Download Fraction Division

Fraction Division
Objective To introduce division of fractions and relate the
operation of division to multiplication.
o
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Math Boxes 8 12
• Find common denominators for pairs of
fractions. [Number and Numeration Goal 5]
Math Journal 2, p. 290
Students practice and maintain skills
through Math Box problems.
• 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.
Study Link 8 12
Math Masters, p. 248
Students practice and maintain skills
through Study Link activities.
[Operations and Computation Goal 5]
• Write equations to model number stories.
[Patterns, Functions, and Algebra Goal 2]
Key Activities
Ongoing Assessment:
Informing Instruction
See page 683. Ongoing Assessment:
Recognizing Student Achievement
Use journal page 289. [Operations and Computation Goal 5]
Materials
Math 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
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 144–147
Unit 8
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Playing Build-It
Student 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.
ENRICHMENT
Exploring the Meaning of the Reciprocal
Math Masters, p. 249
calculator
Students explore the meaning of the
reciprocal.
EXTRA PRACTICE
Students 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.
680
Curriculum
Focal Points
Fractions and Ratios
Dividing with Unit Fractions
Math Masters, p. 253B
Students practice using visual models to
divide fractions.
Mathematical Practices
SMP1, SMP2, SMP4, SMP6
Content Standards
Getting Started
5.NF.7a, 5.NF.7b, 5.NF.7c
Mental Math and Reflexes
Math Message
Pose questions about unit fractions. Suggestions:
1
1
1
How many _2 s are in 1 whole? 2
How many _2 s are in _2 ? 1
1
1
1
How many _2 s are in 4? 8
How many _4 s are in _2 ? 2
1
1
1
How many _2 s are in 2_2 ? 5
How many _
s are in 1? 3
3
1
_
How many s are in 2? 8
Solve Problems 1 and 2 on journal page 288.
4
1
1
How many _4 s are in 1_
?6
2
3
1
_
_
How many s are in ? 3
4
Study Link 8 11 Follow-Up
Have partners share answers and resolve
differences. Ask volunteers to explain their
solution strategies for Problem 9.
4
1 Teaching the Lesson
▶ Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Journal 2, p. 288: Math Masters, p. 440B)
Discuss students’ solutions. Use a transparency of Math Masters,
page 440B to illustrate Problems 1a–1c.
Problem 1a
0
inches
1
2
3
4
5
6
2
3
4
5
6
Problem 1b
Student Page
0
inches
1
Date
Time
LESSON
8 12
Fraction Division
Math Message
Problem 1c
1.
Use the ruler to solve Problems 1a –1c.
0
inches
0
inches
1
2
3
4
5
6
1
2
3
1. a. How many 2s are in 6?
1 s are in 6?
b. How many _
2
3?
1 s are in _
c. How many _
8
4
2. a. How many 2s are in 10?
1 s are in 10?
b. How many _
5
6
3 segments
12 segments
_
_ of an inch? 6 segments
c. How many -inch segments are in
a.
How many 2-inch segments are in 6 inches?
b.
1
How many _
2 -inch segments are in 6 inches?
3
4
1
8
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.
4
2. a.
How many 2-pound boxes of nuts can be made from 10 pounds of nuts?
5 boxes
Use the visual below to help you solve the problem.
Sample answer:
2
3
4
1
1 lb
b.
1 lb
1 lb
1 lb
1 lb
1 lb
1 lb
1 lb
5
1 lb
1 lb
1
How many _
2 - pound boxes can be made from 10 pounds of nuts?
20 boxes
Draw a picture to support your answer.
1 lb
Sample answer:
1 lb
1 lb
1 lb
1 lb
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1 lb
1 lb
1 lb
1 lb
1 lb
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
2
Math Journal 2, p. 288
288-291_EMCS_S_MJ2_G5_U08_576434.indd 288
3/16/11 2:31 PM
Lesson 8 12
681
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
1 s are in 6? 6 ÷ _
1 =s
b. How many _
2
2
3? _
3 ÷_
1 s are in _
1 =s
c. How many _
8
4 4
8
2. a. How many 2s are in 10? 10 ÷ 2 = b
1 s are in 10? 10 ÷ _
1 =b
b. How many _
2
2
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-CLASS
DISCUSSION
(Math Journal 2, p. 289; Student Reference Book,
pp. 79– 80B)
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
1 s, how many quarter loaves
friends. If she cuts each loaf into _
4
will she have to share with her friends?
Student Page
Date
Time
LESSON
Dividing with Unit Fractions
8 12
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
1 =
4÷_
3
2.
slices in all.
Edith has 2 inches of ribbon. She wants to cut the ribbon
1
1
_
into _
4 -inch pieces. How many 4 pieces can she cut?
8
Edith can cut
3.
12
Students should conclude that one way to illustrate the solution is
to divide each of the rectangles into 4 equal parts.
12
1 =
pieces. So, 2 ÷ _
4
8
0
inches
1
2
.
1 1 1 1
4 4 4 4
1
Two students equally share _
3 of a granola bar. Divide the rectangle
at the right to show how much of the bar each will get.
1 1 1 1
4 4 4 4
1 1 1 1
4 4 4 4
1
_
Each student will get
1 ÷ =
_
2
3
4.
1
_
6
of a granola bar.
1
3÷_
4 = 12
6
Ask:
1
Three students equally share _
4 of a granola bar. Divide the rectangle
at the right to show how much of the bar each will get.
1
_
Each student will get
1 ÷ =
_
3
4
5.
1
_
12
●
of a granola bar.
12
What number model represents this problem? 3 ÷ _14 = 12
1 = 12 below their rectangles.
Ask students to write 3 ÷ _
●
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.
4
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.
Math Journal 2, p. 289
288-291_EMCS_S_MJ2_G5_U08_576434.indd 289
682
Unit 8
4/1/11 9:01 AM
Fractions and Ratios
1 s are in 3? 12
How many _
4
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 _15 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 _15 )
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.
1
Pose the following problem: Three family members equally share _
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
1
Watch for students who record the answer as _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 _15 of a loaf to begin with,
when it is divided into three equal parts, each part of the corn
1
bread that is cut up is _
of the entire loaf. So each person will
15
1
_
get 15 of the loaf of corn bread.
1
5
÷3=
1
15
1 ÷3=_
1
Ask: What number model represents this problem? _
5
15
1 ÷3=_
1 ” below their rectangles.
Ask students to write “_
5
15
Lesson 8 12
683
Student Page
Date
Relationship Between Multiplication and Division
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.
a.
Division
Multiplication
1 =
5÷_
n
4
1 = _
n ∗ 4_
4 51
5
1
_
b. 5
÷4=n
1
n∗4=_
5
1
_
c. 4 ÷ 5 = n
1 =
n∗_
5
4
9
_
d. 10
9
3
=_
n∗_
5
10
3
_
e. 5
f.
2.
3
÷_
=n
5
9
÷_
=n
10
Have students solve Problems 1–6. Circulate and assist. Briefly
discuss solutions.
1 =
n∗_
4
5
1 ÷ _
4_
4 15 = n
5
3
9
=_
n∗_
5
10
Solve the following division number sentences (from above). Use the related
multiplication sentences to help you find each quotient.
a.
1 =
5÷_
4
1
_
c. 4 ÷ 5 =
20
20
1
_
b. 5
Ongoing Assessment:
Recognizing Student Achievement
1
_
÷4=
1
1
_
_
d. 4 5 ÷ 4 5 =
20
1
4.
Sample answers: Dividing
1
1
_
How is dividing 5 by _
4 different from dividing 5 by 4?
_1
1
5 by _
4 results in a quotient that is greater than 5. Dividing 5 by
_1 , you are
1
÷
4 results in a quotient that is less than _
.
With
5
4
_1 5
1
finding how many _
4 s are in 5. With 5 ÷ 4, you are finding how
_
1
many 4s are in 5 , which is a very tiny number.
1 Answers vary.
Write a number story for 5 ÷ _
4.
5.
1 ÷
Write a number story for _
4.
5
3.
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.
Time
LESSON
Journal
Page 289
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.
[Operations and Computation Goal 5]
Answers vary.
Math Journal 2, p. 289A
288-291_EMCS_S_MJ2_G5_U08_576434.indd 289A
4/1/11 9:01 AM
▶ Relationship between
WHOLE-CLASS
DISCUSSION
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.
1 ÷ 5, think: What number times 5 is _
1 ? Or n ∗ 5 = _
1.
● To solve _
10
10
10
1
_
50
●
●
●
1 , think: What number times _
1 is 6? Or n ∗ _
1 = 6. 30
To solve 6 ÷ _
5
5
5
2
2
2 = 6. 9
_
_
To solve 6 ÷ , think: What number times is 6? Or n ∗ _
3
3
3 , think: What number times _
1 ÷_
3 is _
1?
To solve _
10
10
10
10
1
3 =_
1._
Or n ∗ _
10
3
10 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 ÷ _23
and to illustrate their solution using the four circles.
683A Unit 8
Fractions and Ratios
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
3 . This shows that 4 wholes is
to renaming each whole as _
3
12 .
equivalent to _
3
2
–
3
2
–
3
2
–
3
2
–
3
2
–
3
2
–
3
12
2
_
÷_=6
3
3
12 ÷ _
2 = 6 under the circles on the board. Students will
Write _
3
3
2 . Emphasize that the
readily see that there are 6 groups of _
3
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.
Step 2 Divide the numerators, and divide the denominators.
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.
48
1 ÷6=_
1 ÷_
_
8
=
=
=
8
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.
Student Page
Date
Time
LESSON
Common Denominator Division
8 12
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.
Problem
Solution
4
4÷_
5 =?
20
4
4
_
_
4÷_
5 = 5 ÷ 5 = 20 ÷ 4 = 5
5
1
_
_
6 ÷ 18 = ?
5
15
1
1
_
_
_
_
6 ÷ 18 = 18 ÷ 18 = 15 ÷ 1 = 15
5
1
_
3_
3 ÷ 6 =?
5
10
5
20
5
1
_
_
_
_
_
3_
3 ÷ 6 = 3 ÷ 6 = 6 ÷ 6 = 20 ÷ 5 = 4
Examples:
3
3
12 ÷ _
=_
3÷_
4
4
4
12 ÷ 3
=_
=
1.
4 =
4÷_
5
1
_
4. 2
1 =
÷_
8
3
3
18
3
÷_
=_
÷_
3_
5
5
5
5
18 ÷ 3
=_
5÷5
6
=_
1 , or 6
2
8.
1
_
5. 6
1 =
÷_
18
15
3.
5
1 ÷_
=
3_
3
6
6.
1 =
6÷_
4
1
_
÷4=
24
4
24
bags
necklaces
Eric is planning a pizza party. He has 5 large pizzas. He wants to cut
3
each pizza so that each serving is _
5 of a pizza. How many people
can get a full serving of pizza?
8
10.
4
5
_
2. 6
Regina is cutting string to make necklaces. She has 15 feet of string
1
and needs 1_
2 feet for each necklace. How many necklaces can
she make?
10
9.
5
1
Chase is packing flour in _
2 -pound bags. He has 10 pounds of flour.
How many bags can he pack?
20
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.
=
6÷6
2
_
1 , or
Solve.
7.
Links to the Future
1 ÷ _
1 =_
2 ÷ _
1
_
3
6
6
6
2÷1
=_
4÷4
4
_
1 , or 4
people
3
3
_
2
A rectangle has an area of 3 _
10 m . Its width is 10 m. What is its length?
11
meters
Math Journal 2, p. 289B
288-291_EMCS_S_MJ2_G5_U08_576434.indd 289B
3/16/11 2:31 PM
Lesson 8 12 683B
Student Page
Date
Math Boxes
8 12
Find the whole set.
1.
▶ Practicing Common
Time
LESSON
2.
a.
1
10 is _
5 of the set.
b.
3
12 is _
4 of the set.
50
16
d.
5
15 is _
8 of the set.
e.
3
9 is _
5 of the set.
Decimal
Percent
0.8
80%
12.5%
55%
5
_1
28
2
_
c. 8 is 7 of the set.
Denominator Division
Complete the table.
Fraction
4
_
0.125
8
11
_
0.55
0.6
20
24
2
_
3
857
_
1,000
15
Add.
5
1_
7
6_
8
4
10 _
2 Ongoing Learning & Practice
1
14
_
= 5_
8 + 8
3
1
_
= 4_
10 + 6 2
5
e.
580 boxes
13
9_
15
1
2
_
_
c. 6 5 + 3 3 =
d.
A worker can fill 145 boxes of crackers
in 15 minutes. At that rate, how many can
she fill in 1 hour?
3
5
_
=_
8 + 6
24
b.
19 20
108 109
70
5.
Write a fraction or a mixed number for
each of the following:
15
1
_
or _
4
40
2
_
, or _
a.
15 minutes = 60 ,
b.
40 minutes = 60
45
_
60 , or
25
_
, or
c.
45 minutes =
d.
25 minutes = 60
e.
Assign Problems 1–10 on the journal page. Have students work with
a partner. Circulate and assist. Briefly share solutions as needed.
2
66 _
3%
89 90
4.
1
4_
4
3
1
_
2_
4 + 12 =
a.
(Math Journal 2, p. 289B)
85.7%
0.857
74 75
3.
12
_
60 , or
12 minutes =
PARTNER
ACTIVITY
6.
▶ Math Boxes 8 12
Measure the line segment below to the
1
nearest _
inch.
4
(Math Journal 2, p. 290)
hour
2
3 hour
3
_
4 hour
5
_
12 hour
1
_
5 hour
INDEPENDENT
ACTIVITY
in.
62 63
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.
183
Math Journal 2, p. 290
288-291_EMCS_S_MJ2_G5_U08_576434.indd 290
3/22/11 9:02 AM
▶ Study Link 8 12
INDEPENDENT
ACTIVITY
(Math Masters, p. 248)
Home Connection Students practice operations with
fractions and mixed numbers.
3 Differentiation Options
Name
Date
STUDY LINK
8 12
1. a.
b.
2. a.
Time
Mixed-Number Review
▶ Playing Build-It
32
1
, so there will be
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.
1
Two families equally share _
of a garden. Show how they can
3
divide their portion of the garden.
b.
_1
The drawing shows that _
÷2=
3
_1
6
gets
of the total garden.
1
6
, so each family
Common Denominator Division
Step 1 Rename the numbers using a common denominator.
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
7 , and _
5 would become 3_
1, _
1, _
1, _
1 , 3_
1,
tossing a 3, the fractions _
5 4 3 12
6
5
4
7 , and 3_
5 . Renamed as fractions, the list would be _
16 , _
13 , _
10 ,
1 , 3_
3_
Step 2 Divide the numerators, and divide the denominators.
Solve. Show your work.
3.
2
5÷_
=
5.
4_
÷_
=
8
4
3
15
_
_1
2 , or 7 2
11
_
_1
2 , or 5 2
3
1
4.
3
4 ÷ _
_
=
5
6.
6_
÷_
=
3
9
7
2
7
20
_
21
60
_
_4
7 , or 8 7
Practice
5
7.
1
4_
= 3_
9.
3
1
1_ + 2_ =
11.
8
4
7_
- 5_
=
9
9
13.
3
2
5_ + 2_ =
15.
3
3 ∗ 3_ =
4
4
5
5
3
4
4
8.
3_45
1_5
10.
9
12.
5
17
_
7_
12 , or 8 12
9
1
9_, or 11_
4
4
14.
16.
22
1_68 , or 1_34
8
8
38
3
4_
, or 5_
2
4
35
+ 1 _ = 35
3_
7
5
1
_
2
3
7
_ = 3_
5
3
5
4 - 1_
=
4
6
2 _
∗ =
4_
7
3
4
28
_
7 , or 4
Math Masters, p. 248
Unit 8
4/1/11 9:13 AM
Fractions and Ratios
12
43 , and _
23 .
_
12
6
3
5
3_ - 1_ =
221-253_EMCS_B_MM_G5_U08_576973.indd 248
684
15–30 Min
(Student Reference Book, p. 300; Math Masters,
pp. 446 and 447)
Four pizzas will each be cut into eighths. Show how they can
be cut to find how many slices there will be in all.
The drawing shows that 4 ÷ _
=
8
32 slices in all.
PARTNER
ACTIVITY
READINESS
Study Link Master
6
5
4
3
Teaching Master
ENRICHMENT
▶ Exploring the Meaning
PARTNER
ACTIVITY
15–30 Min
of the Reciprocal
Name
Time
Exploring the Meaning of the Reciprocal
8 12
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.
(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.
Date
LESSON
1.
Example 1:
Example 2:
3º?=1
_1 º ? = 1
2
3
1
3 º _3 = _3 = 1
_1 º 2 = _2 = 1
2
2
_1 is the reciprocal of 3
3
1
2 is the reciprocal of _2
1
3 is the reciprocal of _3
_1 is the reciprocal of 2
2
Find the reciprocals.
_1
_1
6
a. 6
b.
2.
1
_
7
7
c.
5
What do you think would be the reciprocal of _6 ?
9
_1
d. 9
20
_6
5
20
Reciprocals on a Calculator
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.
9 , and _
9 =_
36 = 1. The
4 is _
4 ∗_
For example, the reciprocal of _
9
4
9
4
36
reciprocal of a whole number is a unit fraction that has the whole
1,
number as its denominator. For example, the reciprocal of 8 is _
8
8 = 1.
1 =_
so 8 ∗ _
8
8
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.
1
_1
_
0.04 , 25
8-1 0.125 , 8
b. 5-2
c. 2-3
a.
4.
Write the key sequence you could use to find the reciprocal of 36.
5.
3
Write the key sequence you could use to find the reciprocal of _7 .
6.
What pattern do you see for the reciprocal of a fraction?
3
(–)
6
3
n
7
F D , or 3
1
(–)
d
1
0.125 ,
_1
8
1
6
, or 3
F D
7
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.
Math Masters, p. 249
221-253_EMCS_B_MM_G5_U08_576973.indd 249
EXTRA PRACTICE
▶ Dividing with Unit Fractions
3/25/11 2:00 PM
PARTNER
ACTIVITY
5–15 Min
(Math Masters, p. 253B)
Students practice using visual models to divide fractions.
Teaching Master
Name
Date
LESSON
Number Stories: Division with Fractions
8 12
1.
2.
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.
1
The drawings show that 5 ÷ _
=
4
slices in all.
Jake has a 3-inch strip of metal.
He would like to find out how many
1
_
-inch strips he can cut.
2
6
Jake can cut
3.
Time
20
0
, so there will be
20
1
2
inches
6
1
strips. So, 3 ÷ _
=
2
3
.
Two students equally share _
of a granola bar. They would
4
like to know how much of the bar each will get.
1
a.
Show how the piece of granola bar will be cut.
b.
1
The drawing shows that _
÷2=
4
_1
8
student will get
4. a.
_1
8
, so each
of a granola bar.
Drawing A can be used to find _
÷ 5.
3
1
1
of _
,
Drawing B can be used to find _
5
3
1
∗ _. Use the drawings to show
or _
5
3
1
1 _
1
∗ .
÷5=_
that _
5
3
3
1
b.
1
Complete.
1 _
1
_
∗ =
5
3
1
_
÷5=
A
B
1
_
15
1
_
3
1
1
_
∗
÷5=_
3
3
15
_1
5
1
_
=
15
Math Masters, p. 253B
253A-253B_EMCS_B_MM_G5_U08_576973 .indd 253B
3/16/11 1:26 PM
Lesson 8 12
685
Name
Date
STUDY LINK
Mixed-Number Review
8 12
1. a.
b.
2. a.
b.
Time
Four pizzas will each be cut into eighths. Show how they can
be cut to find how many slices there will be in all.
The drawing shows that 4 ÷ _
=
8
slices in all.
1
, so there will be
Two families equally share _
of a garden. Show how they can
3
divide their portion of the garden.
1
The drawing shows that _
÷2=
3
gets
of the total garden.
1
, so each family
Common Denominator Division
Step 1 Rename the numbers using a common denominator.
Step 2 Divide the numerators, and divide the denominators.
Solve. Show your work.
3.
2
5÷_
=
4.
3
4 ÷ _
_
=
5
5.
4_
÷_
=
8
4
6.
6_
÷_
=
3
9
8.
7
_ = 3_
3
1
3
7
2
7
7.
1
4_
= 3_
9.
3
1
+ 2_ =
1_
5
5
10.
3
5
3_
- 1_
=
8
8
11.
8
4
7_
- 5_
=
9
9
12.
2
4
+ 1_ =
3_
7
5
13.
3
2
+ 2_ =
5_
3
4
14.
3
4 - 1_
=
4
15.
3
3 ∗ 3_
=
4
16.
∗_=
4_
7
3
4
248
4
5
2
5
6
Copyright © Wright Group/McGraw-Hill
Practice
Name
Date
LESSON
8 12
1.
2.
Number Stories: Division with Fractions
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 ÷ _
=
4
slices in all.
1
0
1
inches
strips. So, 3 ÷ _
=
2
1
2
3
.
Two students equally share _
of a granola bar. They would
4
like to know how much of the bar each will get.
1
a.
Show how the piece of granola bar will be cut.
b.
The drawing shows that _
÷2=
4
1
student will get
4. a.
Copyright © Wright Group/McGraw-Hill
, so there will be
Jake has a 3-inch strip of metal.
He would like to find out how many
1
_
-inch strips he can cut.
2
Jake can cut
3.
Time
of a granola bar.
Drawing A can be used to find _
÷ 5.
3
1
1
_
of
,
Drawing B can be used to find _
5
3
1
1 _
1
∗ . Use the drawings to show
or _
5
3
1
1 _
1
_
∗ .
that 3 ÷ 5 = _
5
3
b.
, so each
A
B
Complete.
1 _
1
_
∗ =
5
3
1
_
÷5=
3
1
1
_
∗
÷5=_
3
3
=
253B
Name
Date
Time
Rulers
0
inches
1
2
3
4
5
6
0
inches
1
2
3
4
5
6
0
inches
1
2
3
4
5
6
Copyright © Wright Group/McGraw-Hill
440B