Holt CA Course 1 4-5 Dividing Fractions and Mixed Numbers Vocabulary reciprocal multiplicative...
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Holt CA Course 1
4-5 Dividing Fractions and Mixed Numbers
Vocabularyreciprocal
multiplicative inverse
One of two numbers whose product is 1. (flip a fraction over to find its reciprocal)
One of two numbers whose product is 1.
Holt CA Course 1
4-5 Dividing Fractions and Mixed Numbers
Reciprocals can help you divide by fractions. Two numbers are reciprocals or multiplicative inverses if their product is 1. The reciprocal of is 3 because
13
13
3= 13
31
= 33
= 1.
Dividing by a number is the same as multiplying by its reciprocal.
6 ÷ 3 = 26 ÷ 3 = 2 13
6 6 = 2 = 2
same answer
reciprocals
Holt CA Course 1
4-5 Dividing Fractions and Mixed Numbers
You can use this rule to divide by fractions.
Holt CA Course 1
4-5 Dividing Fractions and Mixed NumbersExample 1: Dividing Fractions
Divide. Write each answer in simplest form.
A. 37 ÷ 2
537
÷ 25
= 37 ·
52
= 37
· 5· 2
=1514
or 114
1
Multiply by the reciprocal of . 25
B. 38
÷ 12
38
÷ 12 =38
· 112
=38
· 112
1
4
=
Multiply by the reciprocal of 12.
132
Simplify.
Holt CA Course 1
4-5 Dividing Fractions and Mixed Numbers
Divide. Write each answer in simplest form.
A. 523
÷ 1 14
5 23
÷ 114
= 17 3
÷ 54
= 17 3
· 45
= 6815
or 4 815
Write mixed numbers as improper fractions.
Multiply by the reciprocal of 54
B. 34
÷ 212
34
÷ 2 12
= 34
÷ 52
= 34
· 25
=3 · 24 · 5
1
2= 3
10
Write 2 as an improper fraction.12
Multiply by the reciprocal of . 52
Simplify.
.
Example 2: Dividing Mixed Numbers
Holt CA Course 1
4-5 Dividing Fractions and Mixed NumbersExample 3: Social Studies Application
The life span of a golden dollar coin is 30 years, while
paper currency lasts an average of 1 years. How many12
times longer will the golden dollar stay in circulation?
30 ÷ 1 12
= 30 1
÷ 32
Write the number as an improper fraction.
=30 1
· 23
Multiply by the reciprocal of .32
= ·Simplify.
30 21 3
10
1= 20
1or 20
The golden dollar will stay in circulation about20 times longer than paper currency.
·
Holt CA Course 1
4-5 Dividing Fractions and Mixed NumbersCheck It Out! Example 1
Divide. Write the answer in simplest form.35 ÷ 1
235
÷ 12
= 35 ·
21
= 35
· 2· 1
=65
or 151
Multiply by the reciprocal of . 12
Holt CA Course 1
4-5 Dividing Fractions and Mixed Numbers
Divide. Write each answer in simplest form.
35
÷ 125
35
÷ 1 25
= 35
÷ 75
= 35
· 57
=3 · 55 · 7
1
1
= 3 7
Write 1 as an improper fraction.25
Multiply by the reciprocal of . 75
Simplify.
Check It Out! Example 2
Holt CA Course 1
4-5 Dividing Fractions and Mixed Numbers
Check It Out! Example 3
The average life of a queen ant is approximately 3 years.The life span of a worker ant is year. How many 3
7times longer will the queen ant live?
3 ÷ 37
= 31
÷37 Write the number as an improper fraction.
=31
· 73
Multiply by the reciprocal of .37
= · Simplify.3 71 3
1
1= 7
1or 7
The queen ant will live 7 times longer than the worker ant.
·