1. Dividing Fractions and Mixed Numbers
LESSON 3-5
Problem of the Day
Trent bought 2 CDs one week, 6 the following week, and 10 in the third week. If he continues this pattern, how many CDs will he buy in the seventh week? 26
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2. Dividing Fractions and Mixed Numbers
LESSON 3-5
Check Skills You’ll Need
(For help, go to Lesson 3-4.)
1. Vocabulary Review Which operation do you use to find
a product?
Find each product.
• •
• • 1 3 7 2 3 5 9 1 2 9 10 2 9 4 5
Check Skills You’ll Need
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3. Dividing Fractions and Mixed Numbers
LESSON 3-5
Check Skills You’ll Need
Solutions
1. multiplication 2 7 3
1 • 2
7 • 1 1
• = • =
5 • 1
9 • 2 5 18 9 1 2 =
• = 2. 3. 9 10 50 1 5
5 • 9
1 • 1
50 • = • =
= 45 1 2 9 4 5 20
4 • 1
1 • 1 1 = 4. 5. 2
• = • 1 1 4
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4. Dividing Fractions and Mixed Numbers
LESSON 3-5
Definition – new terms – concepts to know
Reciprocal – Two numbers are reciprocals if their product is 1.
To find the reciprocal of a fraction, interchange the numerator and denominator
To divide by a fraction, multiply by its reciprocal
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5. Dividing Fractions and Mixed Numbers
LESSON 3-5
Steps to follow
Follow these steps to divide fractions and mixed numbers
Re-write mixed numbers as improper fractions as needed
Multiply by the reciprocal of the divisor
Multiply numerators
Multiply denominators
Simplify }
} OR cross-cancel
} common factors
Algebra:
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6. Dividing Fractions and Mixed Numbers
LESSON 3-5
Additional Examples – dividing by a fraction
Find ÷ 3 10 2 5 3 10 2 5 ÷
= • 3 10 5 2
Multiply the reciprocal of , which is . =
3 • 5
10 • 2 2 1
Divide 5 and 10 by their GCF, which is 5. = 3 4
Simplify.
Quick Check
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7. Dividing Fractions and Mixed Numbers
LESSON 3-5
Additional Examples – Dividing by mixed numbers
Find 4 ÷ 1 . 2 3 4
= ÷ 14 3 7 4
Write the mixed numbers as improper fractions. 2 3 4 ÷ 1
Multiply by the reciprocal of , which is .
= • 14 3 4 7 =
14 • 4
3 • 7 2 1
Divide 14 and 7 by their GCF, which is 7. = 8 3
Multiply.
= 2 2 3
Write as a mixed number.
Quick Check
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8. Dividing Fractions and Mixed Numbers
LESSON 3-5
Additional Examples – word problems
You have a piece of yarn that is ft long. You need to cut
it into strips that are 1 ft long. How many strips will you have? 1 2 4 1 4 2
To find how many 1 -ft long strips are in ft, divide by 1 2 4 ÷
12 ÷ 1, or 12
Estimate 12
Write the mixed numbers as improper fractions. 1 2 4
÷ = ÷ 12 25 5
Multiply the reciprocal of , which is . 25 2 4 5
= • =
25 • 4
2 • 5
Divide 25 and 5 by their GCF, 5. Divide 4 and 2 by their GCF, 2. 1 2 5
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9. Dividing Fractions and Mixed Numbers
LESSON 3-5
Additional Examples
(continued)
= = 10 10 1
Simplify.
There are ten ft strips of yarn in ft. 1 4 2
Check for Reasonableness The answer, 10, is close to the estimate, 12.
The answer is reasonable.
Quick Check
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10. Dividing Fractions and Mixed Numbers
LESSON 3-5
Lesson Quiz
Find each quotient.
1. ÷ ÷
÷ ÷ 1 8 3 4 2 3 3 8 1 6 1 7 9 5 6 2 5 2 7 1 5 55 72 16 3 7
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11. Dividing Fractions and Mixed Numbers
LESSON 3-5
Homework
Lesson 3-5: p. 144 – 145: # 10 – 48 e
Quiz tomorrow on Lessons 3-1 to 3-4
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