Homework Problems
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Quick Look
Today, we divided whole numbers by fractions and whole numbers by mixed numbers. We can think of
dividing by a fraction just like dividing by a whole number. For example, 20 ÷ 4 means the number of
groups of 4 that can be made from 20. So 20 ÷ 1 means the number of groups of 1 that can be made
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from 20. You can draw a model and think: How many 1 pizzas are in 20 whole pizzas?
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One way to divide a whole number by a fraction or mixed number is to use an algorithm. Consider 6 ÷ 4 .
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PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 3 Cycle 3 Lesson 7
Homework Problems
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Directions for questions 1–12: Divide.
1) 40 ÷ 2 2
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2) 18 ÷ 3 3
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3) 12 ÷ 6 2 ; Explain your thinking.
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4) Jim made 14 gallons of a sports drink for his teammates. Each teammate drank 7 of a gallon. How
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many servings were there in all? Explain your thinking.
5) The office supply store received 29 pounds of recycled copy paper. They need to divide it into piles of
3 of a pound. How many piles will they have in all?
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6) Principal Berger ordered 72 pizzas for her school’s Pizza Celebration Day. Principal Berger figured on
serving would be 3 of a pizza. How many servings of pizza did Principal Berger order?
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7) Noah’s rain barrel contains 65 gallons of rainwater. Each time Noah waters his garden, he uses
6 1 gallons of water. How many times can Noah water his garden from the water he has in his
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rain barrel?
8) Elsie works as a dental hygienist. She spends 33 hours per week cleaning patients’ teeth. Each
cleaning she performs takes 3 of an hour. How many patients does Elsie see in a week? Explain
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your thinking.
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PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 3 Cycle 3 Lesson 7
Homework Problems
9) Martin has $39 in his account. The cereal bar he likes costs 3 of a dollar at the drug store. How many
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cereal bars could Martin buy with the money in his account?
10) 4 ÷ 9 1
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11) 64 ÷ 3 17
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12) 3 ÷ 5 1 ; Explain your thinking.
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Mixed Practice
13) Is 3 closest to 0, 1 , or 1?
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2
14) Multiply 2 × 5
3 19
15) Divide 4,200 ÷ 5 using mental math.
16) Find the GCF of 28 and 84.
Word Problem
17) Rochelle has 6 yards of fabric. She uses 3 yard to make one scarf. How many scarves can
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she make?
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 3 Cycle 3 Lesson 7
Homework Problems
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For the Guide on the Side
Today your student learned how to divide whole numbers by fractions and mixed numbers. Your student
used what he or she knew about dividing whole numbers and multiplying fractions to do it.
Your student should be able to answer these questions about fraction division:
What is the product of reciprocals?
Why does 8 ÷ 1 equal 56?
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Does 5 ÷ 1 = 5 × 10 ? Explain.
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1
What is the reciprocal of 18? What is the reciprocal of 3 1 ?
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When is the quotient of a whole number and mixed number less than the divisor? When is it greater than
the divisor?
Here are some activities to try:
1) Write a word problem that can be solved by dividing whole numbers by fractions or mixed numbers.
2) Think of times you have to divide a whole amount into fractional parts.
3) Model 3 ÷ 3 and 4 ÷ 5 using centimeter paper and colored pencils.
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4) Use Khan Academy to review how to write the reciprocal of a mixed number:
http://www.khanacademy.org/math/arithmetic/fractions/v/reciprocal-of-a-mixed-number
5) Use Khan Academy to review dividing whole numbers by fractions.
http://www.khanacademy.org/math/arithmetic/fractions/v/dividing-mixed-numbers-and-fractions
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PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 3 Cycle 3 Lesson 7
Homework Problems
Homework Answers
1) 18
2) 5
3) 1 4 ; Possible explanation: I renamed 6 2 as the improper fraction, 20 . Then I changed 12 ÷ 20 to
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3
3
3
3
multiplying by the reciprocal. Then I solved. 12 × 3 = 12 ÷ 4 ×
= 3 × 3 = 9 =14.
20
1
20 ÷ 4
1
5
5
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4) There were 30 servings in all. Possible explanation: I saw that this was a division problem. 14 ÷ 7 . I
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changed the division problem to multiplying by the reciprocal: 14 × 15 . Then I solved. 14 × 15 =
7
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14 ÷ 7 × 15 = 2 × 15 = 30.
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7÷7
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1
5) They will have 67 2 piles in all.
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6) She ordered 384 servings.
7) Noah can water his garden 10 times.
8) Elsie sees 44 patients each week. Possible explanation: I saw that this was a division problem.
33 hours ÷ 3 hour. I changed the division problem to multiplying by the reciprocal: 33 × 4 . Then I
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solved. 33 × 4 = 33 ÷ 3 × 4 = 11 × 4 = 44 patients.
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1
1
1
3÷3
9) Martin could buy 65 cereal bars.
10) 40
91
12)
11) 16 4
5
7 ; Possible explanation: After I changed the mixed number to an improper fraction, I used Keep It,
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Change It, Flip It to change the division problem to a multiplication one. 3 ÷ 5 1 = 3 ÷ 36 = 3 × 7
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7
36
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Then I solved. 3 × 7 = 3 ÷ 3 ×
= 1 × 7 = 7 .
36
1
1
12
12
36 ÷ 3
Mixed Practice
13) It is closest to 1 .
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14) 10
57
15) 840
16) 28
Word Problem
17) Rochelle can make 8 scarves.
PowerTeaching: i3
© 2012 Success for All Foundation
Level F Unit 3 Cycle 3 Lesson 7
Homework Problems
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