fraction division - everyday math - login · lesson 8 12 683 a unit fraction can also be divided by...

$: Fraction Division - Everyday Math - Login · Lesson 8 12 683 A unit fraction can also be divided by a whole number. Read and discuss the examples on page 80A of the Student Reference$
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eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshopGame™

AssessmentManagement

Family Letters

CurriculumFocal Points

680 Unit 8 Fractions and Ratios

��

Key Concepts and Skills• Find common denominators for pairs of

fractions. [Number and Numeration Goal 5]

• Use diagrams and visual models for

division of fractions problems.

[Operations and Computation Goal 5]

• Solve number stories involving division of a

fraction by a whole number, division of a

whole number by a fraction, and division of

a fraction by a fraction.


• Write equations to model number stories.

[Patterns, Functions, and Algebra Goal 2]

Key ActivitiesStudents use diagrams and visual models to

divide fractions. They solve number stories

involving division of a fraction by a whole

number, division of a whole number by a

fraction, and division of a fraction by a

fraction. Students use visual fraction models

and equations to represent the problem.

Ongoing Assessment: Informing Instruction See page 683.

Ongoing Assessment: Recognizing Student Achievement Use journal page 289. [Operations and Computation Goal 5]

MaterialsMath Journal 2, pp. 288–289B

transparency of Math Masters, p. 440B

Student Reference Book, pp. 79–80B

Study Link 8 �11

slate or half-sheets of paper

Math Boxes 8�12Math Journal 2, p. 290

Students practice and maintain skills

through Math Box problems.

Study Link 8�12Math Masters, p. 248

Students practice and maintain skills

through Study Link activities.

READINESS

Playing Build-ItStudent Reference Book, p. 300

Math Masters, pp. 446 and 447

per partnership: 1 six-sided die

Students compare and order fractions and

rename mixed numbers as fractions.

ENRICHMENTExploring the Meaning of the ReciprocalMath Masters, p. 249

calculator

Students explore the meaning of the

reciprocal.

EXTRA PRACTICEDividing with Unit FractionsMath Masters, p. 253B

Students practice using visual models to

divide fractions.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Fraction DivisionObjective To introduce division of fractions and relate the

operation of division to multiplication.o

Common Core State Standards

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 144–147

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Fraction DivisionLESSON

8 � 12

Date Time

Math Message

1. Use the ruler to solve Problems 1a –1c.

0 1 3 5 6inches

2 4

a. How many 2-inch segments are in 6 inches? 3 segments

b. How many 1 _ 2 -inch segments are in 6 inches?

12 segments

c. How many 1 _ 8 -inch segments are in

3

_ 4 of an inch? 6 segments

2. a. How many 2-pound boxes of nuts can be made from 10 pounds of nuts?

Use the visual below to help you solve the problem. 5 boxes

1 lb 1 lb 1 lb 1 lb 1 lb 1 lb 1 lb 1 lb 1 lb 1 lb

1 2 3 4 5Sample answer:

b. How many 1 _ 2 - pound boxes can be made from 10 pounds of nuts?

Draw a picture to support your answer. 20 boxes

Sample answer:

12

12

1 lb12

12

1 lb12

12

1 lb12

12

1 lb12

12

1 lb

12

12

1 lb12

12

1 lb12

12

1 lb12

12

1 lb12

12

1 lb

288-291_EMCS_S_MJ2_G5_U08_576434.indd 288 3/16/11 2:31 PM

Math Journal 2, p. 288

Student Page

Lesson 8�12 681

Getting Started

1 Teaching the Lesson

▶ Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Math Journal 2, p. 288: Math Masters, p. 248)

Discuss students’ solutions. Use a transparency of Math Masters, page 440B to illustrate Problems 1a–1c.

Problem 1a

inches0 1 2 3 4 5 6

Problem 1b

inches0 1 2 3 4 5 6

Problem 1c

inches0 1 2 3 4 5 6

Point out that each problem on the journal page asks: How many x’s are in y? Ask students to translate each problem into a question of this form. Record the questions on the board.

1. a. How many 2s are in 6?

b. How many 1 _ 2 s are in 6?

c. How many 1 _ 8 s are in 3 _ 4 ?

2. a. How many 2s are in 10?

b. How many 1 _ 2 s are in 10?

Math MessageSolve Problems 1 and 2 on journal page 288.

Study Link 8�11 Follow-UpHave partners share answers and resolve differences. Ask volunteers to explain their solution strategies for Problem 9.

Mental Math and Reflexes Pose questions about unit fractions. Suggestions:

How many 1

_ 2 s are in 1 whole? 2

How many 1

_ 2 s are in 4? 8

How many 1

_ 2 s are in 2

1

_ 2 ? 5

How many 1

_ 4 s are in 2? 8

How many 1

_ 4 s are in 1

1

_ 2 ? 6

How many 1

_ 4 s are in

3

_ 4 ? 3

How many 1_2 s are in

1_2 ? 1

How many 1_4 s are in

1_2 ? 2

How many 1_3

s are in 1? 3

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�

�

Dividing with Unit FractionsLESSON

8 � 12

Date Time

1. Four pizzas will each be sliced into thirds. Use the circles to show

how the pizzas will be cut. Find how many slices there will be in all.

The drawings show that there will be 12 slices in all.

4 ÷ 1 _ 3 = 12

2. Edith has 2 inches of ribbon. She wants to cut the ribbon

into 1 _ 4 -inch pieces. How many 1

_ 4 pieces can she cut?

Edith can cut 8 pieces. So, 2 ÷ 1 _ 4 = 8 .

3. Two students equally share 1 _ 3 of a granola bar. Divide the rectangle

at the right to show how much of the bar each will get.

Each student will get 1 _ 6

of a granola bar.

1 _ 3 ÷ 2 =

1 _ 6

4. Three students equally share 1 _ 4 of a granola bar. Divide the rectangle

at the right to show how much of the bar each will get.

Each student will get 1 _ 12

of a granola bar.

1 _ 4 ÷ 3 =

1 _ 12

5. When you divide a whole number by a unit fraction (less than 1), is the quotient

larger or smaller than the whole number? Explain.

Sample answer: The quotient is larger than the whole

number because you are finding how many small parts fit

into something that is larger.

6. When you divide a unit fraction (less than 1) by a whole number, is the quotient

larger or smaller than the fraction? Explain.

Sample answer: The quotient is smaller than the fraction

because you are dividing up the fraction into an equal

number of smaller parts.

0 inches 1 2

288-291_EMCS_S_MJ2_G5_U08_576434.indd 289 4/1/11 9:01 AM


Student Page


Refer students to the illustrations and questions for Problems 1 and 2, and ask what division open number sentence fits the first question. 6 ÷ 2 = s

Continue for the other problems, writing the division open number sentence next to each question on the board. Ask students to refer to the visual models, if needed.

1. a. How many 2s are in 6? 6 ÷ 2 = s

b. How many 1 _ 2 s are in 6? 6 ÷ 1 _ 2 = s

c. How many 1 _ 8 s are in 3 _ 4 ? 3 _ 4 ÷ 1 _ 8 = s

2. a. How many 2s are in 10? 10 ÷ 2 = b

b. How many 1 _ 2 s are in 10? 10 ÷ 1 _ 2 = b

NOTE The division number models use b (for the number of boxes) and s (for the

number of segments) to represent the unknowns. Students may prefer to use other

letters or symbols. To avoid confusion in this introduction to division of fractions, the

number models use ÷ rather than / to show division.

▶ Dividing with Unit Fractions WHOLE-CLASSDISCUSSION

(Math Journal 2, p. 289; Student Reference Book,

pp. 79 and 80A)

Read and discuss the first example on page 79 of the Student Reference Book on dividing a whole number by a unit fraction. A unit fraction is a fraction with a numerator of 1. Briefly discuss the solution.

� Draw 3 rectangles on the board, and ask students to copy the rectangles on a sheet of paper or slate.

� Ask students to use the rectangles to illustrate the following problem: Jane has 3 loaves of banana bread to share with her friends. If she cuts each loaf into 1 _ 4 s, how many quarter loaves will she have to share with her friends?

Students should conclude that one way to illustrate the solution is to divide each of the rectangles into 4 equal parts.

14

14

14

14

14

14

14

14

14

14

14

14

3 ÷ 1

_ 4 = 12

Ask:

● How many 1 _ 4 s are in 3? 12

● What number model represents this problem? 3 ÷ 1 _ 4 = 12

Ask students to write 3 ÷ 1 _ 4 = 12 below their rectangles.

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Lesson 8�12 683

A unit fraction can also be divided by a whole number. Read and discuss the examples on page 80A of the Student Reference Book.

Draw a rectangle on the board, and divide it into 5 equal parts with 1 _ 5 shaded. Ask students to draw the same diagram on a piece of paper or slate.

Tell students that you can represent a unit fraction (such as 1 _ 5 )

being divided by a whole number (such as 3) by drawing a model for the fraction and then cutting it up into smaller equal parts. Pose the following problem: Three family members equally share 1 _ 5 of a loaf of corn bread. How much of the loaf of corn bread will each person get?

Have students divide their rectangles to show how the corn bread can be divided to find the solution to the problem.

Ongoing Assessment:Informing Instruction

Watch for students who record the answer as 1

_ 3 . Have students draw the line

for thirds to extend across the rectangle in order to visualize the total number of

parts out of 15.

Have a volunteer come to the board to show the solution. The student should divide the shaded fifth into three equal parts using horizontal lines. If necessary, model the lines extended all the way across the larger rectangle, with one small part double shaded. Explain that because the family only has 1 _ 5 of a loaf to begin with, when it is divided into three equal parts, each part of the corn bread that is cut up is 1 _

15 of the entire loaf. So each person will

get 1 _ 15 of the loaf of corn bread.

115

15 ÷ 3 =

Ask: What number model represents this problem? 1 _ 5 ÷ 3 = 1 _ 15

Ask students to write “ 1 _ 5 ÷ 3 = 1 _ 15 ” below their rectangles.


Date Time

Relationship Between Multiplication and DivisionLESSON

8 � 12

1. Each division number sentence on the left can be solved by using a related

multiplication sentence on the right. Draw a line to connect each number sentence

on the left with its related number sentence on the right.

Division Multiplication

a. 5 ÷ 1 _ 4 = n n ∗ 4 1

_ 5 = 4 1 _ 5

b. 1 _ 5 ÷ 4 = n n ∗ 4 = 1

_ 5

c. 4 ÷ 1 _ 5 = n n ∗ 1

_ 4 = 5

d. 9

_ 10 ÷ 3

_ 5 = n n ∗ 9

_ 10 = 3

_ 5

e. 3

_ 5 ÷ 9

_ 10 = n n ∗ 1 _ 5 = 4

f. 4 1 _ 5 ÷ 4 1

_ 5 = n n ∗ 3

_ 5 = 9

_ 10

2. Solve the following division number sentences (from above). Use the related

multiplication sentences to help you find each quotient.

a. 5 ÷ 1 _ 4 = 20 b. 1

_ 5 ÷ 4 = 1 _ 20

c. 4 ÷ 1 _ 5 = 20 d. 4 1

_ 5 ÷ 4 1 _ 5 = 1

3. How is dividing 5 by 1 _ 4 different from dividing 1

_ 5 by 4?

4. Write a number story for 5 ÷ 1 _ 4 . Answers vary.

5. Write a number story for 1 _ 5 ÷ 4. Answers vary.

Sample answers: Dividing

5 by 1 _ 4 results in a quotient that is greater than 5. Dividing 1

_ 5 by

4 results in a quotient that is less than 1 _ 5 . With 5 ÷ 1

_ 4 , you are

finding how many 1 _ 4 s are in 5. With 1

_ 5 ÷ 4, you are finding how

many 4s are in 1 _ 5 , which is a very tiny number.

288-291_EMCS_S_MJ2_G5_U08_576434.indd 289A 4/1/11 9:01 AM

Math Journal 2, p. 289A

Student Page

683A Unit 8 Fractions and Ratios

Have students read through Problems 1–4 on journal page 289. Ask them to describe how Problems 1 and 2 are different from Problems 3 and 4. Sample answer: In Problems 1 and 2, you are dividing a whole number by a unit fraction. In Problems 3 and 4, you are dividing a unit fraction by a whole number.

Have students solve Problems 1–6. Circulate and assist. Briefly discuss solutions.

Ongoing Assessment: Recognizing Student Achievement

Use journal page 289, Problems 1 and 2 to assess students’ ability to divide

a whole number by a unit fraction using a visual model. Students are making

adequate progress if they are able to solve Problems 1 and 2. Some students

may be able to solve Problems 3 and 4, which involve dividing a unit fraction by a

whole number.


▶ Relationship between WHOLE-CLASSDISCUSSION

Multiplication and Division(Math Journal 2, p. 289A)

Another way to solve a fraction division problem is to think about it as a related fraction multiplication problem. Remind students of the relationship between multiplication and division. For example, to solve 63 ÷ 7, you can think: What number times 7 is 63? or n ∗ 7 = 63. 9

Write the following problems on the board to show how the relationship helps when dividing with fractions.

● To solve 1 _ 10 ÷ 5, think: What number times 5 is 1 _ 10 ? Or n ∗ 5 = 1 _ 10 . 1 _ 50

● To solve 6 ÷ 1 _ 5 , think: What number times 1 _ 5 is 6? Or n ∗ 1 _

5 = 6. 30

● To solve 6 ÷ 2 _ 3 , think: What number times 2 _ 3 is 6? Or n ∗ 2 _ 3 = 6. 9

● To solve 1 _ 10 ÷ 3 _ 10 , think: What number times 3 _ 10 is 1 _ 10 ? Or n ∗ 3 _ 10 = 1 _ 10 . 1 _ 3

Ask students to solve the problems on journal page 289A. Circulate and assist.

▶ Introducing Common

WHOLE-CLASS ACTIVITY

Denominator Division(Math Journal 2, p. 289B)

Draw four circles on the board, and ask students to copy these circles on a sheet of paper. Ask them to solve the problem 4 ÷ 2 _ 3 and to illustrate their solution using the four circles.

Journal

Page 289 �

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Date Time

One way to divide fractions is to use common denominators. This method can be used

for whole or mixed numbers divided by fractions.

Step 1 Rename the fractions using a common denominator.

Step 2 Divide the numerators, and divide the denominators.

Examples:

Solve.

1. 4 ÷ 4 _ 5 = 5

2. 5

_ 6 ÷ 1 _ 18 = 15

3. 3 1 _ 3 ÷

5

_ 6 = 4

4. 1 _ 2 ÷ 1

_ 8 = 4 5. 1

_ 6 ÷ 4 = 1 _ 24

6. 6 ÷ 1 _ 4 = 24

7. Chase is packing flour in 1 _ 2 -pound bags. He has 10 pounds of flour.

How many bags can he pack?

20 bags

8. Regina is cutting string to make necklaces. She has 15 feet of string

and needs 1 1 _ 2 feet for each necklace. How many necklaces can

she make?

10 necklaces

9. Eric is planning a pizza party. He has 5 large pizzas. He wants to cut

each pizza so that each serving is 3

_ 5 of a pizza. How many people

can get a full serving of pizza?

8 people

10. A rectangle has an area of 3 3

_ 10 m2. Its width is 3

_ 10 m. What is its length?

11 meters

Common Denominator DivisionLESSON

8 � 12

3 ÷ 3

_ 4 = 12

_ 4 ÷ 3

_ 4

= 12 ÷ 3

_ 4 ÷ 4

= 4 _ 1 , or 4

1 _ 3 ÷ 1

_ 6 = 2 _ 6 ÷ 1

_ 6

= 2 ÷ 1

_ 6 ÷ 6

= 2 _ 1 , or 2

3 3

_ 5 ÷ 3

_ 5 = 18

_ 5 ÷

3

_ 5

= 18 ÷ 3

_ 5 ÷ 5

= 6

_ 1 , or 6

288-291_EMCS_S_MJ2_G5_U08_576434.indd 289B 3/16/11 2:31 PM

Math Journal 2, p. 289B

Student Page

Links to the Future

Lesson 8�12 683B

After a few minutes, bring the class together to discuss their solutions. Use the students’ responses to emphasize that one method for obtaining the solution is to divide each of the circles into 3 equal parts. As you illustrate this method on the board, point out that dividing each circle into 3 equal parts is equivalent to renaming each whole as 3 _ 3 . This shows that 4 wholes is equivalent to 12 _ 3 .

2–32–3

2–32–3

2–32–3

12

_ 3 ÷

2

_ 3 = 6

Write 12 _ 3 ÷ 2 _ 3 = 6 under the circles on the board. Students will readily see that there are 6 groups of 2 _ 3 . Emphasize that the answer is the result of dividing the numerators 12 ÷ 2 = 6.

Guide the discussion toward the following algorithm for division with fractions:

Step 1 Rename the numbers using a common denominator.


Discuss the examples at the top of journal page 289B. Point out that this method works for fractions divided by fractions or for mixed numbers or whole numbers divided by fractions. Use the following example to show that this method also works for fractions divided by whole numbers.

1 _ 8 ÷ 6 = 1 _ 8 ÷ 48 _ 8

= 1 ÷ 48 _ 8 ÷ 8

= 1 ÷ 48 _ 1

= 1 _ 48

Solve Problems 1−3 on journal page 289B as a class. Ask students to come up to the board to record their steps.

Problem Solution

4 ÷ 4 _ 5 = ? 4 ÷ 4

_ 5 = 20

_ 5 ÷ 4

_ 5 = 20 ÷ 4 = 5

5

_ 6 ÷ 1 _ 18 = ?

5

_ 6 ÷ 1 _ 18 =

15

_ 18 ÷ 1 _ 18 = 15 ÷ 1 = 15

3 1 _ 3 ÷

5

_ 6 = ? 3 1 _ 3 ÷

5

_ 6 = 10

_ 3 ÷

5

_ 6 = 20

_ 6 ÷

5

_ 6 = 20 ÷ 5 = 4

The algorithm introduced in this lesson focuses students on the meaning of

division with fractions. The standard algorithm that involves multiplying by the

reciprocal will be introduced in Sixth Grade Everyday Mathematics.

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Math Boxes LESSON

8 �12

Date Time

2. Complete the table.

3. Add.

a. 2 3

_ 4 + 1 1 _ 2 =

b. = 3

_ 8 + 5

_ 6

c. 6 1 _ 5 + 3 2

_ 3 =

d. = 5 1 _ 8 + 14

_ 8

e. = 4 3

_ 10 + 6 1 _ 2

6. Measure the line segment below to the

nearest 1 _ 4 inch.

2 in.

Fraction Decimal Percent

4 _ 5

0.125

11

_ 20

66 2 _ 3 %

0.857

0.8

0.6

1 _ 8

857

_ 1,000 2 _ 3

80%

55%0.55

12.5%

85.7%

4 1

_ 4

1 5

_ 24

9 13

_

15 6

7

_ 8

10 4

_ 5

4. A worker can fill 145 boxes of crackers

in 15 minutes. At that rate, how many can

she fill in 1 hour?

580 boxes

1. Find the whole set.

a. 10 is 1 _ 5 of the set.

50

b. 12 is 3

_ 4 of the set. 16

c. 8 is 2 _ 7 of the set.

28

d. 15 is 5

_ 8 of the set. 24

e. 9 is 3

_ 5 of the set. 15

74 75 89 90

19 20 108 10970

62 63 183

5. Write a fraction or a mixed number for

each of the following:

a. 15 minutes = 15

_ 60 , or 1

_ 4 hour

b. 40 minutes = 40

_ 60 , or 2

_ 3 hour

c. 45 minutes = 45

_ 60 , or

3

_ 4 hour

d. 25 minutes = 25

_ 60 , or

5

_ 12 hour

e. 12 minutes = 12

_ 60 , or 1 _ 5 hour

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Student Page

Name Date Time

STUDY LINK

8�12 Mixed-Number Review

1. a. Four pizzas will each be cut into eighths. Show how they can

be cut to find how many slices there will be in all.

b. The drawing shows that 4 ÷ 1

_ 8 = 32 , so there will be

32 slices in all.

2. a. Two families equally share 1

_ 3 of a garden. Show how they can

divide their portion of the garden.

b. The drawing shows that 1

_ 3 ÷ 2 =

1

_ 6 , so each family

gets 1

_ 6 of the total garden.

Common Denominator Division



Solve. Show your work.

3. 5 ÷ 2 _ 3 =

15

_ 2 , or 7 1 _ 2 4. 4 _ 7 ÷

3 _

5 =

20

_ 21

5. 4 1

_ 8 ÷

3

_ 4 =

11

_ 2 , or 5 1 _ 2 6. 6 2

_ 3 ÷

7

_ 9 =

60

_ 7 , or 8 4 _ 7

Practice

7. 4 1 _ 4 = 3 _

4 5 8. _

5 = 3 7 _

5 22

9. 1 3

_ 5 + 2

1

_ 5 =

3 4

_ 5 10. 3

3

_ 8 - 1

5

_ 8 =

1 6

_ 8 , or 1

3

_ 4

11. 7 4

_ 9 - 5

8

_ 9 =

1 5

_ 9 12. 3

2

_ 7 + 1

4

_ 5 =

4 38

_ 35 , or 5

3

_ 35

13. 5 2

_ 3 + 2

3

_ 4 =

7 17

_ 12 , or 8

5

_ 12 14. 4 - 1

3

_ 4 =

2 1

_ 4

15. 3 ∗ 3 3

_ 4 =

9 9

_ 4 , or 11

1

_ 4 16. 4

2

_ 3 ∗

6

_ 7 =

28

_ 7 , or 4

221-253_EMCS_B_MM_G5_U08_576973.indd 248 4/1/11 9:13 AM

Math Masters, p. 248

Study Link Master


▶ Practicing Common PARTNER ACTIVITY

Denominator Division(Math Journal 2, p. 289B)

Assign Problems 1–10 on the journal page. Have students work with a partner. Circulate and assist. Briefly share solutions as needed.

2 Ongoing Learning & Practice

▶ Math Boxes 8�12

INDEPENDENT ACTIVITY

(Math Journal 2, p. 290)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-10. The skill in Problem 6 previews Unit 9 content.

▶ Study Link 8�12

INDEPENDENT ACTIVITY

(Math Masters, p. 248)

Home Connection Students practice operations with fractions and mixed numbers.

3 Differentiation Options

READINESS PARTNER ACTIVITY

▶ Playing Build-It 15–30 Min

(Student Reference Book, p. 300; Math Masters,

pp. 446 and 447)

To practice comparing and ordering fractions and renaming mixed numbers as fractions, have students play this variation of Build-It. If students did not keep their Fraction Cards, they will need to cut the cards from Math Masters, page 446.

Students play the game as introduced in Lesson 8-1 except that at the end of each round, they toss a six-sided die to determine a whole-number part for each of their 5 fractions. Students then rename the mixed numbers as fractions. For example, after tossing a 3, the fractions 1 _ 5 , 1 _ 4 , 1 _ 3 , 7 _ 12 , and 5 _ 6 would become 3 1 _ 5 , 3 1 _ 4 ,

3 1 _ 3 , 3 7 _ 12 , and 3 5 _ 6 . Renamed as fractions, the list would be 16 _ 5 , 13 _ 4 , 10 _ 3 , 43 _ 12 , and 23 _ 6 .


LESSON

8�12

Name Date Time

Exploring the Meaning of the Reciprocal

Lamont and Maribel have to divide fractions. Lamont doesn’t want to use common

denominators. He thinks using the reciprocal is faster, but he’s not sure what a reciprocal is.

Maribel looks it up on the Internet and finds this: One number is the reciprocal of another

number if their product is 1.

Example 1: Example 2:

3 º ? = 1 1

_ 2 º ? = 1

3 º 1

_ 3 = 3

_ 3 = 1 1

_ 2 º 2 = 2

_ 2 = 1

1

_ 3 is the reciprocal of 3 2 is the reciprocal of 1

_ 2

3 is the reciprocal of 1

_ 3 1 _ 2 is the reciprocal of 2

1. Find the reciprocals.

a. 6 b. 1

_ 7 c. 20 d. 1

_ 9

2. What do you think would be the reciprocal of 5

_ 6 ?

Reciprocals on a Calculator

On all scientific calculators, you can find a reciprocal of a number by raising

the number to the -1 power.

3. Write each number in standard notation as a decimal and a fraction.

a. 8-1 , b. 5-2 , c. 2-3 ,

4. Write the key sequence you could use to find the reciprocal of 36.

3 6 (–) 1 F D , or 3 6 1

5. Write the key sequence you could use to find the reciprocal of 3

_ 7 .

3 n 7 d (–) 1 F D , or 3 7

6. What pattern do you see for the reciprocal of a fraction?

Once the original number is written as a fraction, the

reciprocal is the original fraction written with the numerator

as the denominator and the denominator as the numerator.

0.125

7 1

_ 6

1

_ 20

6

_ 5

9

1

_ 8

1

_ 25 1

_ 8 0.04 0.125

221-253_EMCS_B_MM_G5_U08_576973.indd 249 3/25/11 2:00 PM

Math Masters, p. 249

Teaching Master

LESSON

8�12 Number Stories: Division with Fractions

Name Date Time

1. Five pies will each be sliced into fourths.

Ira would like to find out how many

slices there will be in all.

a. Show how the pies will be cut.

b. The drawings show that 5 ÷ 1

_ 4 = 20 , so there will be 20

slices in all.

2. Jake has a 3-inch strip of metal.

He would like to find out how many

1

_ 2 -inch strips he can cut.

0 inches 1 2 3

Jake can cut 6 strips. So, 3 ÷ 1

_ 2 = 6 .

3. Two students equally share 1

_ 4 of a granola bar. They would

like to know how much of the bar each will get.

a. Show how the piece of granola bar will be cut.


_ 4 ÷ 2 =

1 _ 8 , so each

student will get 1 _ 8 of a granola bar.

4. a. Drawing A can be used to find 1

_ 3 ÷ 5.

Drawing B can be used to find 1

_ 3 of

1

_ 5 ,

or 1

_ 3 ∗

1

_ 5 . Use the drawings to show

that 1

_ 3 ÷ 5 =

1

_ 3 ∗

1

_ 5 . A B

b. Complete.

1

_ 3 ∗

1

_ 5 =

1

_ 15

1

_ 3 ÷ 5 =

1

_ 15

1

_ 3 ÷ 5 =

1

_ 3 ∗

1 _ 5 = 1

_ 15

253A-253B_EMCS_B_MM_G5_U08_576973 .indd 253B 3/16/11 1:26 PM

Math Masters, p. 253B

Teaching Master

Lesson 8�12 685

ENRICHMENT PARTNER ACTIVITY

▶ Exploring the Meaning 15–30 Min

of the Reciprocal(Math Masters, p. 249)

To explore the relationship between a number and its reciprocal, have students use what they know about fractions, fraction multiplication, and their calculators

to find the reciprocals of numbers.

When students have finished the Math Masters page, ask them to describe the pattern for finding the reciprocal of a number. Guide students to see that the reciprocal of a fraction is the fraction with the numerator and denominator interchanged, or inverted. For example, the reciprocal of 4 _ 9 is 9 _ 4 , and 4 _ 9 ∗ 9 _ 4 = 36 _ 36 = 1. The reciprocal of a whole number is a unit fraction that has the whole number as its denominator. For example, the reciprocal of 8 is 1 _ 8 , so 8 ∗ 1 _ 8 = 8 _ 8 = 1.

EXTRA PRACTICE PARTNER ACTIVITY

▶ Dividing with Unit Fractions 5–15 Min

(Math Masters, p. 253B)

Students practice using visual models to divide fractions.


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248

Name Date Time

STUDY LINK

8�12 Mixed-Number Review

1. a. Four pizzas will each be cut into eighths. Show how they can

be cut to find how many slices there will be in all.

b. The drawing shows that 4 ÷ 1

_ 8 = , so there will be

slices in all.

2. a. Two families equally share 1

_ 3 of a garden. Show how they can

divide their portion of the garden.


_ 3 ÷ 2 = , so each family

gets of the total garden.

Common Denominator Division



Solve. Show your work.

3. 5 ÷ 2 _ 3 = 4. 4 _

7 ÷

3 _

5 =

5. 4 1

_ 8 ÷

3

_ 4 = 6. 6

2

_ 3 ÷

7

_ 9 =

Practice

7. 4 1 _ 4 = 3 _

4 8. _

5 = 3 7 _

5

9. 1 3

_ 5 + 2

1

_ 5 = 10. 3

3

_ 8 - 1

5

_ 8 =

11. 7 4

_ 9 - 5

8

_ 9 = 12. 3

2

_ 7 + 1

4

_ 5 =

13. 5 2

_ 3 + 2

3

_ 4 = 14. 4 - 1

3

_ 4 =

15. 3 ∗ 3 3

_ 4 = 16. 4

2

_ 3 ∗

6

_ 7 =

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253A

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LESSON

8�2

Name Date Time

Solving Mixed-Number Addition Problems

Add. Write each sum as a mixed number in simplest form. Show your work.

1. 5 1

_ 5 + 2

4

_ 5 = 2. 3

2

_ 5 + 5

3

_ 10

=

3. 4 3

_ 4 + 2

1

_ 12

= 4. 4 2

_ 3 + 2

3

_ 4 =

5. Josiah was painting his garage. Before lunch, he painted 1 2

_ 3 walls.

After lunch, he painted another 1 2

_ 3 walls. How many walls did he

paint during the day?

6. Julie’s mom made muffins for Julie and her friends to share.

Julie ate 1 3

_ 4 muffins. Her friends ate 3

1

_ 2 muffins. How many

muffins did Julie and her friends eat altogether?

Without adding the mixed numbers, insert <, >, or =.

Explain how you got your answer.

7. 1 3

_ 8 + 6

2

_ 3 8

8. 5 2 1

_ 5 + 2

7

_ 8

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LESSON

8�12 Number Stories: Division with Fractions

Name Date Time

1. Five pies will each be sliced into fourths.

Ira would like to find out how many

slices there will be in all.

a. Show how the pies will be cut.

b. The drawings show that 5 ÷ 1

_ 4 = , so there will be

slices in all.

2. Jake has a 3-inch strip of metal.

He would like to find out how many

1

_ 2 -inch strips he can cut.

0 inches 1 2 3

Jake can cut strips. So, 3 ÷ 1

_ 2 = .

3. Two students equally share 1

_ 4 of a granola bar. They would

like to know how much of the bar each will get.

a. Show how the piece of granola bar will be cut.


_ 4 ÷ 2 = , so each

student will get of a granola bar.

4. a. Drawing A can be used to find 1

_ 3 ÷ 5.

Drawing B can be used to find 1

_ 3 of

1

_ 5 ,

or 1

_ 3 ∗

1

_ 5 . Use the drawings to show

that 1

_ 3 ÷ 5 =

1

_ 3 ∗

1

_ 5 . A B

b. Complete.

1

_ 3 ∗

1

_ 5 =

1

_ 3 ÷ 5 =

1

_ 3 ÷ 5 =

1

_ 3 ∗ =

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Name Date Time

440B

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Rulers

inches0 1 2 3 4 5 6

inches0 1 2 3 4 5 6

inches0 1 2 3 4 5 6

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fraction division - everyday math - login · lesson 8 12 683 a unit fraction can also be divided by...

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