir. Salt gets disloved. How can we separate the components from this mixture? Filter this solution using a fi lter paper. The sand can be separated from the salt solution by fi ltration.

Set up the apparatus as shown in the picture. Take the salt solution in a conical fl ask and heat it strongly. The water vapours pass through the delivery tube and get collected in a test tube. The test tube is placed inside a pack of ice cubes. The water vapours get cooled and condense into water. Salt remains as residue in the conical fl ask, once the whole water gets evaporated. When the vapours of a substance get cooled, they condense into liquid. This process is known as condensation.

water

Salt waterIce cubes

Condensation

I want to get back both salt and water. What should I do for

this?

Shall we complete the table?

Mixture Method of separationPhysical states of the

components (Solid,Liquid, Gas)

sand and waterrava and watersalt and water

Need for applying more than one method of separation

The various substances which we use in our life, reach our hand only after undergoing different methods of separation and purifi cation.

For example, in the preparation of sugar from sugarcane juice, the methods of separation like fi ltration, evaporation and crystallization are used. More than one method of separation are used to extract metals like iron, gold, alluminium and copper in pure state from their ores.

Do you know?

Evaporation and Condensation are the basic processes involved in the Water cycle. Formation of rain involves these two processes.

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We are going to separate the iron fi lings, salt and chalk power from the given mixture.

We need: bar magnet, beaker, water, fi lter paper, funnel, tripod stand, glass rod, watch glass, match box, wire gauze, spirit lamp.

1. We take the mixture in a watch glass and stir it using a bar magnet.

Our observation Substance separated

2. We take the remaining portion of the mixture containing salt and chalk powder in a beaker. Then we add water and stir it well using a glass rod. We allow the liquid to remain undisturbed.

Our observation :

_________________________________________________________

_________________________________________________________

Activity 3 We Do

3. We fold the fi lter paper into a cone shape and keep it inside a funnel.4. We keep the funnel on a tripod stand and place a beaker below it.5. We transfer the liquid mixture slowly into the funnel using a glass rod.

Our observation Substance separated

6. We take the beaker containing the salt water and place it over a wire gauze on a tripod stand. We heat the solution strongly using a spirit lamp.

Our observation Substance separated

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EvaluationI. Choose the correct answer

1. Suitable method to separate lighter impurities from a mixture a) winnowing b) handpicking c) evaporation d) magnetic separation

2. In a mixture, solids of different size can be separated by a) magnetic separation b) winnowing c) sieving d) evaporation 3. The method used to separate the seeds from the fruit juice is

a) fi ltration b) sieving c) crystallization d) winnowing

4.Separation of common salt from the sea water is by a) sieving b) evaporation c) magnetic separation d) winnowing5. The method used to separate substances differing in colour, size and

shape from a solid mixture a) magnetic separation b) decantation

c) handpicking d) sieving

II. Encircle the odd one and give reason:

3. hand picking, evaporation, winnowing, sieving

4. fi ltration, sedimentation ,decantation, condensation

Our inference:

S.No. Separated substance Method used for separation

Facts at a glance:1. Crude oil is a mixture from which nearly eighty six substances like

petrol, kerosene and naphtha are obtained.

2. Air is a mixture of gases.

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5. evaporation, magnetic separation, condensation, crystallization6. fi lter paper, sieve, funnel, glass rod

III. Write the correct method of separation instead of the wrong method given in the following statements.

a) We can separate the different kinds of vegetables by winnowing.

b) Lighter particles present in a mixture can be separated by magnetic separation.

c) The method of converting liquid into vapour by heating is known as condensation.

d) Sieving method is used to separate a magnetic substance from a mixture.

IV. Draw and label the apparatus used for fi ltration in the laboratory.

V. Explore and answer

1. Amudha’s family gets drinking water from the nearby pond which is turbid in nature. Suggest her some methods to convert the water into pure drinking water.

2. We do not apply the same method of separation to separate a mixture of chalk powder and water, a mixture of green peas and ground nuts, and iron objects from garbage. why?

3. Why is separation of substances necessary in our daily life?

4. You are given a sample of salt solution. You are asked to separate the salt from it. Filtration method cannot be applied here. Why? Mention the correct method of separation.

5. Differentiate the following:

a. fi ltrate and residue

b. winnowing and sieving

6. While preparing lemonade, how will you remove the seeds of the fruit from the juice? We add ice cubes to get chilled juice. When will you add sugar to the juice before or after adding ice cubes? Why? When can you dissolve more amount of sugar?

7. A mixture contains saw dust and iron nails. Which method will the carpenter use to separate the iron nails from the saw dust?

8. During winter season we see dewdrops on grass and plants. Can you give reason for this?

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P W X N C B A T I M C F I L T I Q F OQ R A C O N D O L I N I A I E X Y I EL T C R N Y S N I X Y L O Q U I D L VT O L Z D E C A N T A T I O N A C T AS J S I E V S O L U T H Y X O U V E PM I X E N W A T E R V A P O U R T R OT L R E S I D U E E X T L M O S Q P RI S E V A P T I O S I E V I N G O A AC R Y S T A L L I S A T I O N N G P TL I Q U I D V A P T N I O I A Q R E II L T S O L U T I O N L E O T X Y R OQ M A G N E T I C S E P A R A T I O N

VII. Spot out the different methods of separation in this word puzzle

VI. Fill in the boxes with suitable answers:

Crystallization

Separation of solid mixture

Separation of substances

Separation of dissolved solids from

liquids

Separation of insoluble solids from

liquids

Filtration

Sieving

9. Can we separate tiny white stones from 100kg of rice by the method of hand picking? Give reason for your answer.

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VIII. Observe the pictures given and arrange them in proper order based on the activities given in them. Encircle the methods of separation found in them.

Sowing

Cooking

Ploughing Winnowing Hand picking

Thrashing HarvestingEating

1. _____________________________ 2. _____________________________

3. _____________________________ 4. _____________________________

5. _____________________________ 6. _____________________________

7. _____________________________ 8. _____________________________

Project:

1. List the various methods of separation used in our day-to-day life. Describe the method and places they are used in. Mention their signifi cance.

3. Discuss in groups how salt is obtained from sea water. Collect relevant pictures and stick them in your scrapbook. Find out the places of salt pans in Tamil Nadu.

.

Web sites:http://en.wikipedia.org/wiki/separation_process

http://encarta.msn.com/encyclopedia_761574279_2/evaporation.html.

Further reference

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Types Of Energy 3Do you watch television? What

a wonderful invention it is! We can only hear radio programmes. But, we can both hear and watch programmes on Television. You like to watch quiz programme on television, don't you? It is interesting to see people participating and answering questions in a quiz competition live.

Recently, an English television channel conducted a programme an interesting question was put forth where to the participated. The T.V. programme was about a science conference held on the terrace of a multistoreyed building. Many students took part in this conference. Each student used different modes of transport to reach that building.

A student reached the terrace directly by a parachute.

Another student reached the by terrace lift

Two other students sailed in a boat A student reached the building by claimbing the stairs.

Yet another student rode very fast on a bicycle and reached the terrace.

The question is:What type of energy did each student

use? This is a thought-provoking question. To answer this question, we should fi rst know about energy. Let us learn about the various forms of higher energy in this lesson.

In the pictures given , we see people in various activities, and the machines used by them.

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How do they perform these activities? Don't they need energy to do these activities? From where do they get this energy? Moving air, working machines and fl owing river do the work, don't they? To do this work energy is spent.

Walking, running, washing etc. will not take place without energy. The energy required to do these activities is obtained from the food we eat.

Do you know why you feel hungry? Have you seen ants and bees working busily? They too spend energy to do their work.

To perform these activities what type of energy do we need? Shall we learn about them now?

Energy in day-to-day activities

Activity 1(Teacher)

Take a pinch of baking soda in a bottle and add a few drops of lime juice or vinegar in to it. Cover the bottle with a cork. What happens to the cork after some time?

The cork jumps out of the bottle, doesn't it? What is the reason for this? It is due to the release of energy.

Activity 1 We Observe

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Sl.No Activity Required energy1 To dry clothes heat energy from the sun.

2 To run a bus energy from diesel (or) petrol.

3

4

Activity 2 I Do

Where do we get energy to do our day-to-day activities? Think of it and list out a few.My list

I have inferred _______________________________________________________ _______________________________________________________

From the above activity, we learn that energy is defi ned as the capacity or ability to do work don't we? The unit of energy is Joule.

Let us learn about the different types of energy now.

Mechanical energy, chemical energy, light energy, sound energy, electrical energy, heat energy, wind energy are the different types of energy. Let us learn about some types of energy we use.

1. Mechanical energyWater stored in a dam, a fl owing

river, a moving bus, a galloping horse, a freely falling stone, and water stored in a tank possesses energy.

When water is stored in a dam the stored water will have potential energy. When water is allowed to fl ow down,

this potential energy is changed into kinetie energy. This kinetic energy will make the wheels of a turbine to rotate. This mechanical energy is changed into electrical energy with the help of magnetic fi eld.

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Potential energy and kinetic energy are the two types of mechanical energy.

Uses: i) Mechanical energy can bring a

moving body to rest or can make a resting body move.

(ii) Using wind energy we can generate electricity through wind mills.

2. Chemical energyThe energy released during a

chemical reaction is called chemical energy. For example, chemical energy is released due to the chemical reaction that takes place when wood, charcoal, petrol etc., are burnt.

The food we eat undergoes chemical reaction and releases energy to enable us to work.

Similarly things like a compressed spring, stretched rubber band etc. have potential energy.

Chemical energy

In Mettur and Bhavani- sagar, electricity is generated using

hydroelectric power.

"Heat is a form of energy" - James Joule.

The unit of energy (Joule) is named after

him.

Hence, the energy possessed by an object with respect to its position or confi guration is called potential energy.

Similarly, a moving bus, a galloping horse and running water possess kinetic energy.

The energy possessed by a body by virtue of its motion is called kinetic energy.

compressedspring

stretched rubber band

Mechanical energy

Uses:1. The chemical energy stored in the

food of plants and animals is used for their growth and function.

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2. A battery or a cell converts chemical energy into electrical energy.

3. While using fuels, chemical energy is converted into heat energy and light energy.

3. Electrical energyDo you know why a fan rotates or

an electric bulb glows when we switch them on? In an electric bulb, electrical energy is converted into light energy and in an electric fan, electrical energy is converted into mechanical energy. In a wind mill, the wind energy (kinetic energy) is converted into electrical energy.

Wind mill- (Electric power generation) at Kayathar

(Thirunelveli), Aralvoimozhi (Kanyakumari) and also in

Coimbatore,Tirupur Districts.

Electrical energy

The chemical energy stored in wood and cooking gas is converted into heat energy. Due to friction and chemical reaction heat energy is produced. Discuss with your friends and fi nd out the various other sources of heat energy.

Uses:1. We get rain from the heat energy

obtained by the sun.

2. In a thermal power station electricity is generated from the heat energy obtained by burning coal.

Uses:1. In industries, electrical energy is

used to operate machines and is also used in telecommunication.

2. In cities, electrical energy is used to run electric trains.

Shall we discuss and fi nd out the various sources of electrical energy?

4. Heat energyDo you know what the primary

source of heat energy is? It is the Sun.

In your house do you use wood or cooking gas for cooking? What energy is released when you burn wood or cooking gas?

Heat energy

Hold a magnesium ribbon with tongs and burn it. Observe the energy changes in it.

Activity 3 We Observe

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3. In an electric stove, electric iron etc., electrical energy is converted into heat energy.

5. Solar energy The energy obtained from the sun

is called solar energy. What are the types of energy obtained directly from the sun? can you list?

Uses:(i) Solar energy is directly used in

solar heater, solar cooker etc.,

(ii) Solar cells are used in artifi cial satellites and calculators.

(iii) Solar energy is used to operate solar vehicles.

_________________________________________________

_________________________________________________

Share what you have observed in this activity with your friends.

Activity 4 We Do

Different ways of using solar energy

Do you know?ln 212 BC, Archimedes the

Greek scientist, used magnifying glasses to burn Roman warships with solar energy.

Let us know how energy is obtained directly from the sun

We need :Magnifying lens, bits of paper

1. Using the magnifying lens focus the sunlight on the bits of paper.

2. Observe the changes on the bits of paper after some time.

We observed and inferred

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Can we convert one type of energy into another?

Look at the pictures given below. What do we understand from them?

We know that most forms of energy are obtained from the sun.

1.In Tamillnadu at the Neyveli and Ennore Thermal Power Stations coal is burnt to generate electricity.Here the chemical energy of coal is fi rst converted into heat energy and then into electrical energy.

2. Loudspeaker converts electrical energy into sound energy

3. When water stored at a height fl ows down, its potential energy is converted into kinetic energy. The water rotates the turbines of a generator and electrical energy is generated.

4. When wood, charcoal, petrol, diesel and other fuel are burnt, chemical energy is converted into heat energy.

5. During photosynthesis plants convert light energy from the sun into chemical energy and store it.

6. In electric bells and horns of automobiles electrical energy is converted into sound energy.

7. In a torch light, the chemical energy of the cell is fi rst converted into electrical energy and then into light energy.

From the above examples, we learn that one type of energy is converted into another type of energy. We know that when one type of energy is used, an equal amount of another energy is released.

Therefore, energy can neither be created nor destroyed, but can be transformed from one form into another form. This is called Law of Conservation of Energy.

Moreover in any conversion of energy the total amount of energy will not be changed.

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Discuss in small groups how diesel and petrol can be consumed economically . Present a report.

A man carried a heavy load on his head to his house which is at the top of a mountain. He left the load by the side of his house and took rest. After sometime he came back and noticed that the load had rolled down and had reached the ground.

1. From where did he get the energy to lift the load?

2. What energy did the load possess when it was placed on the mountain?

3. From where was the energy obtained for the load to roll down?

4. What energy did the load possess while rolling?

5. What energy did the load possess on reaching the ground?

6. Write down the energy changes in the above activity,in sequential order.

We discuss the small groups the various uses of solar energy in our daily life and list them out.

My list

1. To get salt from sea water 2. For rain3. ____________________ 4 . ___________________5 . ____________________ 6. ___________________

For example, let us see how the energy conversion is taking place when the electric motor pumps water.

To operate the electric motor electrical energy is used. This electrical energy is converted into kinetic energy, sound energy and heat energy.

Electric energy → Kinetic energy + Sound energy + Heat energy

(To operate the (to lift water) (released when electric motor works)

electric motor)

Activity 6

Activity 5 We Do

Activity 6 We Do

Activity 7 We Do

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Evaluation

I. Choose the correct answer. 1. Energy required to dry clothes quickly ______

a) solar energy b) sound energy

c) kinetic energy d) potential energy

2. "Heat is a form of energy". This was discovered by _______

a) Voltas b) James Joule

c) Thomas Alva Edison d) Galileo

3. Which of the following requires electrical energy?

a) windmill b) industry

c) bicycle d) parachute

4. The energy that cannot be used to run vehicles

a) solar energy b) chemical energy

c) electrical energy d) sound energy

We answer

Shall we discuss and answer the following questions related to this event?

Our answers1 . ___________________________________________________

2 . ___________________________________________________

3 . ___________________________________________________

4 . ___________________________________________________

5 . ___________________________________________________

6 . ___________________________________________________

We have learnt

______________________________________________________

______________________________________________________

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5. When charcoal is burnt, chemical energy is converted into

a) heat energy b) sound energy

c) mechanical energy d)solar energy

II. Tick the correct answer:

1. Energy obtained by wind energy in wind farms

(Chemical energy/Electrical energy)

2. Energy possessed by a rustling leaf

(Kinetic energy/Chemical energy)

3. Energy possessed by a person landing from a parachute

(Kinetic energy of wind/ Chemical energy in food)

4. Energy produced by rubbing the two palms of your hands

(Heat energy/Electrical energy)

III. Match the following1. Electric bell : Electrical energy

Solar cooker : ______________

2. The sailing of yacht : ______________

Air fi lled in a balloon : potential energy

3. For the growth of living things : Chemical energy in food

To run vehicles : Chemical energy in__________

IV. Say true or false?

1. Energy is the capacity or the ability to do work

2. Potential energy and kinetic energy are the types of mechanical energy

3. Electrical energy is released during chemical reaction

4. Heat energy is released due to friction

5. One type of energy cannot be converted into another type of energy

V. Find out what type of energy, the following possess.1) sun 2) charcoal 3) water in a lake4) solar cell 5) waterfalls 6) compressed spring7) fuel 8) moving cloud 9) fi rewood

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VI. Find out the change in energy that taken place in the following1. Torchlight _________ _________

2. Radio _________ _________

Diesel can Gas cylinder Plant

(1) (2) (3)

1.__________________________________________________

2.__________________________________________________

3.__________________________________________________

3. Iron (box) _________ _________

4. Generator _________ _________

VII. Explore and answer1. We know that we need energy when we go to school by bicycle , while

playing or doing any work. How do we defi ne the energy used in these activities? What is its unit?

2. The coconut in the picture possesses three types of energy. Can you fi nd out what they are?

1. ______________

2. ______________

3. ______________

3. What type of energy is stored in the abject shown in the pictures given below? In which way this energy is useful to us?

4. We know that water stored in dams like Mettur, Bhavanisagar, etc is used to generate electricity. List out the conversion of energy in the hydro electric power stations.

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S.No Name of the gadget Change in energy Uses

1. Electric bulb Electric energy into light energy to get light

2.

3.

4.

5.

IX. Project work

Write down the names of the gadgets used in your house, the changes in energy and their uses in the tabular column given below.

Chemical energy

energy stored in the muscles the stone at

a particular heightstone moves

up

when the stone falls down

When the stone hits the ground

a stone is thrown upwards.... ....when the stone falls down

Heat energy_________ __________________VIII. Answer the following

1. Differentiate potential energy from kinetic energy.

2. Explain the Law of Conservation of Energy with an example.

5. Observe the given pictures below and write down the energy possessed by the stone at each level.

Websiteshttp://www.tutorvista.comhttp://www.arvindguptatoys.comhttp://www.wikipedia.org

FURTHER REFERENCE

Unit 3