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RATIONAL NUMBERS

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CHAPTER

MATHEMATICS FOUNDATION 1

70 | CHAPTER 2 | RATIONAL NUMBERS

Section 2.1Recognizing, Reading, Writing and SimplifyingFractions

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What is a fraction?You have a circle. Cut it into two equal parts. Each part is called a half of a circle. Each part is a fraction of the circle.

We can write a half as 21

We now cut a circle into 4 equal parts (fractions). Each part is called one fourth (or ‘one quarter’) of a circle.

We write this as 41

If we take one part away, there are now three quarters left.We can write this as

43

RECOGNIZING, READING AND WRITING FRACTIONS | 71

A fraction is made of two parts:The numerator tells you how many parts you have. The denominator tells you how many equal parts in total.

Note that all of the parts in the fraction must be of equal size.

There is 1 part shaded, so the numerator is 1.

There are 3 total parts in the shape, so the denominator is 3.

So the fraction shaded is 13

.

There are 5 parts shaded, so the numerator is 5.

There are 12 total parts in the shape, so the denominator is 12.

So the fraction shaded is 125 .

Don’t forget that the parts must be of equal size!



Practice 1

What fraction is shaded in the shapes below ?

________________________

a)

________________________

b)

________________________

c)

________________________

d)

________________________

e)

________________________

f)

To write a fraction in words, we use numbers for the numerator, and ordinal numbers for the denominator.

RECOGNIZING, READING AND WRITING FRACTION | 73

�EXAMPLE

Write the fractions in words.

a) 53 �� b)

13 one-third

c)65 �� d)

42 two-fourths

two-quarters

Practice 2


a)52

________________________ b)83

________________________

c) 110

________________________d)

32

________________________

e)94

________________________ f) 14

________________________

or

________________________

Exception – when the denominator is “2”, we do NOT say “second”. Instead, we say “half” (or

the plural, “halves”, if there is more than one).

�EXAMPLE

21 one-half

23 three-halves



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53��a)

85��b)

32

two-thirdsc)

Practice 3

Write the words as fractions

_______seven-tenthsb)_______six-seventhsa)

_______one-half d)_______��c)

_______three quartersf)_______�� e)

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710

72

Write the fractions found in the sentences.

a) Seven out of ten people enjoy going swimming.

b) Two of the seven Emirates begin with the letter A.

PROPER FRACTIONS, IMPROPER FRACTIONS AND MIXED NUMBERS | 75

Practice 4

Write the fractions found in the sentences.

a) �� _____________

b) Six of the seven Emirates joined at the same time in 1971. _____________

c) Two of my three brothers like ice cream. _____________

d) �� _____________

e) Six of my nine notebooks are blue. _____________

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�EXAMPLE

22 =

99 =

1515 =

105105 = 1 whole

Practice 5

Write the numerator to make each of the fractions below, equal to 1 whole.

__ __ __ __ __3 5 12 7 22

There are three different kinds of fractions; proper fractions, improper fractions and mixed numbers.

43 The numerator is less than the denominator.

This is called a proper fraction.A proper fraction is less than one whole one.



74

The numerator is greater than the denominator.

This is called an improper fraction.

An improper fraction is greater than one whole one.

A proper fraction is less than one whole one.

We can also write 74

as 143

1 43 is called a mixed number.

We have added a whole number to a fraction:

1 + 43 = 1

43

whole fraction mixed numbers

We say this as, one and three-quarters.

PROPER FRACTIONS, IMPROPER FRACTIONS AND MIXED NUMBERS | 77

�EXAMPLE

State whether each of these is a proper fraction, an improper fraction, or as a mixed number. Then write the fraction in words.

Nine-seventhsImproper fraction79a)

Five-tenthsProper fraction105b)

Two and three-quartersMixed number2 43c)

Practice 6

State whether each of these is a proper fraction, an improper fraction, or as a mixed number. Then write the fraction in words.

76

a)

4 15

b)

32

c)

94d)

863e)



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Percent means out of 100.

90% = 10090

What percent of each diagram is shaded?

a)

Since there are a total of 100 squares, the

denominator is 100. There are 3 shaded squares, so the fraction is 100

3 .

This means that 3% of the diagram is shaded.

b)

There are 34 shaded squares,

so the fraction is 10034 .

This means that 34% of the diagram is shaded.

PERCENT FRACTIONS | 79

Practice 7What percent of each diagram is shaded?

a) _______ % b) _______ %

There are also “special” percentages and their related fractions and decimals that you should be able to remember:

10025 =

41 = 0.25 = 25% 100

50 = 21 = 0.5 = 50%

10075 =

43 = 0.75 = 75% 100

100 = 1 = 100% (one whole)



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Compare the diagrams below:

84

63

42

21

We can say that 21 ,

42 ,

63 and

84 are all the same part of a whole.

They are called equivalent fractions because they have the same value. They are equal.

We use the sign = for (equal to) or (equivalent to):

21 =

42 or

42 =

84 or

63 =

84

Finding a fraction that is equal but with smaller numbers is called simplifying a fraction. This is done very easily with a calculator.

acb

On a calculator the fraction button looks like this:

SIMPLIFYING FRACTIONS WITH A CALCULATOR | 81

�EXAMPLE

Using your calculator, simplify the fractions.

a) 93 Enter 3 a

cb 9 = b)

2012 Enter 12 a

cb 20 =

13 5

3

So with our calculator, we found that 93 �� 1

3 , or 9

3 = 13

and that 2012

��53 , or

2012 =

53 .

Practice 8

Using your calculator, simplify the fractions.

a)105

___________b)

104

___________c)

1512

___________d)

5035

___________

e)3018

___________ f)98

___________ g)10050

___________ h)2011

___________

� ��!�� simplest form? That’s okay! Not all fractions will simplify.



Section 2.1 Exercises

1. Write the fractions in words.

a)54

________________________b) 1

3________________________

c) 110

________________________ d)21

________________________

e)125

________________________ f) 43 ________________________

or

________________________

2. Write the words as fractions

a) one-third ________________________ b) two quarters ________________________

�#�� ________________________ d) one-half ________________________

e) three-thirtieths________________________ f) seven-eighths ________________________

3. Write the fractions found in the sentences.

a) Six out of ten people go to college. ________

b) Two boxes of chocolate are shared by six people. ________

�#�� $$$$$$$$

d) My mother had four of her seven brothers and sisters over for lunch. ________

�#�� $$$$$$$$

EXERCISES | 83

4. What fraction is shaded in the shapes below?

a)

________________________

b)

________________________

c)

________________________

d)

________________________

5. Write the numerator to make each fraction equal to 1.

a)

5b)

17c)

8d)

331

6. State whether each of these is a proper fraction, an improper fraction, or as a mixed number. Then write the fraction in words.

a)98

b)3

72

c) 32



7. What percent of each diagram is shaded?

a) _______ % b) _______ %

8. Using your calculator, simplify the fractions.

a)42

___________ b)6036 ___________ c)

124

___________ d)10080

___________

e)1815

___________ f)306

___________ g) 78

___________ h)4527

___________

Section 2.2 Reading, Writing, Comparing and Rounding Decimals

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Do you recall learning about reading and writing whole numbers?

Thousands Ones

hund

red

thou

sand

s

ten

thou

sand

s

thou

sand

s

hund

reds

tens

ones

3 1 6 0 4 5

Our table shows that each place gets 10 times bigger as you move to the left. For example, 1 hundred is ten times bigger than 1 ten. 1 thousand is 10 times bigger than 1 hundred, and so on. This is the ‘decimal system’. We also use it for numbers that are smaller than one whole.

Thousands Ones . Decimal

hund

red

thou

sand

s

ten

thou

sand

s

thou

sand

s

hund

reds

tens

ones

tten

ths

hund

redt

hs

thou

sand

ths

3 1 6 0 4 5 . 7 2 9

�01�01�01�01�01

READING AND WRITING DECIMALS | 85



As you move to the right, the tenths’ place comes after the ones’ place.

0.1 = one tenth

We use a decimal point ( . ) to separate the units and tenths place.Look carefully at the difference between the place names. All place names to the right of the decimal point end with “th”.

tenthhundredththousandth

Thousands Ones . Decimal

hund

red

thou

sand

s

ten

thou

sand

s

thou

sand

s

hund

reds

tens

ones

tten

ths

hund

redt

hs

thou

sand

ths

0 . 7 2 9

“Zero point seven two nine.”

�EXAMPLE

For the number 0.729 above, write the place value of the digit.

a) 7 tenths b) 2 hundredths

c) 0 ones d) 9 thousandths

READING AND WRITING DECIMALS | 87

Practice 1

For the number 0.483, write the place value of the digit.

a) 0 ______________________________ b) 3 ______________________________

c) 8 ______________________________ d) 4 ______________________________

�EXAMPLE

Write the numbers in the correct place on the table.

Thousands Hundreds Tens Ones tenths hundredths thousandths

2 432 2 4 3 2 &

2.432 2 & 4 3 2

24.32 2 4 & 3 2

Practise 2

Write the numbers in the correct place on the table.

Thousands Hundreds Tens Ones tenths hundredths thousandths

746.278 &

4 628 &

4.628 &

46.28 &

346.5 &



Practice 3

Write the place value of the underlined digit.

a) 0.295 ______________________________ b) 17.435 4 ______________________________

c) 1.448 ______________________________ d) 0.624 58 ______________________________

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Each digit after the decimal place is read separately.

0.48 is read as “zero point four eight,” and NOT “zero point forty-eight.”

0.729 is read as “zero point seven two nine,” and NOT “zero point seven hundred twenty-

nine.

�EXAMPLE

Write these numbers in words.

a) 3.61 three point six one.

b) 15.236 ��

Practice 4

Write these numbers in words.

a) 0.8 ___________________________________________________________________________

b) 0.25 ___________________________________________________________________________

c) 1.461 __________________________________________________________________________

d) 57.829 ___________________________________________________________________________

There is also another way to read a decimal, by its place value. We use the place value furthest to the right to read the decimal.0.48 is read as forty-eight hundredths because the digit furthest to the right (8) is in the hundredths place.

0.729 is read as seven hundred twenty-nine thousandths because the digit furthest to the right

(9) is in the thousandths place.

WRITING DECIMALS IN WORDS | 89

�EXAMPLE

Write these numbers in words reading the place value.

a) 0.4 four tenths

b) 0.61 sixty-one hundredths

c) 0.236 two hundred thirty-six thousandths

d) 0.008 eight thousandths

Practice 5


a) 0.6 ___________________________________________________________________________

b) 0.37 ___________________________________________________________________________

a) 0.55 ___________________________________________________________________________

b) 0.624___________________________________________________________________________

If there is a whole number in front of the decimal point, we read that number and then say “and” instead of “point” before reading the decimal part of the number.

�EXAMPLE


a) 2.4 two and 4 tenths

b) 45.29 ��

Practice 6


a) 3.7 ___________________________________________________________________________

b) 20.49 ___________________________________________________________________________

c) 9.261 ___________________________________________________________________________

d) 8.009 ___________________________________________________________________________



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�EXAMPLE

Write these numbers in digits.

a) zero point six two 0.62

�#�� 81.351

c) two hundred six point two zero six 206.206

Practice 7

Write these numbers in digits.

a) zero point eight eight ______________________________

b) nine point three six two ______________________________

c) seventy-eight point two ______________________________

�#�� ______________________________

If a number has more than 3 decimal places, it can be written in groups of threes, just like with whole numbers.

Recall: Whole Numbers�� '�!�*/<�� !�� Decimal Numbers� /�>�@�BB� G��

��

We can read the decimal 0.3 as ‘three tenths’.

We also read the fraction 103 as ‘three tenths’.

So, 0.3 = 103

COMPARING DECIMALS | 91

�EXAMPLE

Write these fractions and mixed numbers as decimals.

a) 100543 = 0.543 b) 5

107 = 5.7

c) 1006 = 0.06 d) 65

1009 = 65.09

Practice 8

Write these fractions and mixed numbers as decimals.

a) 1007 = b)

100026 =

c) 1000229 = d) 7

100046 =

e) 1210023 = f)

10001 1 =

-��

You have already studied equivalent fractions. For example:

102 =

10020 =

1000200

When you write these as decimals you see:

102 = 0 . 2

10020 = 0 . 2 0

1000200 = 0 . 2 0 0



�EXAMPLE

Write equivalent decimals for these:

0.90, 0.5, 2.3, 0.680

tenths hundredths thousandths

0.9 0.90 0.900

0.5 0.50 0.500

2.3 2.30 2.300

0.68 0.680

Practice 9

Write equivalent decimals for these:

0.7, 33.9, 0.800, 0.30

tenths hundredths thousandths

0.7

33.9

0.800

0.30

We can also compare decimals, using the signs < or > or =

�EXAMPLE

Write the correct symbol, < or > or =, between these decimal numbers:

a) 0.45 _________ 0.44

Since 5 > 4 we

have

0.45 > 0.44

0.45The tenths place is the

same so we move to the

hundredths place.

0.45Compare the

tenths place.

0.45 > 0.44

COMPARING DECIMALS | 93

b) 0.09 ________ 0.107

0.09 0.107

Compare the

tenths place.

Since 0 < 1 we have

0.09 < 0.107

0.09 < 0.107

c) 0.97 ________ 0.972

0.97 0.972

The tenths’ place is the

same so move to the

hundredths’ place.

The hundredths’ place is

the same so look at the

thousandths’ place.

0.97___ 0.972

The thousandths’ place has no digit. We

know the value

of this place is 0.

The thousandths’ place has the

value of 2.

Since 0 < 2 we have 0.97 < 0.972

0.97 < 0.972

d) 0.970 _____ 0.97

The tenths’ and the hundredths’ place have

the same value.

In the second number the

thousandths’ place has no

digit. We know the value of

this place is 0.

0.970 = 0.97These numbers are the same.


MATHS FOUNDATION 1

Practice 10

Write the correct symbol, > or < = between these decimal numbers:

a) 9.42 _____ 9.04 b) 6.3 _____ 0.75

c) 3.871 _____ 3.9 d) 0.04 _____ 0.039

e) 4.0234 _____ 4.0243 f) 9.987 _____ 9.897

��

We round decimals in a very similar way to whole numbers.

The only difference when rounding decimals, instead of replacing digits to the right of the given place value with zeros, we remove those digits.

Therefore the steps to rounding decimals are as follows:

Rules for Rounding Decimals:Step 1 Underline the digit of the given place value.

Step 2 Circle the digit to its right.

Step 3 a) If that circled digit is from 0 to 4, the digit in the given place stays the same. b) If that circled digit is from 5 to 9, add 1 to the digit in the given place.

Step 4 Remove all digits to the right of the given place.

ROUNDING DECIMALS | 95

Do you remember your decimal place values?

. Decimal

tent

hs

hund

redt

hs

thou

sand

ths

. 7 2 9

= 0.729

Let’s try an example rounding with decimals.

�EXAMPLE

Round 0.34 to the nearest tenth

Step 1 Underline the digit of the given place value (tenths).

0 . 3 4

Step 2 Circle the digit to its right (4). 0 . 3 4

Step 3 a) If that circled digit is from 0 to 4, the digit in the given place stays the same.

b) If that circled digit is from 5 to 9, add 1 to the digit in the given place.

Step 4 Remove all digits to the right of the given place value.

0 . 3



�EXAMPLE

Round 0.761 to the nearest tenth.

Step 1 Underline the digit of the given place value (tenths).

0 . 7 6 1

Step 2 Circle the digit to its right (4). 0 . 7 6 1

Step 3 a) If that circled digit is from 0 to 4, the digit in the given place stays the same.

b) If that circled digit is from 5 to 9, add 1 to the digit in the given place. (it is 6, so you add 1 to the underlined digit 7 making it 8)

Step 4 Remove all digits to the right of the given place value.

0 . 8

�EXAMPLE

Round to the nearest tenth.a) 0 . 6 2 0.6 b) 0 . 1 7 3 0.2

Practice 11

Round to the nearest tenth.

a) 0.51 ______________ b) 0.88 ______________ c) 0.75 ______________

d) 0.292______________ e) 0.54 ______________ f) 0.388______________

�EXAMPLE

Round to the nearest hundredth.

a) 0 . 6 2 4 0.62 b) 0 . 1 7 5 0.18

Practice 12

Round to the nearest hundredth.

a) 0.512______________ b) 0.476______________ c) 0.191______________

d) 0.924______________ e) 0.577______________ f) 0.996______________

ROUNDING DECIMALS | 97

�EXAMPLE

Round to the nearest thousandth.a) 0 . 6 2 4 3 0.624 b) 0 . 1 7 5 5 1 0.176

Practice 13

Round to the nearest thousandth.

a) 0.512 4 ________ b) 0.476 7 ________ c) 0.191 81 ________

d) 0.924 99 ________ e) 0.5993 ________ f) 1.9995 ________

We can also round decimals to a given decimal place.

�EXAMPLE

Round 0.38 to one decimal place (1 d.p.).

“3” is the 1st decimal place, so it is the same as rounding to the tenth.0 . 3 8 0.4

�EXAMPLE

Round 0.487 to two decimal place (2 d.p.).

“8” is the 2nd decimal place, so it is the same as rounding to the hundredth.

0 . 4 8 7 0.49

�EXAMPLE

Round 0.194 7 to three decimal place (3 d.p.).

“4” is the 3rd decimal place, so it is the same as rounding to the thousandth.

0 . 1 9 4 7 0.195



Practice 14

Round each number as indicated.

a) 0.83 to 1 d.p. _______ b) 0.67 to one decimal place _______

c) 2.465 to one decimal place _______ d) 7.809 to 1 d.p. _______

e) 0.571 to two decimal places _______ f) 1.345 to 2 d.p. _______

g) 0.097 2 to 2 d.p. _______ h) 2.998 to 2 d.p. _______

i) 0.372 6 to three decimal places _______ j) 5.080 734 to 3 d.p. _______

2��3�,��

�� is a way of writing very large or very small numbers.K�� Qa) A number between 1 and 10. For example, 1.23b) A power with a base of 10, written as x 10exponent.

��4��,��%��

Look at the table below that uses powers with a base of 10. Can you see the pattern?

Decimal NumberMeaningWe say

101010 to the exponent 110 1

10010×1010 to the exponent 210 2

1 00010×10×1010 to the exponent 310 3

10 00010×10×10×1010 to the exponent 410 4

100 00010×10×10×10×1010 to the exponent 510 5

1 000 00010×10×10×10×10×1010 to the exponent 610 6

LARGE NUMBERS | 99

��

�EXAMPLE

V��

a) 428 000 000 Move the decimal point to the left until you have a number between 1 and 10.

4.28 000 000 4.28 is between 1 and 10.

8

4.28 x 108 The number of places you moved the decimal point (8) is the exponent of the power of 10.

b) 56 000 Move the decimal point to the left until you have a number between 1 and 10.

5.6000 5.6 is between 1 and 10.

4 places

5.6 x 104 The number of places you moved the decimal point (4) is the exponent of the power of 10.

Practice 15

Write the numbers in ��

a) 750 000 7.5 x 105

b) 574 000 000 ____________________

c) 8 200 ____________________

d) 406 000 ____________________

e) 820 ____________________

f) 45 600 000 ____________________



��

�EXAMPLE

Write the numbers in decimal form.

The exponent (5) tells you that you moved the decimal point 5 places to the left, so you must move it back to the right.

a) 2.3 x 105

230 000

230 000

“7” places to the right. b) 8.06 x 107

80600000.

80 600 000.

Practice 16

Write the numbers in decimal form��

a) 5.1 x 104 51 000

b) 7.7 x 102 ____________________

c) 4.6 x 105 ____________________

d) 4.32 x 103 ____________________

e) 1.234 x 105 ____________________

f) 2.6 x 107 ____________________

80600000.

LARGE NUMBERS | 101

��,��%��

Now look at the table below that uses powers with a base of 10. Can you see the pattern?

We say Meaning Fraction Decimal Number

10 -1 B/�� XB1

101

100.1

10 -2 B/�� X>101 X

101

1001 0.01

10 -3 B/�� X[101 X

101 X

101

10001 0.001

10 -4 B/�� X'101 X

101 X

101 X

101

10 0010

0.0001

10 -5 B/�� X�101 X

101 X

101 X

101 X

101

100001

00.00001

��

�EXAMPLE

Write the numbers in �� .

a) 0.000 000 052 Move the decimal point to the right until you have a number between 1 and 10. 0 000 000 05.2 5.2 is between 1 and 10.

8

5.2 x 10�� The number of places you moved the decimal point (8) is the exponent of the power of 10. Since you moved in the opposite direction, the exponent is NEGATIVE.

b) 0.007 Move the decimal point to the right until you have a number between 1 and 10.

0 007 7 is between 1 and 10. 3 places 7 x 10�� The number of places you moved the decimal point (3) is the exponent of the power of 10, but NEGATIVE.



Practice 17

Write the numbers in ��

a) 0.002 4 2.4 x 10X[

b) 0.000 056 ____________________

c) 0.000 000 6 ____________________

d) 0.002 04 ____________________

e) 0.0345 ____________________

f) 0.49 ____________________

b) ��

�EXAMPLE

Write the numbers in decimal form.

a) 4.3 x 10X� The �� tells you that you moved the decimal point 5 places to the right, so you must move it back to the left.

0.000043

0.000 043

b) 8.06 x 10X* “7” places to the left.

0.000000806

0.000 000 806

.00004

.00000080

LARGE NUMBERS | 103

Practice 18

Write the numbers in decimal form��

a) 4.6 x 10X� 0.000 046

b) 2.1 x 10X[ ____________________

c) 3.25 x 10X@ ____________________

d) 1.06 x 10X> ____________________

e) 7.8 x 10X' ____________________

f) 8.204 x 10X* ____________________

5��,��

\�� !�� ]� �� calculator.

�EXAMPLE

Multiply. 34 000 x 1 000 000

3.410The answer is too large for the calculator, so you see 3.410 on your display.

3.4 x 1010 This display actually means ��

34 000 000 000 You now know that this can also be written in decimal form.



�EXAMPLE

If a calculator displays 5.2XBB!�� ^�

The answer is too large for the calculator, so you see 3.410 on your display.5.2��

This display actually means �� .5.2 x 10��

You now know that this can also be written in decimal form.0.000 000 000 052

Practice 19

Write the calculator displays in �� and decimal form.

��

a) 5.513 5.5 x 1013 55 000 000 000 000

b) 7.3XB' 7.3 x 10��" 0.000 000 000 000 073

c) 1.04XBB ____________________ ____________________

d) 6.3510 ____________________ ____________________

e) 9.3XB> ____________________ ____________________

f) 9.917 ____________________ ____________________

EXERCISES | 105


1. For the number 0.167, write the place value of the digit.

a) 0 ____________________ b) 1 ____________________

c) 6 ____________________ d) 7 ____________________

2. State the place value of the underlined digit.

a) 0.365 ____________________ b) 2.376 ____________________

c) 1.299 ____________________ d) 0.452 ____________________

3. Write these numbers in words.

a) 0.8 __________________________________________________

b) 0.25 __________________________________________________

c) 12.1 __________________________________________________

d) 6.259 __________________________________________________

e) 350.12 __________________________________________________

f) 0.990 __________________________________________________

4. Write these numbers in words using place value.

a) 0.8 __________________________________________________

b) 0.25 __________________________________________________

c) 12.1 __________________________________________________

d) 6.259 __________________________________________________

e) 350.12 __________________________________________________

f) 0.990 __________________________________________________



5. Write these numbers in digits.

a) zero point one seven ______________

�#��G�� $$$$$$$$$$$$$$

c) seventy and twenty-six hundredths ______________

�#�� $$$$$$$$$$$$$$

e) six and two thousandths ______________

f) two hundred twenty-one and three hundred six thousandths ______________

6. Write these fractions and mixed numbers as decimals.

a) 10075 = b)

100032 =

c) 100

14 54 = d) 1000

2 4 =

7. Write equivalent decimals for these:

0.60. 0.8, 9.4, 0.200

thousandthshundredthstenths

0.60

0.8

9.4

0.200

8. Write the correct symbol, > or < = between these decimal numbers:

a) 8.32 _____ 8.04 b) 5.37 _____ 0.64

c) 7.843 _____ 12.9 d) 0.06 _____ 0.029

e) 3.0234 _____ 3.0423 f) 4.217 _____ 4.017

9. Round the number to the nearest tenth.

a) 0.49 _____ b) 0.81 _____ c) 0.66 _____ d) 0.354_____ e) 0.19 _____ f) 0.958_____

EXERCISES | 107

10. Round to the nearest hundredth.

a) 0.471 _____ b) 0.778 _____ c) 0.660 _____

d) 0.485 _____ e) 0.495 _____ f) 0.997 _____

11. Round to the nearest thousandth.

a) 0.881 6 _____ b) 2.292 2 _____ c) 11.448 51 _____ d) 0.338 85 _____ e) 0.573 49 _____ f) 1.9995 _____

12. Round each number as indicated.

a) 0.835 to two decimal places _______ b) 0.44 to 1 d.p. _______

c) 1.119 5 to three decimal places_______ d) 2.498 to 2 d.p. _______

e) 6.145 299 to 3 d.p. _______ f) 3.299 to one decimal place _______

g) 0.998 to one decimal place _______ h) 0.998 to 2 d.p. _______

i) 23.77 to 1 d.p. _______ j) 6.199 720 to 3 d.p. _______

B[��V��

a) 7.5XBB ____________________ ____________________

b) 4.1X` ____________________ ____________________

c) 1.04X[ ____________________ ____________________

d) 6.354 ____________________ ____________________



Section 2.3Converting, Comparing and Ordering Decimals, Fractions and Percents

$�� %��.��

How do we compare fractions, decimals and percents to each other? We need to put them all in the same format.

��

You can use your calculator to easily change fractions into decimals.This is done by dividing the numerator by the denominator.

�EXAMPLE

Convert the fractions and mixed numbers to decimals.

answer on the calculator

keystrokes on the calculator

0.3753 8'a)

83

2.525 'b) 25

0.666666…….2 3'c)

32

2.753 4'd) 2

43

10.21 5'e) 10

51

If your answer repeats, like in c), we can write this in an easier way.

32 = 0.666666…… = 0.6

The bar over top of a digit or digits means that they repeat forever.

CONVERTING BETWEEN FRACTIONS AND DECIMALS | 109

Practice 1

Convert the fractions to decimals.

a) 107 ________ b)

53 ________ c)

65 ________

d) 58 ________ e) 3

5048 ________ f) 5

97 ________

��

Recall your decimal place values:

. Decimal te

nths

hund

redt

hs

thou

sand

ths

. 7 2 9

The place value of the digit furthest to the right tells you the denominator of the fraction.

�EXAMPLE

Write each decimal number as a fraction.

a) 0.2 2 is in the tenths place, so… 102

b) 0.31 1 is in the hundredths place, so… 100

13



c) 0.075 5 is in the thousandths place, so… 10 0

750

If there is a number (other than 0) in front of the decimal point, it simply becomes the whole number part of the mixed number.

d) 2.8 8 is in the tenths place, so… 10

2 8 e) 6.25 5 is in the hundredths place, so…

1006 25

f) 15.207 7 is in the thousandths place, so… 1000

15 207

Practice 2

Write each decimal number as a fraction.

a) 0.3 = _____ b) 0.27 = _____ c) 2.13 = _____

d) 30.88 = _____ e) 1.22 = _____ f) 0.9 = _____

g) 4.35 = _____ h) 0.167 = _____

Note: Anytime your answer is a fraction, �� (remember this?) Again this is easy to do with our calculators.

CONVERTING BETWEEN FRACTIONS AND DECIMALS | 111

�EXAMPLE

Write the fractions from the last example in simplest form.

a) 0.2 = 102 =

51

b) 0.31 = 100

13 (simplest form)

c) 0.075 = 10 0

750

= 403

d) 2.8 = 10

2 8 = 254

e) 6.25 = 100

6 25 = 641

f) 15.207 = 1000

15 207 (simplest form)

Practice 3

Write each of your answers from Practice 2 in simplest form (remember, you can use your calculator).

a) = _____ b) = _____ c) = _____ d) = _____

e) = _____ f) = _____ g) = _____ h) = _____



)�� )��.��"��

��"��

To convert a percent to a decimal, you divide by 100.

�EXAMPLE

Convert the percents into decimals.a) 75% 75 ÷ 100 0.75

b) 22% 22 ÷ 100 0.22

c) 3% 3 ÷ 100 0.03

d) 52.5% 52.5 ÷ 100 0.525

e) 258% 258 ÷ 100 2.58

Did you notice something? All the answers look similar to the questions. The only difference is that the decimal point has moved 2 places to the left.

Practice 4

Convert the percents into decimals.

a) 89% ___________ b) 37% ___________

c) 47% ___________ d) 99% ___________

e) 9% ___________ f) 2.5% ___________

g) 8.29% ___________ h) 100% ___________

i) 385% ___________ j) 3500% ___________

CONVERTING BETWEEN PERCENTS AND DECIMALS | 113

��"��

To convert a decimal to a percent, you multiply by 100.

�EXAMPLE

Convert the decimals into percents.

a) 0.35 0.35 x 100 35%

b) 0.82 0.82 x 100 82%

c) 1.7 1.7 x 100 170%

d) 0.003 0.003 x 100 0.3%

e) 10.5 10.5 x 100 1050%

Practice 5

Convert the decimals into percents.

a) 0.48 _________ % b) 0.17 _________ %

c) 0.2 _________ % d) 0.487 _________ %

e) 0.8216 _________ % f) 1 _________ %

g) 2.38 _________ % h) 0.002 _________ %

i) 0.00575 _________ % j) 23.8 _________ %

�� )��.��"��

��"��

Remember, percent (%) means out of 100.

�EXAMPLE

Write each percent as a fraction.

75% = 10075 20% =

10020 54% =

10054



Practice 6

Write each percent as a fraction.

a) 30% = ______ b) 8% = ______ c) 6% = ______

When the percentage is greater than 100, the result is a mixed number.

�EXAMPLE

Write each percent as a fraction or mixed number.

250% =100250 =

1002 50 120% =

100120 =

1001 20 305% =

100305 =

1003 5

Practice 7

Write each percent as a fraction or mixed number.

a) 250% = ______ = ______ b) 305% = ______ = ______

c) 225% = ______ = ______ d) 197% = ______ = ______

e) 552% = ______ = ______ f) 101% = ______ = ______

��"��

��

�EXAMPLE

Write the fractions as percents.

a) 53 Step 1: Convert the fraction into a decimal using

your calculator. 53 = 0.6

Step 2: Convert the decimal into percent ( x100) 0.6 x 100 = 60%

b) 85 = 0.625

0.625 x 100 = 62.5%

CONVERTING BETWEEN PERCENTS AND DECIMALS | 115

Practice 8

V��

a) 2206 2

206 = 2.3 2.3 x 100 = 230%

b) 125

125 = 0.416 0.416 x 100 = 41.6%

c) 83 __________

d) 59

__________

e) 4201 __________

f) 1116

__________

g) 72

__________

h) 1000

7 __________

�� %��.��"��

With the skills learned in this section, we can now convert between all three number forms - - fractions, decimals and percents.

�EXAMPLE

Fill in the chart below using the skills learned in this section.

Fraction Decimal Percent

a)43 3 ÷ 4 = 0.75 0.75 x 100 = 75%

b) 1105 = 1

21 1.5 1.5 x 100 = %150

c) 0.792 = 1000792 =

12599

79.2 ÷ 100 = 0.79279.2%



Practice 9

Complete the chart below using the skills learned in this section.

PercentDecimalFraction or Mixed Number (simplest form)

5023a)

0.45b)

80%c)

32d)

1.2e)

0.3%f)

254g)

0.525h)

99.5%i)

Reminder:Don’t forget to simply your answers with fractions!

CONVERTING BETWEEN PERCENTS AND DECIMALSE | 117

-��!��"��

The easiest way to compare and order fractions, decimals and percents is to convert everything to decimals. You can then use the rules for ordering decimals that you learned in Module 1.

�EXAMPLE

Which number is greater

a) 43 or 7

8

43 = 0.75 7

8 is greater

78

= 0.875 0.875 > 0.75

b) 43 or 0.72

43 = 0.75

43 is greater

c) 43 or 80%

43 = 0.75 80% is greater

80% = 0.80

Practice 10

Which number is greater?

a) 25

or 13

__________________

b) 25

or 0.42 __________________

c) 25

or 35% __________________

d) 1.81 or 235% __________________



�EXAMPLE

Order the numbers in ascending order: 25

, 35%, 0.42, 13

, 50%, 14

First, convert each number to decimal form: 25

35% 0.42 13

50% 14

0.40 0.35 0.42 0.33… 0.50 0.25

Now, order the numbers using the decimal equivalents.

0.25 0.33… 0.35 0.40 0.42 0.50

Finally, write the original numbers that match these decimal equivalents. 14

13

35% 25

0.42 50%

Practice 11

a) Order the numbers in ascending order: 0.88, 0.91,5042 , 90%, 94%

b) Order the numbers in ascending order: 43 , 0.7, 72%, 0.66,

85

c) Order the numbers in descending order: 1.99, 150%, 58 ,

109 , 2.1

EXERCISES | 119


Remember to simplify all fraction answers in this section and from now on!

1. Convert the fractions to decimals.

a) 43 ________ b) 7

8 ________ c)

2011 ________

d)1312 ________ e) 7

54 ________ f) 5

127 ________

2. Write each decimal number as a fraction

a) 0.8 = _____ b) 0.94 = _____ c) 4.446 = _____ d) 8.12 = _____

e) 0.07 = _____ f) 0.054= _____ g) 1.005 = _____ h) 0.250 = _____

3. Convert the percents into decimals.

a) 35% ___________ b) 89% ___________

c) 52% ___________ d) 5.8% ___________

e) 6% ___________ f) 2.5% ___________

g) 0.41% ___________ h) 200% ___________

4. Convert the decimals into percents.

a) 0.31 _________ % b) 0.49 _________ %

c) 0.9 _________ % d) 0.458 _________ %

e) 0.0425 _________ % f) 3 _________ %



5. Write each percent as a fraction or mixed number.

a) 25% = ______ b) 74% = ______ c) 5% = ______

d) 120% = ______ e) 50% = ______ f) 12% = ______

g) 515% = ______ h) 105% = ______ i) 30% = ______

j) 88% = ______ k) 62% = ______ l) 100% = ______

6. Write the fractions and mixed numbers as percents.

a) 241

__________

b) 315 __________

c) 1 15

__________

d) 1112

__________

7. Complete the chart below using the skills learned in this section.

PercentDecimalFraction or Mixed Number(simplest form)

85a)

0.02b)

125%c)

243d)

0.95e)

5.4%f)

EXERCISES | 121

8. Which number is greater?

a) 35

or 32 _______________________________

b) 35

or 0.47 _______________________________

c) 35

or 35% _______________________________

d) 1.61 or 235%_______________________________

9. Put the numbers in ascending order.

38

, 0.31, 103 , 35%, 34%

10. Put the numbers in descending order.

122%, 8

10 , 1.31, 140%, 1.19, 94



Section 2.4Adding, Subtracting, Multiplying and Dividing Fractions

Performing the four arithmetic operations with fractions is very easy when using your ��V�� module.

$�$��

Your calculator makes adding and subtracting fractions very easy.

�EXAMPLE

Add the fractions and mixed numbers. on your calculator

a) 38

+ 25

= 3 ��

8 + 2 ��

5 = 56

b) 183 + 5

7 = 1 �

��

3 ��

8 + 5 ��

7 = 2 556

ADDING, SUBTRACTING, MULTIPLYING AND DIVIDING FRACTIONS | 123

Practice 1

Add the fractions and mixed numbers.

a) 13

+ 43 = ________ b) 2

95 + 6

125 = ________

c) 183 + 3

2415 = ________ d)

718 + 5

9 = ________

The fraction button can be used the same way for all four operations (add, subtract, multiply, divide).

)�$��%��&��

The way you used your calculator in Section A is the same for all math operations. Just be sure which operation is being asked for in the question!

�EXAMPLE

Perform the given operations on the fractions and mixed numbers.

on your calculator

a) 85 �X� 2

5 = 5 �

��

8 - 2 ��

5 = 940

b) 183 x 4

7 = 1 �

��

3 ��

8 x 4 ��

7 = 1114

c) 2101 ÷

103 = 2 �

��

1 ��

10 ÷ 3 ��

10 = 7

d) 11211 + 2 8

15 = 1 �

��

11 ��

12 + 2 ��

8 ��

15 = 46027



Practice 2

Perform the given operations on the fractions and mixed numbers.

a) 31 x

43 = ________ b) 2

95 �X�2

125 = ________

c) 183 ÷

21 = ________ d)

718 + 5

9 = ________

e) 1832 �X�14

65 = ________ f) 2 5

6 + 12

5 = ________

g) 132

÷ 1107 = ________ h)

58 x 2

41 = ________

��,��%��

The word “of” tells you that you must multiply.

�EXAMPLE

a) How much is 21 of 10? Show with a diagram.

Of course, this can be done on a calculator, but it is also important that you can see and understand what is being asked for.

Remember that 21 means that there are 2 total parts and 1

is shaded. We need to separate 10 into two equal parts, and choose one of those parts.

We have now separated the 10 shapes into 2 parts, and chosen 1 of those parts (the shaded circles). Counting the shaded circles, we can see that

21 of 10 = 5

Check on your calculator: 21 x 10 = 5

b) How much is 43 of 16? Show with a diagram.

43 means that there are 4 total parts and 3 are shaded.

We need to separate 16 into 4 equal parts, and choose 3 of those parts. Counting the shaded circles, we can see that

43 of 16 = 12

Check on your calculator: 43 x 16 = 12

FINDING A FRACTION OF A NUMBER | 125

Practice 3

a) How much is 21 of 14? Show with a diagram then check with your calculator.

Diagram: Check on your calculator:

b) How much is 13

of 15? Show with a diagram then check with your calculator.


c) How much is 25

of 25? Show with a diagram then check with your calculator.




��"��,��%��

Remember from the last section that ‘of’ means to multiply.

21 of 20 =

21 x 20 = 10

� �� !�� percent of a number.

You need to remember how to change a percent to a decimal.

25% = 25100

= 0.25 (remember to simply ÷ 100)

�EXAMPLE

Find the percent of the numbers below.

= 12.50.25 x 50Change the percent to a decimal

and multiply.

25% of 50a)

= AED410.082 x 500Change the percent to a decimal

and multiply.

8.2% of AED500b)

In the last example, notice that a unit was used (AED), so we put the units in the answer.

Practice 4

Find the percent of the numbers below. Show how you change the percent to a decimal � ��

a) 15% of 50 = = ______ b) 18% of AED1200 = = ______

c) 8% of 250kg = = ______ d) 5.5% of AED150 = = ______

FINDING A PERCENT OF A NUMBER | 127


1. Perform the given operations on the fractions and mixed numbers.

a) 109 �X�

43 = ________ b)

85 ÷ 1

6 = ________

c) 121 + 5

32 = ________ d) 7

8 x

43 = ________

e) 272 x 1

4 = ________ f) 12

5�X�

32 = ________

g) 943 x 5

6 = ________ h) 7

18 ÷ 1

122 = ________

2. Draw a diagram and check with your calculator to solve the multiplication questions.

a) 13

of 12


b) 78

of 25


3. Find the percent of the numbers below. Show how you change the percent to a decimal � ��

a) 30% of 50 = = ______ b) 15% of AED650 = = ______

c) 5% of AED1250 = = ______ d) 2.75% of 50 = = ______



Section 2.5Ratios and Proportions

$��3��

Ratio – the comparison of two numbers.For example, from the diagram below, the ratio of shaded squares to non-shaded squares is 2 to 3. This means that there are 2 shaded squares and 3 non-shaded squares.

There are three ways that we write a ratio:

2 to 3 2 : 3 32

However, all three ways are said the same way, “two to three.”

�EXAMPLE

Use the shapes above to write the ratios. Write the ratios in three different ways.

RatioDescription

5:2, 5 to 2,25a) The ratio of shaded circles to non-shaded circles.

4:2, 4 to 2, 42

b) The ratio of non-shaded squares to non-shaded circles.

5:7, 5 to 7, 57

c) The ratio of shaded circles to all circles.

EQUIVALENT RATIOS AND PROPORTIONS | 129

In example c), the ratio included all circles, which means you must add the shaded circles and non-shaded circles together.

Practice 1

Use the shapes above to write the ratios. Write the ratios in three different ways.

Description Ratio

a) The ratio of shaded squares to non-shaded squares.

b) The ratio of non-shaded squares to all squares.

c) The ratio of all squares to all circles.

d) The ratio of shaded circles to shaded squares.

e) The ratio of all squares to non-shaded circles.

)�-6�� "��

The ratio of non- shaded squares to shaded squares is 1 to 2. When we write this ratio in

another form, it is 21 .

This means that there is 1 non-shaded square for every 2 shaded squares.

The picture above still shows a ratio of 1 non-shaded square for every 2 shaded squares. Looking at all the squares together, the ratio of non-shaded squares to shaded squares is 2 to 4. Since both ratios describe the same thing, they are called equivalent ratios.

21 = 2

4



�EXAMPLE

Write equivalent ratios for the shapes in the diagram above.

= 48

= 36

= 242

1non-shaded squares toshaded squares

Practice 2

Write equivalent ratios for the shapes in the diagram above.

===51

moons tostars

The order of a ratio is very important! For example,

32 is not the same as 3

2 .

Let’s look at the relationship between equivalent ratios.

= 48

= 36

= 242

1

Ratios are equivalent if they have their cross products are equal.

21 3

6 2 x 3 = 6 and 1 x 6 = 6, so these ratios are equivalent (equal).

32 4

8

2 x 8 = 16, and 3 x 4 = 12, so these ratios are not equivalent.

When two or more ratios are equivalent, they are said to be in proportion.

21 = 3

6 The above ratios are equivalent, so they are in proportion.

EQUIVALENT RATIOS AND PROPORTIONS | 131

�EXAMPLE

Are the ratios equivalent (in proportion)? Show your work.

a) 51 and

102 1 x 10 = 10

5 x 2 = 10Yes, the ratios are in proportion (equivalent).

b) 32 and

43 2 x 4 = 8

3 x 3 = 9No, the ratios are not in proportion (not equivalent).

Practice 3

Are the ratios equivalent (in proportion)? Show your work.

a) 32 and

96

b) 35

and 2012

c) 14

and 16

d) 43 and 9

12

e) 16

and 312



��

Very similar to simplifying fractions, we can simplify ratios.

Recall simplifying fractions with your calculator.

410

= 25

410

and 25

are equivalent (have the same value), but 25

is in simplest form.

The same is true for ratios. However be careful, because a ratio must always have 2 parts, or

terms!

�EXAMPLE

Simplifying the ratios:

If this were a fraction, it would simplify to 1

21 .

However we need to keep 2 parts or terms, so it must remain as 3

2 .

b) 64

= 32

Simplifying the ratio is exactly the same as simplifying a fraction.

a) 36

= 21

Practice 4

Simplify the ratios using your calculator. Be sure your answers have 2 terms!

a) 68

= b) 912

= c) 1545

=

d) 104

= e) 1510

= f) 7

21 =

g) 2016 = h) 18

24 = i)

26 =

SOLVING PROPORTIONS | 133

�� "��

We learned that a proportion is when 2 ratios are equal to each other. For example, the ratios

32 and

96 make a proportion because they are equal (2 x 9 = 18; 3 x 6 = 18).

We write a proportion like this:

32 =

96

K�� !��

32 = 6

Since we know the cross products must be equal, we know that

2 x ___ = 18

3 x 6 = 18

Therefore, the missing value must be 9 (2 x 9 = 18)

To complete the proportion, it looks like this: 32 =

96

�EXAMPLE

Complete the proportions. Show your work.

a) 21 =

8

1 x 8 = 82 x __ = 8

The missing number must be 4, because 2 x 4 = 8.The completed proportion is

21 = 4

8

b) 5 = 156

5 x 6 = 30__ x 15 = 30

The missing number must be 2, because 2 x 15 = 30.The completed proportion is

25 = 15

6



Practice 5

Complete the proportions. Show your work.

a) 21 = 6

b) 510

= 20

c) 6 = 128

d) 3

= 189

e) 25 =

6

EXERCISES | 135


1. Use the shapes above to write the ratios. Write the ratios in three different ways. Description Ratio

a) The ratio of shaded circles to non-shaded circles.

b) The ratio of all circles to all squares.

c) The ratio of shaded squares to shades circles.

d) The ratio of shaded squares to all squares.

e) The ratio of non-shaded circles to shaded circles.

2. Write equivalent ratios from the picture above.

boysto

girls 32 = =



3. Are the ratios equivalent (in proportion)? Show your work using cross products.

a) 32 and

96

b) 35

and 2012

c) 14

and 51

d) 43 and 9

12

e) 16

and 312

f) 27

and 410

4. Simplify the ratios using your calculator. Be sure your answers have 2 terms!

a) 68

= b) 912

= c) 1545

=

d) 104

= e) 1510

= f) 7

21 =

g) 2016 = h) 18

24 = i)

26 =

5. Complete the proportions. Show your work.

a) 32 =

12

b) 5

= 156

c) 38

= 9

d) 7 = 6

14

e) 46

= 24

SUBTITLE | 137

SKILL BUILDERS



SKILL BUILDERS – Section 2.1 Recognizing, Reading, Writing and Simplifying Fractions

$� ��

1. What fraction is shaded in the shapes below?

_____________

a)

_____________

b)

_____________

c)

_____________

d)

2. Write the fractions in words.

a) 85 ___________________ b)

41 ___________________

c) 92 ___________________ d)

21 ___________________

e) 2011 ___________________ f)

43 ___________________

or

___________________

SKILL BUILDERS | 139

)��

2. Write the words as fractions

a) one-half ____ b) three fourths ____

��#�� $$$$� � � �#�� $$$$

e) nine-twelfths ____ f) one-tenth ____

3. Write the fractions found in the sentences.

a) One out of every three students go to college. ________

b) Five out of eight people went to Dubai to shop. ________

�#�� $$$$$$$$

d) Three of my four sisters are coming home for dinner tonight. ________

e) I scored nine out of ten on the quiz today. ________

��"��*��&�+��,��%��

4. Write the numerator to make each of the fractions below, equal to 1 whole.

5

11

35

47

28

5. State whether each of these is a proper fraction, an improper fraction, or as a mixed number. Then write the fraction in words.

a) 437

b)104

c) 112



��"��

6. What percent of each diagram is shaded?

a) _______ % b) _______ %

E. Simplifying Fractions with a Calculator

7. Using your calculator, simplify the fractions.

a) 63 _______ b)

2010 _______ c)

128 _______ d)

5044 _______

e) 3025 _______ f) 9

45 _______ g)

115 _______ h) 50

75 _______

SKILL BUILDERS – Section 2.2 Reading, Writing, Comparing and Rounding Decimals

$� ��

1. For the number 0.946, write the place value of the digit.

a) 4 ____________________ b) 9 ____________________

c) 6 ____________________ d) 0 ____________________

2. State the place value of the underlined digit.

a) 0.141 ____________________ b) 3.556 ____________________

c) 0.496 ____________________ d) 0.401 ____________________


)��

3. Write these numbers in words.

a) 0.2 __________________________________________________

b) 0.36 __________________________________________________

c) 56.7 __________________________________________________

d) 8.829 __________________________________________________

e) 771.84 __________________________________________________

f) 7.009 __________________________________________________

4. Write these numbers in words using place value.

a) 0.5 __________________________________________________

b) 0.89 __________________________________________________

c) 7.6 __________________________________________________

d) 2.105 __________________________________________________

e) 200.02 __________________________________________________

f) 0.921 __________________________________________________

��

5. Write these numbers in digits.

a) zero point three ______________

b) one point two two six ______________

c) six and fourteen hundredths ______________

d) nine and eight thousandths ______________

�#�� $$$$$$$$$$$$$$

�#�� $$$$$$$$$$$$$$



��

6. Write these fractions and mixed numbers as decimals.

a)10049 = b)

100072 =

c)

10012 26 = d)

10003 15 =

7. Write equivalent decimals for these:

0.40. 0.3, 7.2, 0.600

thousandthshundredthstenths

0.40

0.3

7.2

0.600

-��,��%��

8. Write the correct symbol, > or < = between these decimal numbers:

a) 7.32 _____ 8.06 b) 5.41 _____ 0.64

c) 7.843 _____ 11.6 d) 0.04 _____ 0.018

e) 3.0135 _____ 3.0351 f) 6.207 _____ 6.017

��

9. Round the number to the nearest tenth.

a) 0.58 _____ b) 0.72 _____ c) 1.39 _____

d) 2.511_____ e) 0.27 _____ f) 0.955_____


10. Round to the nearest hundredth.

a) 0.336 _____ b) 0.492 _____ c) 0.293 _____

d) 1.478 _____ e) 0.994 _____ f) 0.998 _____

11. Round to the nearest thousandth.

a) 0.223 6 _____ b) 2.292 2 _____ c) 11.448 51 _____

d) 0.444 76 _____ e) 0.339 5 _____ f) 1.989 7 _____

12. Round each number as indicated.

a) 0.85 to one decimal place _______ b) 0.32 to 1 d.p. _______

c) 1.195 to two decimal places _______ d) 3.808 to 2 d.p. _______

e) 6.145 91 to 3 d.p. _______ f) 3.29 to one decimal place _______

g) 0.799 to one decimal place _______ h) 0.005 to 2 d.p. _______

i) 15.15 to 1 d.p. _______ j) 1.055 72 to 3 d.p. _______

2��3�,��

B[��V��

a) 4.5X< ____________________ ____________________

b) 3.7X' ____________________ ____________________

c) 5.23X� ____________________ ____________________

d) 8.354 ____________________ ____________________



SKILL BUILDERS – Section 2.3Converting, Comparing and Ordering Decimals,Fractions and Percents

$�� %��.��

1. Convert the fractions to decimals.

a) 54 ________ b) 1

8 ________ c)

204 ________

d) 26 ________ e) 3

21 ________ f) 4

1612 ________

2. Write each decimal number as a fraction

a) 0.2 = _____ b) 0.25 = _____ c) 0.182 = _____ d) 4.72 = _____

e) 0.05 = _____ f) 0.106= _____ g) 2.001 = _____ h) 0.119= _____

)�� %��.��"��

3. Convert the percents into decimals.

a) 25% ___________ b) 14% ___________

c) 8% ___________ d) 7.5%___________

e) 99% ___________ f) 5.75%___________

g) 0.82%___________ h) 150%___________

4. Convert the decimals into percents.

a) 0.20 _________ % b) 0.75 _________ %

c) 0.7 _________ % d) 0.425_________ %

e) 0.003_________ % f) 10 _________ %


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5. Write each percent as a fraction or mixed number.

a) 20% = ______ b) 75% = ______ c) 10% = ______

d) 175% = ______ e) 60% = ______ f) 88% = ______

g) 750% = ______ h) 101% = ______ i) 81% = ______

j) 64% = ______ k) 0.8% = ______ l) 5 000% = ______

6. Write the fractions and mixed numbers as percents.

a) 152

__________

b) 205

__________

c) 122

__________

d) 78

__________

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7. Complete the chart below using the skills learned in this section.

Fraction or Mixed Number (simplest form)

Decimal Percent

a) 36

b)0.15

c)210%

d) 1

246

e)1.4

f)2.75%



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8. Which number is greater?

_________________________a) 3

5 or

32

_________________________b) 3

5 or 0.47

_________________________c) 3

5 or 35%

_________________________d) 1.61 or 235%

9. Put the numbers in ascending order.

54 , 0.78,

10085 , 81%, 95%

10. Put the numbers in descending order.

275%, 104

, 2.9, 300%, 2.41, 72


SKILL BUILDERS – Section 2.4Adding, Subtracting, Multiplying and Dividing Fractions

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1. Using your calculator, perform the given operations on the fractions and mixed numbers.

a) 109 �X� 2

5 = ________ b)

85 ÷ 1

4 = ________

c) 2 18

+ 27

= ________ d) 21 x

43 = ________

e) 78

x 14

= ________ f) 410

�X� 13

= ________

g) 2109 x 1

4 = ________ h)

96 ÷ 1

21 = ________

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2. Draw a diagram and check with your calculator to solve the multiplication questions.

a) 14 of 12


b) 32 of 9




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1. Find the percent of the numbers below. Show how you change the percent to a decimal � ��

a) 30% of 20 = = ______ b) 15% of AED300 = = ______

c) 4% of AED 840 = = ______ d) 5.5% of 8 = = ______

SKILL BUILDERS – Section 2.5 Ratios and Proportions

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1. Use the shapes above to write the ratios. Write the ratios in three different ways.

Description Ratio

a) The ratio of all squares to all circles.

b) The ratio of shaded squares to all circles.

c) The ratio of non-shaded squares to shaded circles.

d) The ratio of shaded squares to all squares.

e) The ratio of all circles to all squares.

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2. Write equivalent ratios from the picture above.

boysto

girls

14

= =


3. Are the ratios equivalent (in proportion)? Show your work using cross products.

a) 32 and

128

b) 35

and 1830

c) 14

and 102

d) 54 and 9

12

e) 16

and 315

f) 110

and 10010

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4. Simplify the ratios using your calculator. Be sure your answers have 2 terms!

a) 108 = b)

2015 = c) 10

30 =

d) 128

= e) 3040 = f) 12

4 =

g) 10080 = h)

109 = i)

10005 =

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5. Complete the proportions. Show your work.

a) 56

= 12

b) 5

= 130

c) 1820

= 9

d) 2 = 1421

e) 46

=18

mathematic foundation 1(fnd...

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