seminar 3 welcome. agenda decimal/fraction notation addition, subtraction, multiplication/division...

Seminar 3

Welcome

Agenda

• Decimal/Fraction Notation• Addition, Subtraction, multiplication/division

with Decimals

3Copyright © 2008 Pearson

Education, Inc. Publishing as Pearson Addison-Wesley

• To add when denominators are different:

• a) Find the least common multiple of the denominators. That number is the least common denominator, LCD. .

• c) Add the numerators, keeping the same denominator.

• d) Simplify, if possible.

8

1

4

3 =

8

1

24

23

8

1

4

3 = =

8

1

8

6 =

8

7

8

16

8

1

4

3 =

8/4=2 2x3=68

6

7

2

5

3 =

7

2

5

3

9

4

6

5

=

=

57

52

75

73

=35

10

35

21

35

31

35

1021

=

7

2

5

3

35

?

35

?

9

4

6

5 =

69

64

96

95

=54

24

54

45

54

151

54

69

54

2445

=

Adding Mixed Numbers

Example:5

32

5

13

5

32

5

13

5

3

5

123

5

315

5

45

5

45

Subtraction of Fractions

9

4

7

6

Subtraction of Fractions

More examples:

9

4

7

6

79

74

97

96

63

28

63

54

63

2854 26

63

Examples of multiplying fractionsExamples of multiplying fractions

2 ½ X ¼

5 1

2 4X

5

8

9

4

7

6x

9

4

7

6x

11

8

63

24

Examples of dividing fractionsExamples of dividing fractions

5 10

9 12

KEEPSWITCH to

multiply

FLIP number following the division

sign (Reciprocal)

59

x12

10

10

12

9

5x

9

6

90

603

2

9

4/

7

6

4

9

7

6x

28

241

28

547

61

For Project Unit 3

• A recipe for a drink calls for 2/5 quart water and 1/4 quart apple juice.

• How much liquid is needed?

• 2/5 + 1/4 = 8/20 + 5/20 = 13/20

• Now if the recipe is doubled?

13/20

• 13/20 + 13/20 = 26/20 =1 6/20= 1 3/10• Or• 13/20 * 2 = 13/20 *2/1 =26/20 = 1 6/20 =1 3/10

If the recipe is halved?

13/20

• 13/20 / 2 = 13/20 / 2/1 = 13/20 * ½= 13/40

42.3245

• 4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten-thousandths

• We read this number as

• “Forty-two and three thousand two hundred forty-five ten-thousandths.”

• The decimal point is read as “and”.

• Write a word name for the number in this sentence: The top women’s time for the 50 yard freestyle is 22.62 seconds.

• Write a word name for the number in this sentence: The top women’s time for the 50 yard freestyle is 22.62 seconds.

• Twenty-two and sixty-two hundredths

25 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

To convert from decimal to fraction notation,

• a) count the number of decimalplaces,

• b) move the decimal point thatmany places to the right, and

• c) write the answer over a denominator with a 1 followed by that number of zeros

4.98

4.98

2 zeros

2 places

Move

2 places.

498

100


• Write fraction notation for 0.924. Do not simplify.

• 0.924 =


• Write fraction notation for 0.924. Do not simplify.

• Solution

• 0.924

9240.

0924

100

3 places

3 zeros

0.924.


Example D•Write 17.77 as a fraction and as a mixed numeral.


Example D•Write 17.77 as a fraction and as a mixed numeral.

•Solution•To write as a fraction:

•17.77 177717

0.77

10

2 zeros

2 places

17.77

7717.77 17

100

To write as a mixed numeral, we rewrite the whole number part and express the rest in fraction form:


To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000 and so on,

a) count the number of zeros, and

b) move the decimal point thatnumber of places to the left. Leaveoff the denominator.

8.679.Move

3 places.

3 zeros

8679

1000

86798.679

1000


Example E

Write decimal notation for53

.10


Example E

Write decimal notation for

Solution

53.

10

53

105.3. 53

105.3

1 place1 zero


Section 3.1

1. In the number 623,841, which digit tells the number of 10 thousands?

a) 5

b) 8

c) 6

d) 2


Section 3.1

2. Write a word name for 8.032.

a) Eight and thirty-two ten thousandths

b) Eight thousand, thirty-two

c) Eight and thirty-two hundredths

d) Eight and thirty-two thousandths


Section 3.1

3. Write decimal notation for

a) 4.3

b) 0.53

c) 0.053

d) 0.0053

53.

1000


•Adding with decimal notation is similar to adding whole numbers.

•First we line up the decimal points so that we can add corresponding place-value digits.

•Add the digits from the right.

•If necessary, we can write extra zeros to the far right of the decimal point so that the number of places is the same.


Example A

• Add: 4.31 + 0.146 + 14.2

• Solution Line up the decimal points and write extra zeros.4 . 3 1 0

• . 1 4 6• 1 4 . 2 0 0

65681 .


Example D

• Subtract 574 – 3.825


Example D

• Subtract 574 – 3.825

• Solution 5 7 4 . 0 0 0

– 3 . 8 2 5 5717 0 .5

9 9 103


Section 3.2

1. Add: 2.15 + 13.07 + 25.

a) 14.47

b) 40.22

c) 59.57

d) 47.81


Section 3.2

4. Subtract: 70 – 8.231.

a) 61.231

b) 62.769

c) 62.231

d) 61.769


To multiply using decimals: 0.8 0.43

a) Ignore the decimal points, and multiply as though bothfactors were whole numbers.

b) Then place the decimal point in the result. The number of decimal places in the product is the sum of the number of places in the factors. (count places from the right).

0.43

3

0.8

4 4

2

0.43

0.8

0.344

(2 decimal places)

(1 decimal place)

(3 decimal places)

Ignore the decimal points for now.


•To divide by a whole number;

•a) place the decimal point•directly above the decimal•point in the dividend, and

•b) divide as though•dividing whole numbers.

7 5.88

560

28

28

0.84

0

Quotient

Dividend

Remainder

Divisor

Mileage

Molly bought gasoline when the odometer read 8,678.9. After the next filling, the odometer read 8,999.9. It took 9.8 gal to fill the tank.

• a) How many miles did she drive?• b) How many miles per gallon (mpg) did the

car get?

Molly bought gasoline when the odometer read 8,678.9. After the next filling, the odometer read 8,999.9. It took 9.8 gal to fill

the tank.

• First Step Subtraction• 8,999.9- 8,678.9 321 .0 She drove 321 milesNext divide 321 by 9.8 = 32.7 miles to the

gallon.

Drew filled his truck’s gas tank and noted that the odometer read 62,957.1. After the next filling, the odometer read 63,247.5. It took 17.6 gal to fill the tank. How many miles per gallon did the truck get?

Drew filled his truck’s gas tank and noted that the odometer read 62,957.1. After the next filling, the odometer read 63,247.5. It took 17.6 gal to fill the tank. How many miles per gallon did the

truck get?

63247.5 -62957.1 290. 4

290.4 / 17.6 = 16.5

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