Dividing with Fractions

Math 7Fraction Review 3Essential UnderstandingsBeing able to compute fluently means making smart choices about which tools to use and when to use them.

Numbers can be represented in multiple ways.

The same operations can be applied in problem situations that seem quite different from another.

Knowing the reasonableness of an answer comes from using good number sense and estimation strategies.

Key KnowledgeThe operation of division is used to:

• find how many of portions of one quantity is in another quantity.• to share equally• repeated subtraction

Asking 8 ÷ 12= 8 × 2 since it takes two groups of one-half of a unit to make a whole

unit.

Examples:

8 ÷ 12= 8 × 2 since it takes 2 one-half's to make a whole

8 ÷ 34= 8 × 4

3 since it takes four-thirds of three-fourths of a unit to make one

whole unit.

Key QuestionsWhen does a situation call for division?

How is dividing related to multiplying?

Why is knowing what the “whole” is important?

Key SkillsI can recognize when a situation calls for the use of division.

I can represent dividing whole numbers and fractions using multiple representations.

I can divide whole numbers and fractions with fluency.

After Teaching

Name ________________ Date _______ Class # ______

Adaptive Reasoning • Strategic Competence • Productive Disposition • Procedural Fluency • Conceptual Understanding page 1

Strands✓Adaptive Reasoning

✓Strategic Competence

✓Productive Disposition

✓Procedural Fluency

✓Conceptual Understanding

Math 7Fraction Review 3-1

Name ________________ Date _______ Class # ______


GoalsI can represent dividing whole numbers and fractions using multiple representations.

Story Calculations

Drawing

How many equal serving sizes of popcorn could be made if you had a total of 8 cups of popcorn and each serving size was 2 cups?

Fraction Review 3-1 Follow-UpA complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question.

1. How many equal size servings of popcorn could be made (or fractions of serv-ings) if:

a. the bag contained 5 cups of popcorn and each serving was 2 cups?

b. the bag contained 5 cups of popcorn and each serving was 1 cup?

c. the bag contained 5 cups of popcorn and each serving was one-half cup?

d. the bag contained two and one-half cups of popcorn and each serving was one-half cup?

Name ________________ Date _______ Class # ______



Name ________________ Date _______ Class # ______



Story Calculations

Drawing

1 1

2

3

2

3

2

3

Must b

e able

to

be so

lved

with

divisi

on.

Fraction Review 3-23 Follow-UpA complete answer for each of the problems will include a story, calcu-lations connected to the diagram, and finally a complete sentence which answers the question.

1.1 1

2

3

2

3

2

3

1

2

3

2

3

2.1 1

Name ________________ Date _______ Class # ______



Name ________________ Date _______ Class # ______



Story Calculations

Drawing

Ms. Phillips brought jars of jelly-beans to be shared equally by stu-dent teams who won the annual math competition. How much candy will each student get if a four-person team gets a total of one-half of a kilogram of candy.

Solve

two w

ays:

divisi

on an

d mult

iplica

tion


1. What fraction of a kilogram of candy would each member of the winning math team get if

a. a four person team wins one-half kilogram of candy and shares it equally?

b. a three person team wins one-fourth kilogram of candy and shares it equally?

c. a three person team wins one-third kilogram of candy and shares it equally?

d. a two person team wins one-fifth of a kilogram of candy and shares it equally?

Name ________________ Date _______ Class # ______


Solve

two w

ays:

divisi

on an

d mult

iplica

tion


Name ________________ Date _______ Class # ______



Story Calculations

Drawing

A local candy store donated long chocolate bars that were used for prizes in a team competition. What fraction of a whole bar will each team member get if a two person team wins four-fifths of a bar and shares it equally?

Solve

two w

ays:

divisi

on an

d mult

iplica

tion


1. A local candy store donated long chocolate bars that were used for prizes in a team competition. What fraction of a whole bar will each team member get if

a. a four person team wins eight-ninths of a bar and shares it equally?

b. a four person team wins one and three-fourths of a bar and shares it equally?

Name ________________ Date _______ Class # ______


Solve

two w

ays:

divisi

on an

d mult

iplica

tion


Name ________________ Date _______ Class # ______


GoalsI can represent multi-plying whole numbers and fractions using multiple representa-tions.

Story Calculations

Drawing

34÷ 4 = ?[ ]

⎡⎣⎢

⎤⎦⎥×

⎡⎣⎢

⎤⎦⎥= ?[ ]

Solve

two w

ays:

divisi

on an

d mult

iplica

tion

Fraction Review 3-5 Follow-Up

1. A complete answer for each of the problems below will include a story, a clearly labeled diagram, calculations connected to the diagram, the value for ?[ ] which makes the equation true, and a complete sentence which answers the question posed in your story.

a. 13÷ 5 = ?[ ]

b. 25÷ 8 = ?[ ]

2. Solve each of your story problems from above using multiplication. A complete answer will include how the calculations are connected to the drawings from problem 1.

Name ________________ Date _______ Class # ______



Name ________________ Date _______ Class # ______



Story Calculations

Drawing

Sam has a job of decorating confer-ences badges using ribbon. Each conference badge uses one-sixth of a meter of ribbon. How many badges can be made from one-half of a me-ter of ribbon? (If there is any left over ribbon, tell what fractional part of an-other badge Sam could make.)


1. How many conference badges can Sam make from the following amounts of rib-bon assuming that each badge requires one-sixth of a meter of ribbon?

a. Three-fourths meter

b. Five-eights meter

c. Two and two-thirds meters

Name ________________ Date _______ Class # ______



Name ________________ Date _______ Class # ______



Story Calculations

Drawing

Jade is working on a different order of bows for the conference. She uses two-thirds of a meter of ribbon to make one bow. How many bows can Jade make from four-fifths me-ters of ribbon?


1. Jade is working on a different order of bows for the conference. She uses two-thirds of a meter of ribbon to make one bow. How many bows can Jade make from each of the following amounts of ribbon.

a. Eight-ninths meters

b. One and three-fourths meters

c. Two and one-third meters

Name ________________ Date _______ Class # ______


Math 7Fraction Review 3Practice 1

A complete answer for each of the problems below will include a clearly labeled diagram, calculations connected to the diagram, and finally a complete sentence which answers the question.

1. Max has 2 cups of popcorn. If the size of each serving is two-thirds of a cup, how many servings, and fractions of servings, can he make?

2. A tailor needs 323

yards of material to make a suit. How many suits can she

make from 22 yards of material?

Name ________________ Date _______ Class # ______




Name ________________ Date _______ Class # ______



Story Calculations

Drawing

Max has 3 23

cups of popcorn. If the

size of each serving is three-fourths of a cup, how many servings, and fractions of servings, can he make?


1. Max has 2 34

cups of popcorn. If each serving is 34

cups, how many servings, or

fractions of servings, can Max make?

2. Max has 2 cups of popcorn. If each serving is 2 23

cups, how many servings, or

fractions of servings, can Max make?

Name ________________ Date _______ Class # ______



Name ________________ Date _______ Class # ______



Story Calculations

Drawing

Kayla is baking bagels. She has 1 kilogram of flour but the recipe calls

for 43

of a kilogram. What fraction of

a recipe can she make with the flour she has?


1. A recipe calls for 54

of a kilogram of flour and you have 1 kilogram of flour on

hand. What fraction of a recipe can you make?







4. Whatʼs the connection between all of these problems? Why do you think this happens?

Name ________________ Date _______ Class # ______


5. (No drawings need to be made.) A recipe calls for AB

kilograms of flour and you

have 1 kilogram of flour on hand. What fraction of a recipe can you make if:

a. 13 b. 4

3 c. 7

5 d. 5

7

6. (No drawings need to be made.) A recipe calls for AB

kilograms of flour and you

have C kilogram of flour on hand. What fraction of a recipe can you make if:

a. A = 2, B = 3, C = 2 b. A = 2, B = 3, C = 2 c. A = 2, B = 3, C = 2

Name ________________ Date _______ Class # ______


Problem Bank

Show how to use the diagram below to solve the problems.

With

14d of paint you can paint 2

5m2 of a wall. How many m2

can you paint with 1d of paint?

With




With




0 1

0 1

0 1

Name ________________ Date _______ Class # ______


A student used the diagram at right to show

her answer to the problem, “With

34d of paint

you can paint 25m2 of a wall. How many m2

can you paint with 1d of paint?” Can you ex-plain her work?

0 1

2

5÷ 3

!"#

$%&' 4

2

5÷ 3

!"#

$%&' 4 =

2

5'1

3

!"#

$%&' 4

=2 '15 ' 3

!"#

$%&' 4

=2

15

!"#

$%&' 4

=8

15

Name ________________ Date _______ Class # ______


Dividing with Fractions

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