ALGEBRA READINESS

LESSON 5-4Warm Up

ALGEBRA READINESS

LESSON 5-4Warm Up

ALGEBRA READINESS

“Dividing Rational Numbers” (5-4)

What are “reciprocals”?

How do you find the reciprocal of a number?

Reciprocals: two numbers whose product is 1 – The reciprocal of is , since • = 1.

To find the reciprocal of a number, simply switch the numerator and denominator around. In the case of a whole number, make it a fraction by putting it over 1 first (so, the reciprocal of a whole number will always be 1 over the number)

Example: What is the reciprocal of 9?

9 = Make the whole number into a fraction by putting it over 1.

= Turn the fraction over so that the numerator and denominator are switched

9 • = • = 1 Check using rule of reciprocals (a number times I ts reciprocal equals 1)

ab

ba

91

91

19

19

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Write the reciprocal of each number.

49

a. b. 5

Since • = 1, the49

94

reciprocal of is .49

94

Since 5 • = 1, the

reciprocal of 5 is .15

15

Dividing Rational NumbersLESSON 5-4

Additional Examples

ALGEBRA READINESS

“Dividing Rational Numbers” (5-4)

How do you divide by a fraction?

How do you model the division of fractions?

To divide by a fraction, multiply by its reciprocal.

Rule: = • = , where b, c, and d do not equal 0.

Example: What is the ?

= • To divide by a fraction, multiply by its reciprocal

• = Multiply the numerators and denominators separately.

= = 4 The fraction bar means divide, so divide the numebrator into the denominator to simplify.

= , so there are 4 one-eighth parts in one- half.

ab

cd

ab

dc

adbc

12

18

12

18

81

12

12

81

1 • 8 2 • 1

82

12

48

ALGEBRA READINESS

One bow takes yards of ribbon. How many bows

could you make from a roll of ribbon that is 12 yards long?

34 1

2

You need to find how many -yard pieces there are in 12 yards.34

12

Divide 12 by .34

12

Multiply by , the reciprocal of .252

43= • 3

443

252

34

12

34

Write 12 as an improper fraction.1212 ÷ = ÷

Dividing Rational NumbersLESSON 5-4

Additional Examples

ALGEBRA READINESS

(continued)

Divide numerator and denominatorby their GCD, 2.

252

43= •

1

2

Multiply. Write the fraction as amixed number.

= = 16503

23

Because you cannot make of a bow, you can make 16 bows. 23

Dividing Rational NumbersLESSON 5-4

Additional Examples

ALGEBRA READINESS

Write the reciprocal of each number.

1. 2. 11

Find each quotient.

3. 4.

5. Megan has 3.5 quarts of punch. One serving is quart. How many servings does she have?

14

111

14

(–1 ) ÷ (1.5)78

47

–

– 16

– 34

÷ ( )

74

–

29

14–1

Dividing Rational NumbersLESSON 5-4

Lesson Quiz