5
•
Applying Fractions
Add, subtract, multiply,
and divide to solve fraction
problems.
Key Vocabulary
compatible numbers (p. 232)
like fractions (p. 236)
reciprocal (p. 258)
unlike fractions (p. 237)
Real-World Link
Baking The measurements found on measuring
cups and spoons are written as fractions. You will use
fractions to find how much of each ingredient is
needed when you make part of a whole recipe.
Applying Fractions Make this Foldable to help you organize your notes.
Begin with a plain sheet of 11” by 17” paper, four index cards, and glue.
1 Fold the paper in half
widthwise.
2 Open and fold along
1
the length about 2_”
2
from the bottom.
3 Glue the edge on each
side to form two pockets.
4 Label the pockets
Fractions and Mixed
Numbers, respectively.
Place two index cards
in each pocket.
228
Chapter 5 Applying Fractions
Fractions
Mix
Numbeed
rs
GET READY for Chapter 5
Diagnose Readiness You have two options for checking Prerequisite Skills.
Option 2
Math Online
Option 1
Take the Online Readiness Quiz at glencoe.com.
Take the Quick Quiz below. Refer to the Quick Review for help.
Example 1
Find the LCD of each pair of
fractions. (Lesson 4-8)
5 3
1. _ , _
5
7
3.
1
8 ,_
_
15
6
Multiply or divide.
2.
_1 , _4
4.
7
_3 , _
2
5
3
Find the LCD of _
and _
.
6
9
4
10
The LCD is the LCM of the denominators,
6 and 10, or 30.
10
Example 2
(Prior Grade)
5. 1.8 × 12
6. 99 ÷ 12
Find 7.8 ÷ 0.25.
7. 83 ÷ 100
8. 4.6 × 0.3
31.2
0.25 7.80 0
-7 5
_____
30
-25
____
50
-50
____
0
9. MEASUREMENT How many
1.6-meter sections of rope can
be cut from a length of rope
6.4 meters? (Prior Grade)
10. COINS Manuel owes each of
Move the decimal point 2
places to the right and divide
as with whole numbers.
8 friends $0.35. How much does
he owe in all? (Prior Grade)
Complete to show equivalent mixed
numbers. (Prior Grade)
Example 3
1
11. 3_ = 2 _
12.
mixed numbers.
13. 6_ = 5 _
4
4
14. 8_ = 7 _
5
1
15.
5
2
9_
=
3
6
7
_5
3
7
2
RECIPES A recipe calls for 4_
cups
3
of flour. This is equivalent to 3 cups
of flour plus an additional how
many cups of flour? (Prior Grade)
2
Complete 4_
=
9
11
_
to show equivalent
9
2
2
= 3 + 1_
4_
9
9
9
2
=3+_
+_
9
11
=3+_
11
= 3_
9
9
9
Chapter 5 Get Ready for Chapter 5
229
5-1
Estimating with Fractions
MAIN IDEA
Estimate sums,
differences, products,
and quotients of
fractions and mixed
numbers.
New Vocabulary
MAMMALS The table below lists the average length for a
few mammals.
1. Graph 9_ on a number line. To the nearest whole number,
1
4
how long is an American Bison?
2. Graph 3_ on a number line. To the nearest whole number,
3
4
how long is a dingo?
compatible numbers
Math Online
3. About how much longer is the American bison than
a dingo?
glencoe.com
Mammal
• Extra Examples
• Personal Tutor
• Self-Check Quiz
Length (ft)
Brown Bear
6_
American Bison
9_
Opossum
2_
Dingo
3_
1
2
1
4
1
2
3
4
To estimate the sum, difference, product, or quotient of mixed numbers,
round the mixed numbers to the nearest whole number.
9
1
1
94
92
Round down.
9 _41 ≈ 9
3
94
10
Round up.
9 _21 ≈ 10, 9 _43 ≈ 10
Estimate with Mixed Numbers
_ _
_ _
1 Estimate 3 2 + 5 1 .
2 Estimate 6 2 × 1 7 .
2 _
3_
+ 51 ≈ 4 + 5 or 9
3
6
5
8
2
7
6_ × 1_ ≈ 6 × 2 or 12
5
8
The sum is about 9.
The product is about 12.
3
6
Estimate.
a. 2_ + 3_
1
5
230
Chapter 5 Applying Fractions
1
2
b. 4_ × 5_
3
8
1
4
c. 8_ ÷ 2_
7
9
3
4
To estimate the sum, difference, product, or quotient of fractions,
1
, or 1, whichever is closest. Number lines
round each fraction to 0, _
2
and fraction models, like the ones shown below, can help you decide
how to round.
Fractions Close to 0
0
1
6
Fractions Close to
1
_1
1 5
2 8
0
1
7
Fractions Close to 1
2
9
10 1
0
1
4
9
5
6
The numerator is much
The numerator is about half of
smaller than the denominator. the denominator.
The numerator is almost as
large as the denominator.
Estimate with Fractions
_ _
3 Estimate 1 + 2 .
8
3
1 is much smaller than 8, so
2 is close to half of 3, so
Estimating with Fractions
If one of the fractions is
a mixed number, such as
5
2 , round the
3_
+_
3
8
_1 ≈ 0.
8
_2 ≈ _1 .
3
2
_1 + _2 ≈ 0 + _1 = _1 The sum is about _1 .
8
3
2
2
2
_ _
4 Estimate 6 - 7 .
7
mixed number to the
nearest whole number
and the fraction to the
10
5
2 ≈
nearest half. 3 _
+_
3
8
4 + _21 or about 4_21 .
6 is almost as large as 7, so
6
7 1
0
1
2
0
7
10
7 is about half of 10, so
1
7
1
1
_6 - _
≈1-_
=_
7
2
10
_6 ≈ 1.
7
_7 ≈ _1 .
10
2
1
The difference is about _
.
2
2
_ _
5 Estimate 8 ÷ 5 .
9
6
_8 ≈ 1 and _5 ≈ 1.
_8 ÷ _5 ≈ 1 ÷ 1 = 1
9
9
6
6
The quotient is about 1.
Estimate.
d.
_1 + _3
7
5
e.
_7 - _5
8
9
f.
11
_3 × _
5
12
g.
_7 ÷ _2
8
5
Lesson 5-1 Estimating with Fractions
231
Compatible numbers, or numbers that are easy to compute mentally,
can also be used to estimate.
Use Compatible Numbers
Estimate using compatible numbers.
_
6 1 · 14
THINK What is
3
_1 · 14 ≈ _1 · 15 or 5
3
3
_1 of 14?
3
Round 14 to 15, since 15 is divisible by 3.
_1 of 15 is 15 ÷ 3 or 5.
3
_ _
7 97 ÷ 41
Compatible Numbers
When dividing mixed
numbers, round so that the
dividend is a multiple of
the divisor.
5
8
7
1
1
9_
÷ 4_
≈ 10 ÷ 4_
8
5
5
_7
8
1
_
Round 4 to 5, since 10 is divisible by 5.
Round 9 to 10.
≈ 10 ÷ 5 or 2
5
Estimate using compatible numbers.
h.
_1 · 21
i.
4
_1 · 17
j. 12 ÷ 6_
2
3
3
8 MONSTER TRUCKS The height of the wheels on the monster truck at
_
the left is about 2 of the total height of the truck. Estimate the
3
height of the wheels.
Real-World Link
The monster truck
1
shown is 15_ feet tall
2
and weighs 28,000
pounds.
Words
2
Wheel height is _ of the truck height.
Variable
Let x represent the wheel height.
3
Equation
x
2
x≈_
· 15
Round 15 to 15,
3
x ≈ 10
=
2
_
3
·
_1
15
2
_1
2
since 15 is divisible by 3.
_1 of 15 is 5, so _2 of 15
3
3
is 2 · 5 or 10.
Source: Monster Trucks UK
The wheels are about 10 feet high.
k. MEASUREMENT The area of a rectangle is 19_ square feet. The width
3
4
1
of the rectangle is 5_
feet. What is the approximate length of the
4
rectangle?
232
Chapter 5 Applying Fractions
Examples 1–5
(p. 230–231)
Estimate.
1. 8_ + 1_
3
8
5.
Examples 6, 7
(p. 232)
Example 8
(p. 232)
HOMEWORK
For
Exercises
12–19
20–29
30–35
HELP
See
Examples
1, 2
3–5
6–8
2. 2_ - 1_
5
6
4
5
_1 + _2
6
6.
5
3. 5_ · 2_
5
7
1
8
_6 - _1
7
7.
5
4. 9_ ÷ 2_
7
8
2
7
_5 · _8
8
8.
9
2
3
_4 ÷ _6
5
7
Estimate using compatible numbers.
9.
_1 · 15
10. 21_ ÷ 9_
5
6
4
2
3
4
6 5 ft
11. BIRDS A seagull’s wingspan is about _ of a bald
2
3
eagle’s wingspan. The eagle’s wingspan is shown
at the right. Estimate the wingspan of a seagull.
Estimate.
12. 3_ + 4_
13. 1_ + 5_
14. 5_ - 3_
1
6
15. 4_ - 1_
16. 2_ · 6_
17. 1_ · 3_
18. 6_ ÷ 1_
19. 8_ ÷ 2_
3
4
5
6
2
3
1
8
1
3
11
12
4
5
1
3
1
4
1
8
2
3
2
5
1
2
5
8
1
2
20.
_3 + _3
21.
_5 + _3
22.
_5 - _1
23.
_3 - _3
24.
_1 · _3
25.
11
_4 · _
26.
_4 ÷ _7
27.
5
1
_
÷_
8
4
8
4
8
9
7
12
9
6
5
8
28. COOKING Joaquim wants to make the
macaroni and cheese shown at the right, but
3
he has only about 1_
cups of macaroni. About
4
how much more macaroni does he need?
29. MEASUREMENT Isabella is sewing a trim that
1
is 1_
inches wide on the bottom of a skirt
5
4
6
10
Macaroni $ Cheese
3 tbsp butter
2 21 c uncooked macaroni
1 tbsp salt
1
4 tbsp pepper
1 qt milk
1
2 lb cheese
8
7
inches long. Approximately how
that is 15_
8
long will the skirt be?
Estimate using compatible numbers.
30.
_1 · 39
31.
4
_1 · 37
32. 23_ ÷ 3
2
9
6
33. 25_ ÷ 5_
3
10
2
3
34. MONEY Arleta has $22. She uses _ of her money to buy a pair of earrings.
1
3
About how much money did she spend on the earrings?
35. SNACKS A cereal company has 24 pounds of granola to package in bags that
3
contain 1_
pounds of granola. About how many bags will they have?
4
Lesson 5-1 Estimating with Fractions
233
36. FIND THE DATA Refer to the Data File on pages 16–19. Choose some
data and write a real-world problem in which you would estimate with
fractions.
37. SPORTS Paquito and Jeff are on a
basketball team. The table shows
the approximate fraction of the
team’s points that each of them
scored in a game. If the team
scored a total of 72 points, about
how many did Paquito and Jeff
score together?
Fraction of Total
Points Scored
Player’s
Names
Paquito
3
8
Jeff
1
6
38. RESEARCH Research the statistics of any basketball team.
How can you use fractions to analyze the statistics?
39. COOKING Kathryn baked the sheet of
Real-World Link
The femur or thigh
bone is the longest
in length, largest in
volume, and strongest
bone of the human
body.
.
7 in
7 8
brownies shown. She wants to cut it into
brownies that are about 2 inches square.
How many brownies will there be?
12 3 in
8 .
ANALYZE TABLES For Exercises 40–43, use the
following information and the table shown.
The adult human skeleton is made up of
206 bones. The table shows the approximate
fraction of the bones that each body part(s)
makes up.
Body
Part(s)
Fraction of
Total Bones
Feet
1
4
40. About how many bones are in the feet?
Hands &
Feet
1
2
41. About how many bones are in both
hands and feet?
EXTRA PRA CTICE
See pages 679, 708.
H.O.T. Problems
42. About how many bones are in one hand?
43. The length of your thighbone is equal to _ of your height.
1
4
About how many inches long is your thighbone?
44. CHALLENGE In a division expression, the divisor is rounded up and the
dividend is rounded down. How does the new quotient compare to the
original quotient? Explain.
45. OPEN ENDED Select two fractions whose estimated difference and product
1
. Justify your selection.
is _
2
46. NUMBER SENSE Decide which of the following have sums that are less
than 1. Explain.
a.
_1 + _2
5
3
7
_
_
b.
+1
8
2
234
Chapter 5 Applying Fractions
c.
_5 + _2
d.
_1 + _3
6
7
3
9
47. SELECT A TECHNIQUE To make the crust for a peach cobbler, Dion needs
1
2
2
cups of flour, 1_
cups of sugar, and 1_
cups of hot water. He needs to
3_
3
4
3
mix all of these in a large bowl. The largest bowl he can find holds 6 cups.
Which of the following techniques might Dion use to determine whether
he can use this bowl to mix the ingredients? Justify your selection(s).
Then use the technique(s) to solve the problem.
mental math
48.
number sense
estimation
WR ITING IN MATH Explain when estimation would not be the best
method for solving a problem. Then give an example.
49. SHORT RESPONSE A chef has 15_ cups
2
3
50. On a full tank of gasoline, a certain car
1
of penne pasta and 22_
cups of rigatoni
can travel 360 miles. The needle on its
gasoline gauge is shown. Without
refueling, which is the best estimate of
how far the car can travel?
4
pasta. About how much pasta is there
altogether?
A 150 miles
B 180 miles
C 240 miles
GAS GAUGE
D 329 miles
Replace each ● with <, >, or = to make a true sentence.
51.
7
2_
● 2.75
8
52.
-1
-7
_
●_
3
3
53.
(Lesson 4-9)
_5 ● _4
7
5
54. 3_ ● 3_
6
11
9
14
55. SHOPPING A store sells a 3-pack of beaded
necklaces and a 5-pack of beaded bracelets.
How many packages of each must you buy
so that you have the same number of necklaces
and bracelets? (Lesson 4-8)
Write each decimal as a percent.
56. 0.56
57. 0.375
(Lesson 4-7)
58. 0.07
59. 0.019
PREREQUISITE SKILL Find the LCD of each pair of fractions.
60.
5
_3 , _
4 12
61.
7
_1 , _
2 10
62.
_1 , _1
6 8
(Lesson 4-9)
63.
_4 , _2
5 3
Lesson 5-1 Estimating with Fractions
235
5-2
Adding and Subtracting
Fractions
MAIN IDEA
Add and subtract
fractions.
New Vocabulary
like fractions
unlike fractions
INSTANT MESSENGER Sean surveyed ten
classmates to find which abbreviation they
use most when they instant message.
Abbreviation
Number
L8R
5
LOL
3
BRB
2
1. What fraction uses L8R? BRB?
2. What fraction uses either L8R or BRB?
Math Online
glencoe.com
• Extra Examples
• Personal Tutor
• Self-Check Quiz
• Reading in the Content Area
Fractions that have the same denominators are called like fractions.
Key Concept
Add and Subtract Like Fractions
Words
To add or subtract like fractions, add or subtract the
numerators and write the result over the denominator.
Examples
Numbers
Algebra
5 +2
7
_5 + _2 = _
or _
a+b
_ac + _bc = _
c , where c ≠ 0
11
4
11 - 4
7
_
- _ = _ or _
a-b
_ac - _bc = _
c , where c ≠ 0
10
12
10
12
10
12
10
12
Add and Subtract Like Fractions
_ _
1 Add 5 + 2 . Write in simplest form.
9
9
5+2
_5 + _2 = _
9
9
9
7
_
=
9
Write the sum over
the denominator.
_ _
10
10
9
9
1
1
_-_
= _ Subtract the
10
10
10
numerators.
10
_
=4
5
a.
236
Chapter 5 Applying Fractions
_1 + _3
6
6
Add the numerators.
2 Subtract 9 - 1 . Write in simplest form.
8
=_
Write the difference
over the denominator.
8
10
Simplify.
b.
9
10
_3 - _1
7
7
-
1
10
Review Vocabulary
LCD the least common
multiple of the denominators
of two or more fractions;
To add or subtract unlike fractions, or fractions with different
denominators, rename the fractions using the LCD. Then add or subtract
as with like fractions.
Example: the LCD of _
1
4
Add and Subtract Unlike Fractions
2
and _ is 12. (Lesson 4-9)
3
_ _
3 Add 1 + 1 . Write in simplest form.
2
Estimate
6
METHOD 1
_1 + 0 = _1
2
2
Use a model.
_1
2
1
+_
6
____
_4 or _2
6
3
METHOD 2
Use the LCD.
1
1
The least common denominator (LCD) of _
and _
is 6.
2
6
Rename using the LCD, 6.
Renaming Fractions
To rename a fraction,
multiply both the numerator
and the denominator of the
original fraction by the
same number. By doing so,
the renamed fraction has
the same value as the
original fraction.
1×3
_
=
2×3
_1
2
1
+_
6
____
2
6
Check for Reasonableness
3
_3
_3
6
1
+_
6
____
4
_ or _2
6
3
6
1
= +_
6
____
1×1
_
6×1
1
1
2
So, _
+_
=_
.
Add.
2
1
_
≈_ ✔
3
2
_ _
4 Subtract 11 - 3 . Write in simplest form.
12
Estimate
8
1-_=_
1
2
1
2
Since 12 = 22 · 3 and 8 = 23, the LCM of 12 and 8 is 23 · 3 or 24.
Rename each fraction using a denominator of 24. Then subtract.
Think: 12
Think: 8
11 × 2
22
× 2 = 24, so _
or _.
24
12 × 2
3×3
3
9
× 3 = 24, so _
=_
or _.
24
8
8×3
11 × 2
3×3
3
11
_
-_
=_
-_
.
12 × 2
8
12
The LCD of _ and _ is 24.
9
22
=_
-_
24
13
=_
24
Rename the fractions using LCD, 24.
24
Subtract the fractions.
1
13
_
≈_ ✔
2
24
Check for Reasonableness
c.
_8 - _2
9
3
3
8
11
12
8×3
d.
_5 - _3
6
8
e.
_7 + _3
8
4
Lesson 5-2 Adding and Subtracting Fractions
237
Healthy Lunch
SURVEYS In a recent
survey, students were
asked what they would
choose for a healthy
lunch. The results are
shown in the graph.
/POF
PGUIFTF
5 What fraction more
25
9×5
3×4
9
3
_
-_
=_
-_
20
$IJDLFO
OVHHFUT 1J[[B
of the students chose
salad bar rather than
a deli sandwich?
Key Words The phrase
what fraction more
suggests subtraction.
4BMBE
#BS
#VSHFS 'SJFT %FMJ
TBOEXJDI The LCD of
_9 and _3 is 100.
20
25
20 × 5
25 × 4
45
12
=_
-_
Rename the fractions using the LCD.
100
100
33
=_
Subtract the numerators.
100
33
So, _
more students chose salad bar rather than a deli sandwich.
100
6 What fraction of students chose pizza or chicken nuggets?
3
3
1
2
_
+_
=_
+_
20
10
20
5
=_
20
1
=_
4
20
Rename.
Add.
Simplify.
1
So, _
of the students chose pizza or chicken nuggets combined.
4
f. SURVEYS What fraction more of the students chose a deli sandwich
rather than a burger and fries?
Examples 1–4
(pp. 236–237)
Add or subtract. Write in simplest form.
1.
_4 + _2
9
9
1
_
_
5.
+3
6
8
Examples 5, 6
(p. 238)
2.
_5 + _4
3.
6
9
2
_
_
6.
+5
3
6
_3 - _1
8
8
5
_
_
7.
- 7
6
12
4.
_4 - _2
8.
_3 - _1
5
4
5
3
For Exercises 9 and 10, choose an operation to solve each problem. Explain
your reasoning. Then solve the problem.
9. MEASUREMENT Cassandra cuts _ inch off the top of a photo and _ inch off
5
16
3
8
the bottom. How much smaller is the total height of the photo now?
10. CHORES A bucket was _ full with soapy water. After washing the car, the
7
8
1
full. What part of the water was used?
bucket was only _
4
238
Chapter 5 Applying Fractions
HOMEWORK
For
Exercises
11–14
15–22
23–26
HELP
See
Examples
1, 2
3, 4
5, 6
Add or subtract. Write in simplest form.
11.
_3 + _1
12.
_5 + _7
13.
_5 - _1
14.
3
7
_
-_
15.
3
1
_
+_
16.
7
7
_
+_
17.
11
_5 + _
18.
_7 + _5
19.
_7 - _1
20.
_4 - _1
21.
2
_4 - _
22.
3
1
_
-_
7
7
5
15
9
3
8
8
12
10
5
6
6
8
9
6
12
15
10
10
9
6
10
4
For Exercises 23–26, choose an operation to solve each problem. Explain
your reasoning. Then solve the problem.
23. MEASUREMENT Ebony is building a shelf
to hold the two boxes shown. What is the
smallest width she should make the shelf?
4
5 ft
3
4 ft
24. WEATHER Using the information under the photo, find the difference of
the average precipitation for Boise in February and November.
25. MEASUREMENT Makayla bought _ pound of ham and _ pound of turkey.
5
8
1
4
How much more turkey did she buy?
26. ANIMALS The three-toed sloth can travel _ miles per hour while a giant
3
20
17
miles per hour. How much faster, in miles per hour,
tortoise can travel _
100
is the giant tortoise?
Simplify.
Real-World Link
The average
precipitation for
February and
November for Boise,
4
7
Idaho, is _ and _
10
10
inches, respectively.
27.
5
_1 + _1 + _
7
2
31. 1 + _
1
4
28
28.
7
_1 + _5 + _
6
4
32. 1 - _
5
8
12
29.
(
)
_1 + _2 - _1
6
3
4
30.
33. 2 + _
(
)
_5 - _1 + _1
6
2
3
34. 3 - _
2
3
1
6
35. MONEY Chellise saves _ of her allowance and spends _ of her allowance at
1
5
2
3
the mall. What fraction of her allowance remains?
Source: The Weather Channel
36. ANALYZE TABLES Pepita and Francisco
each spend an equal amount of time on
homework. The table shows the fraction
of their time they spend on each subject.
Determine the missing fraction for
each student.
Homework
Pepita
Francisco
Math
English
Science
_
Fraction of
Time
_2
3
_1
6
_1
2
_3
8
_
ALGEBRA Evaluate each expression if a = 3 and b = 5 .
37.
_1 + a
2
38. b - _
7
10
4
39. b - a
6
40. a + b
Lesson 5-2 Adding and Subtracting Fractions
239
41. BOOK REPORTS Four students were scheduled to give book reports in a
2
hour remained. If the next two
1-hour class period. After the first report, _
3
1
1
hour and _
hour, respectively, what fraction of the
students’ reports took _
6
4
hour remained after the final students’ report? Justify your answer.
42. MEASUREMENT Mrs. Escalante was riding a bicycle on a bike path. After
3
2
of a mile, she discovered that she still needed to travel _
of a mile
riding _
3
4
to reach the end of the path. How long is the bike path?
43. CELL PHONES One hundred sixty
How Do You Use
a Cell Phone?
cell phone owners were surveyed.
What fraction of owners prefers
using their cell phone for text
messaging or taking pictures?
Taking
Text
pictures messaging
3
3
8
8
44. MEASUREMENT LaTasha and Eric are
1 Playing
4 games
1
jogging on a track. LaTasha jogs _
of a
4
5
of a
mile and then stops. Eric jogs _
8
EXTRA
mile, stops and then turns around and
PRACTICE
1
jogs _
of a mile. Who is farther ahead
2
See pages 679, 708.
H.O.T. Problems
on the track? How much farther?
45. CHALLENGE Fractions, such as _ or _, whose numerators are 1, are called
1
2
1
3
unit fractions. Describe a method you can use to add two unit fractions
1
1
+_
.
mentally. Explain your reasoning and use your method to find _
99
100
46. OPEN ENDED Provide a counterexample to the following statement.
1
The sum of three fractions with odd numerators is never _
.
47.
3
1
FIND THE ERROR Meagan and Lourdes are finding _
+_
.
5
4
2
Who is correct? Explain.
1+3
_1 + _3 = _
4
5
4+5
1x5 _
_1 + _3 = _
+ 3x4
4
Meagan
48.
5
4x5
5x4
Lourdes
WR ITING IN MATH To make a cake, Felicia needs 1 cup of flour but she
3
2
-measuring cup and a _
-measuring cup. Which method will
only has a _
3
4
bring her closest to having the amount of flour she needs? Explain.
a. Fill the _ -measuring cup twice.
2
3
3
_
c. Fill the -measuring cup twice.
4
240
Chapter 5 Applying Fractions
b. Fill the _ -measuring cup once.
2
3
3
_
d. Fill the -measuring cup once.
4
49. The table gives the number of hours
50. Which of the following is the prime
Orlando spent at football practice for
one week.
Day
factored form of the lowest common
7
11
denominator of _
+_
?
12
Time (hours)
1
Monday
Tuesday
_1
F 2×3
2
G 2 × 32
2
1
2_
3
5
_
1
6
1
2_
2
3
_
1
Wednesday
Thursday
Friday
Saturday
18
H 22 × 32
23 × 3
J
51. Find _ - _.
5
6
4
1
8
4
A _
How many more hours did he practice
over the last three days than he did
over the first three days?
7
3
B _
8
1
h
A _
7
C _
4
12
1
B _
h
17
D _
2
24
2
C _
h
3
3
D _
h
4
Estimate.
(Lesson 5-1)
6
5
52. _ - _
7
12
53. 4_ + 3_
3
4
1
9
54. 16_ ÷ 8_
2
3
55. 5_ · 3_
1
5
4
5
56. WEATHER The table shows about how much rain
falls in Albuquerque and Denver. Which city has
the greater fraction of inches of rain per day?
Explain. (Lesson 4-9)
57. Write 0.248 as a percent. (Lesson 4-7)
ALGEBRA Find each sum if a = -3 and b = 2.
58. a + b
1
3
City
Amount
of Rain (in.)
Number
of Days
Albuquerque, NM
9
60
Denver, CO
15
90
Source: The Weather Channel
(Lessons 2-4 and 2-5)
59. a - b
60. b - a
PREREQUISITE SKILL Complete.
61. 5_ = 5 +
2
3
62. 1 = _
9
63. 1 = _
5
64.
3
=4+_
8
Lesson 5-2 Adding and Subtracting Fractions
241
5-3
Adding and Subtracting
Mixed Numbers
MAIN IDEA
Add and subtract mixed
numbers.
Math Online
BABIES The birth weights
of several babies in the
hospital nursery are
shown.
Birth Weight (pounds)
glencoe.com
8_
1
8
15
7_
16
13
_
6
16
7
5_
8
Jackson
• Extra Examples
• Personal Tutor
• Self-Check Quiz
Nicolás
Rebekah
Mia
1. Write an expression to find how much more Nicolás weighs
than Mia.
2. Rename the fractions using the LCD.
3. Find the difference of the fractional parts of the mixed numbers.
4. Find the difference of the whole numbers.
5. MAKE A CONJECTURE Explain how to find 7_ - 5_. Then use your
conjecture to find the difference.
15
16
7
8
To add or subtract mixed numbers, first add or subtract the fractions.
If necessary, rename them using the LCD. Then add or subtract the
whole numbers and simplify if necessary.
Add and Subtract Mixed Numbers
_
_
1 Find 7 4 + 10 2 . Write in simplest form.
9
9
Estimate 7 + 10 = 17
_
9
2
+ 10_
9
______
6
2
_
17 or 17_
74
3
9
Add the whole numbers and
fractions separately.
Simplify.
_2 ≈ 17 ✔
Check for Reasonableness 17
a. 6_ + 2_
1
8
242
Chapter 5 Applying Fractions
5
8
3
b. 5_ + 2_
1
5
3
10
c. 1_ + 4_
5
9
1
6
_ _
2 Find 8 5 - 2 1 . Write in simplest form.
6
3
Estimate 9 - 2 = 7
5
8_
5
8_
6
6
1
-2_
3
_____
2
-2_
Rename the fraction using
the LCD. Then subtract.
6
_____
3
1
6_
or 6_
6
2
Simplify.
_1 ≈ 7 ✔
Check for Reasonableness 6
2
Subtract. Write in simplest form.
d. 5_ - 1_
e. 13_ - 9_
3
4
f. 8_ - 2_
g. 7_ - 4_
h. 11_ - 3_
i. 9_ - 5_
3
10
4
5
3
4
Improper Fractions An
improper fraction has a
numerator that is greater
than or equal to the
denominator. Examples
of improper fractions are
_5 and 2 _6 .
5
4
7
8
5
6
1
3
2
3
1
8
4
7
1
2
1
2
Sometimes when you subtract mixed numbers, the fraction in the first
mixed number is less than the fraction in the second mixed number.
In this case, rename the first fraction as an improper fraction in order
to subtract.
Rename Mixed Numbers to Subtract
_
_
3 Find 2 1 - 1 2 .
3
3
_1 = _1
Estimate 2 - 1
2
2
1
2
1
Since _
is less than _
, rename 2_
before subtracting.
3
3
3
_3
Change 1 to .
3
_
21
1
2_
3
2
-1_
3
_____
_ _
_
1 3 + 1 or 1 4
=
3
3
3
3
4
1
4
1_
Rename 2_ as 1_.
3
3
3
2
-1_
3
_____
_2
3
Subtract the whole numbers and then the fractions.
Check for Reasonableness
_2 ≈ _1 ✔
3
2
Lesson 5-3 Adding and Subtracting Mixed Numbers
243
_
4 Find 8 - 3 3 .
Estimate 8 - 4 = 4
4
0
Using the denominator of the fraction in the subtrahend, 8 = 8_
.
4
0
3
is less than _
, rename 8 before subtracting.
Since _
4
4
Rename 8 as 7 + 4 or 7 .
Subtract.
Check for Reasonableness 4
j. 11_ - 2_
2
5
k. 5_ - 4_
3
5
3
8
planner is designing a
skateboard park. What
will be the length of the
park and the parking
lot combined?
_1 ≈ 4 ✔
4
l. 7 - 1_
11
12
1
2
5 MEASUREMENT An urban
Real-World Career
How Does an Urban
Planner Use Math?
An urban planner uses
math to measure and
draw site plans for
future development.
4
4
4
3
-3_
4
____
_
41
4
3
-3_
4
_____
_4
_
4
7_
8
1
40 3 ft
1
120 2 ft
3
1
1
2
120_
+ 40_
= 120_
+ 40_
2
3
6
5
= 160 + _
6
6
5
= 160_
6
Math Online
5
feet.
The total length is 160_
For more information,
go to glencoe.com.
6
m. MEASUREMENT Jermaine walked 1_ miles on Saturday and 2_ miles
5
8
1
2
on Sunday. How many more miles did he walk on Sunday?
Examples 1–4
(pp. 242–244)
Example 5
(p. 244)
Add or subtract. Write in simplest form.
1. 1_ + 8_
5
1
7
7
3
1
5. 3_ - 1_
4
4
1
4
2
5
3
2
6. 5_ - 2_
3
5
3. 7_ - 3_
5
6
1
6
3
7. 11 - 6_
8
4. 9_ - 2_
3
4
5
8. 16 - 5_
6
4
5
9. CARS A hybrid car’s gas tank can hold 11_ gallons of gasoline. It contains
9
10
3
gallons of gasoline. How much more gasoline is needed to fill the tank?
8_
4
244
2. 8_ + 3_
Chapter 5 Applying Fractions
HOMEWORK
For
Exercises
10–17
18–23
24–25
26–29
HELP
See
Examples
1, 2
3
4
5
Add or subtract. Write in simplest form.
10. 2_ + 7_
11. 3_ + 4_
3
2
7
7
3
1
_
15. 11 - 4_
3
4
3
1
_
_
19. 6 - 2
4
4
5
1
_
23. 12 - 6_
2
8
1
4
9
9
3
4
_
_
14. 9 - 2
5
10
3
1
18. 9_ - 2_
5
5
1
1
_
22. 14 - 7_
6
3
12. 10_ - 2_
13. 8_ - 6_
6
5
7
7
1
3
_
17. 8 + 10_
8
3
3
3
_
_
21. 4
-1
10
4
5
_
25. 13 - 5
6
4
1
5
5
5
1
_
16. 8
+ 11_
12
4
3
2
_
_
20. 6 - 1
5
3
2
_
24. 8 - 3
3
For Exercises 26–29, choose an operation to solve each problem. Explain your
reasoning. Then solve the problem.
26. HIKING If Sara and Maggie hiked both of the
trails listed in the table, how far did they
hike altogether?
27. JEWELRY Margarite made
Trail
Length (mi)
Woodland Park
2
3_
Mill Creek Way
2_
3
5
6
1
7 4 in.
the jewelry shown at the right.
5
inches
If the necklace is 10_
8
longer than the bracelet, how
long is the necklace that
Margarite made?
bracelet
necklace
28. GARDENS The length of Kasey’s garden is 4_ feet. Find the width of Kasey’s
5
8
7
feet shorter than the length.
garden if it is 2_
8
29. HAIRSTYLES Before Alameda got her haircut, the length of her hair
3
1
inches. After her haircut, the length was 6_
inches. How many
was 9_
2
4
inches did she have cut?
Add or subtract. Write in simplest form.
30. 10 - 3_
31. 24 - 8_
5
11
3
4
32. 6_ + 1_ + 5_
1
6
5
9
2
3
33. 3_ + 2_ - 4_
1
4
5
6
1
3
34. TIME Karen wakes up at 6:00 a.m. It takes her 1_ hours to shower, get
1
4
1
hour to eat breakfast, brush her
dressed, and comb her hair. It takes her _
2
teeth, and make her bed. At what time will she be ready for school?
MEASUREMENT Find the perimeter of each figure.
35.
3
EXTRA
PRACTICE
See pages 680, 708.
3
2 8 yd
2 8 yd
3
2 8 yd
1
5 3 in.
36.
2
4 3 in.
1
3 6 in.
5
4 6 in.
Lesson 5-3 Adding and Subtracting Mixed Numbers
245
H.O.T. Problems
37. NUMBER SENSE Which of the following techniques could be used to
3
4
1
7
+_
is greater than, less than, or equal to 2_
+ 6_
?
determine whether 6_
4
5
9
8
Justify your selection(s). Then use the technique(s) to solve the problem.
number sense
mental math
estimation
38. CHALLENGE A string is cut in half. One of the halves is thrown away.
One fifth of the remaining half is cut away and the piece left is 8 feet long.
How long was the string initially? Justify your answer.
39.
WR ITING IN MATH The fence of a rectangular garden is constructed from
5
feet long.
12 feet of fencing wire. Suppose that one side of the garden is 2_
12
Explain how to find the length of the other side.
40. The distance from home plate to the
41. A recipe for party mix calls for
3
4_
cups of cereal. The amount of
pitcher’s mound is 60 feet 6 inches and
from home plate to second base is 127
4
2
cups less than
peanuts needed is 1_
3
3
feet 3_
inches. Find the distance from
the amount of cereal needed. How
many cups of peanuts and cereal are
needed?
8
the pitcher’s mound to second base.
1
in.
A 68 ft 3_
2nd base
4
3
B 67 ft 8_
in.
4
5
C 67 ft 2_
in.
8
3
D 66 ft 9_
in.
8
1
cups
F 3_
12
1
cups
G 6_
2
5
cups
H 7_
6
1
cups
J 8_
2
Pitcher’s
mound
Home plate
42. SCHOOL Kai did _ of her homework in class and _ more of it on the bus.
1
5
1
3
What fraction of homework does she still need to do?
Estimate.
43.
(Lesson 5-1)
9
_8 ÷ _
9
(Lesson 5-2)
44. 3_ + 6_
1
2
10
45. 8_ × 7_
2
3
4
5
46. 4_ - 1_
1
9
2
9
1
4
47. MEASUREMENT To carpet a living room with a length of 17 feet, 255 square feet
of carpet is needed. Find the width of the living room.
(Lesson 3-6)
48. PREREQUISITE SKILL Andre needs to be at the train station by 5:30 p.m. It
1
1
hour to pack and 1 _
hours to get to the station. Find the latest
takes him _
3
4
time he should begin packing. Use the work backward strategy.
246
Chapter 5 Applying Fractions
(Lesson 3-4)
5
Mid-Chapter Quiz
Lessons 5-1 through 5-3
1. MONEY Latisha spends _ of her money on
3
4
a birthday present for her brother. If she
has $33, estimate the amount she spends
on her brother’s present. (Lesson 5-1)
Estimate.
18. MULTIPLE CHOICE The table shows the
weight of a newborn infant for the first
year. (Lesson 5-3)
Month
Weight (lb)
0
7
_1
4
1
_
12
2
5
_
16
8
4
_
19
5
3
_
23
(Lesson 5-1)
2. 5_ + 1_
1
7
9
8
5
11
4. _ - _
20
8
3
4
_
6. 7 ÷ 1_
5
4
3. 13_ ÷ 7_
3
5. 4_ × 1_
6
1
2
3
4
8
13
_
_
7.
+2
9
15
2
9
2
3
9
12
8. MULTIPLE CHOICE Mrs. Ortega is making 5
batches of muffins for the school bake sale.
1
1
Each batch uses 2_
cups sugar and 1_
cups
2
4
milk. Which is the best estimate of the total
amount of sugar and milk Mrs. Ortega uses
for the muffins? (Lesson 5-1)
A less than 15 cups
20
During which three-month period was the
infant’s weight gain the greatest?
F 0–3 months
H 6–9 months
G 3–6 months
J
9–12 months
19. MEASUREMENT How much does a 50_ -
1
4
7
pounds is
pound suitcase weigh after 3_
8
removed? (Lesson 5-3)
B between 15 and 20 cups
C between 20 and 25 cups
D more than 25 cups
20. MULTIPLE CHOICE The table gives the
Add or subtract. Write in simplest form.
average annual snowfall for several U.S.
cities. (Lesson 5-3)
(Lesson 5-2)
9.
11
1
_
-_
15
15
1
2
11. _ + _
2
9
10.
3
4
_
-_
7
14
5
3
12. _ + _
8
4
39
13. SCIENCE _ of Earth’s atmosphere is made
50
21
is made up of
up of nitrogen while only _
100
oxygen. What fraction of Earth’s atmosphere
is either nitrogen or oxygen?
(Lesson 5-2)
Add or subtract. Write in simplest form.
(Lesson 5-3)
14. 8_ - 2_
3
5
4
12
5
2
16. 2_ + 1_
9
3
15. 5_ - 1_
1
1
6
3
3
13
_
_
17. 2 + 6
5
15
City
Average
Snowfall (in.)
_4
Anchorage, AK
70
Mount
Washington, NH
259
Buffalo, NY
Birmingham, AL
5
_9
10
_3
5
1
_
1
93
2
Source: Fact Monster
On average, how many more inches of snow
does Mount Washington, New Hampshire,
receive than Anchorage, Alaska?
7
A 330_
in.
10
_
B 189 1 in.
10
3
C 166_
in.
10
1
D 92_
in.
10
Chapter 5 Mid-Chapter Quiz
247
Problem-Solving Investigation
5-4
MAIN IDEA: Solve problems by eliminating possibilities.
e–Mail:
ELIMINATE
POSSIBILITIES
MADISON: I am making school pennants to decorate
1 yards of fabric for each
the cafeteria. I use 1_
4
pennant.
YOUR MISSION: Eliminate possibilities to find the
greatest number of pennants Madison can make with
12 yards of fabric. Is it 6, 9, or 12?
Understand
Plan
Solve
You know she has 12 yards of fabric. Each pennant uses 1_ yards of fabric.
1
4
Eliminate the answers that are not reasonable.
Madison needs more than 1 yard of fabric for each pennant. So, she needs more
than 12 yards for 12 pennants. Eliminate this choice.
Now check the choice of 9 pennants.
1
1
1
1
• 1_ + 1_ + 1_ + 1_ = 5.
4
4
4
4
So, Madison can make 4 pennants with 5 yards of fabric. Therefore, she can
make 8 pennants out of 10 yards of fabric.
• She can also make 1 more pennant with the remaining 2 yards.
So, Madison can make 8 + 1 or 9 pennants.
Check
Making 6 pennants would take 1_ + 1_ + 1_ + 1_ + 1_ + 1_ = 7_ yards. This
4
4
4
4
4
4
2
is not the greatest number she can make. So, making 6 pennants is not reasonable.
1
1
1
1
1
1
1
1. Describe different ways that you can eliminate possibilities when solving problems.
2. Explain how the strategy of eliminating possibilities is useful for taking
multiple-choice tests.
3.
248
WR ITING IN MATH Write a problem that could be solved by eliminating possibilities.
Chapter 5 Applying Fractions
EXTRA
PRACTICE
See pages 679, 681.
Eliminate possibilities to solve Exercises 4–6.
4. TRAINS A train passes through an
intersection at the rate of 3 cars per 30
seconds. Assume that it takes 5 minutes for
the train to completely pass through
the intersection. How many cars does the
train have altogether?
A 6 cars
C 30 cars
B 15 cars
D 45 cars
8. BRIDGES A covered bridge has a maximum
capacity of 48,000 pounds. If an average
school bus weighs 10,000 pounds, about
how many school buses could a covered
bridge hold?
9. GEOMETRY Draw the next two figures in
the pattern.
5. PIZZA A pizza shop used 100 pounds of
pizza dough to make 125 pizzas. If a large
pizza requires 1 pound of dough and a
1
medium pizza requires _
pound, how many
2
large- and medium-sized pizzas were made?
14 hours of sleep each day while a teenager
needs about 10 hours of sleep each day.
How much more sleep does a 9-month-old
need than a teenager? Write as a fraction of
a day.
F 40 large, 85 medium
G 65 large, 60 medium
H 55 large, 70 medium
J
10. SLEEP A 9-month-old infant needs about
75 large, 50 medium
6. PILLOWS Pat is making pillows out of fabric.
3
He uses _
yard of fabric for each pillow.
4
What is the greatest number of pillows Pat
can make with 9 yards of fabric: 9, 12, or 15?
Use any strategy to solve Exercises 7–14.
Some strategies are shown below.
Her ticket costs $7.25, drinks are $3.50,
popcorn is $5.75, and pretzels are $4.25.
Which two items can Kristen get from the
concession stand?
7. MEASUREMENT The diagram shows a shelf
1
inch thick,
that holds CDs. Each shelf is _
8
and the distance between shelves is as
shown. How much space is available on
each layer of the shelf for a CD?
in.
3
average annual precipitation is 50_
inches.
5
1
_
Is
inch, 1 inch, or 14 inches the best
49
estimate for the average precipitation
per day?
12. MONEY Kristen has $15 to go to the movies.
G STRATEGIES
PROBLEM-SOLVIN
rn.
• Look for a patte
.
rd
• Work backwa
ized list.
• Make an organ
in.
11. PRECIPITATION In Olympia, Washington, the
13. PIZZA Sebastian ate _ of a pizza while his
2
5
1
sister ate _
of the same pizza. The remainder
3
was stored in the refrigerator. What fraction
of the pizza was stored in the refrigerator?
14. GRADES Jerome had an average of 88 on his
first three science tests. His score on the
second and third tests were 92 and 87.
What was his score on the first test?
Lesson 5-4 Problem-Solving Investigation: Eliminate Possibilities
249
Explore
5-5
MAIN IDEA
Math Lab
Multiplying Fractions
Just as the product of 3 × 4 is the number of square units in a rectangle,
the product of two fractions can be shown using area models.
Use area models to
multiply fractions and
mixed numbers.
_ _
1 Find 3 × 2 using a geoboard.
Math Online
3
4
The first factor is 3 fourths and the second factor is 2 thirds.
glencoe.com
Use one geoband to show fourths and another to show
thirds on the geoboard.
• Concepts In Motion
Use geobands to form a rectangle. Place one geoband on
the peg to show 3 fourths and another on the peg to show
2 thirds.
Connect the geobands to show a small rectangle.
1
3
1
3
1
3
2
3
1
4
1
4
1
4
1
4
3
4
The area of the small square is 6 square units. The area of the large
3
6
2
1
rectangle is 12 square units. So, _
×_
=_
or _
.
3
4
12
2
Find each product using a geoboard.
a.
_1 × _1
4
b.
3
_1 × _1
2
c.
2
_3 × _1
4
_
2 Find 2 × 1 using an area model.
4
2
To represent 2 or _, draw
1
2 large rectangles, side
by side. Divide each rectangle
horizontally into fourths. Color
both large rectangles blue.
250
Chapter 5 Applying Fractions
2
d.
_2 × _1
3
2
4
Color 1 fourth of each large
rectangle yellow.
Shading
Yellow and blue make
green. So, the green
sections have been shaded
twice and represent the
product.
2
1
4
The fraction that compares the number
of green sections, 2, to the number of
2
1
or _
.
sections in one rectangle, 4, is _
4
2
4
1
1
=_
.
So, 2 × _
2
Find each product using a model.
e. 3 × _
f. 2 × _
2
3
g. 4 × _
2
5
h. 3 × _
3
4
1
2
_ _
3 Find 1 2 × 1 using a model.
3
2
Draw 2 rectangles
divided vertically into
thirds and horizontally
2
13
into halves. Color 1_ of the
2
3
squares blue.
Color _ of the squares yellow.
2
1
2
13
Then count the small squares
that are green.
1
2
3
2
Since the green area is _
of the first rectangle and _
of the second
6
6
3
5
5
2
2
1
rectangle, the total area shaded green is _
+_
or _
. So, 1_
×_
=_
.
6
6
6
3
2
6
Find each product using a model.
i. 1_ × _
1
4
1
5
j. 2_ × _
1
2
3
4
k. 1_ × _
2
3
1
3
ANALYZE THE RESULTS
1. Analyze Exercises a–k. What is the relationship between the
numerators of the factors and of the product? between the
denominators of the factors and of the product?
2. MAKE A CONJECTURE Write a rule you can use to multiply
two fractions.
Explore 5-5 Math Lab: Multiplying Fractions
251
5-5
Multiplying Fractions and
Mixed Numbers
MAIN IDEA
Multiply fractions and
mixed numbers.
Math Online
glencoe.com
• Extra Examples
• Personal Tutor
• Self-Check Quiz
LUNCH Two thirds of the students at
the lunch table ordered a hamburger
for lunch. One half of those students
ordered cheese on their hamburgers.
1. What fraction of the students
at the lunch table ordered a
cheeseburger?
2. How are the numerators and
2
1
denominators of _
and _
related
3
2
to the fraction in Exercise 1?
Key Concept
Multiply Fractions
Words
To multiply fractions, multiply the numerators and multiply the
denominators.
Examples
Numbers
Algebra
1×2
2
_1 × _2 = _
or _
2
3
2×3
a·c
ac
_a · _c = _
or _ , where b, d ≠ 0
6
b
d
b·d
bd
Multiply Fractions
Multiply. Write in simplest form.
_ _
1 1×1
2 3
1×1
_1 × _1 = _
2
3
2×3
1
_
=
6
2 2× 3
4
3
3
2
2×_
=_
×_
4
1
4
2
×
3
=_
1×4
6
1
=_
or 1_
2
4
1
2
Multiply the numerators.
Multiply the denominators.
1
3
Simplify.
_
Whole Numbers
When multiplying a fraction
by a whole number, write
the whole number as a
fraction with a denominator
of 1.
252
1 shaded green
6
_2
2
Write 2 as .
1
Multiply the numerators.
Multiply the denominators.
3
4
Simplify.
6 or 1 1 shaded green
2
4
a.
Chapter 5 Applying Fractions
_3 × _1
5
2
b.
_1 × _3
3
4
c.
_2 × 4
3
If the numerator and denominator of either fraction have common
factors, you can simplify before multiplying.
Simplify Before Multiplying
Review Vocabulary
GCF the greatest of the
common factors of two or
more numbers; Example: the
GCF of 8 and 12 is 4.
(Lesson 4-2)
_ _
3 Find 2 × 3 . Write in simplest form.
7
1
8
_2 × _3 = _2 × _3
7
8
7
Divide 2 and 8 by their GCF, 2.
8
4
1×3
3
=_
or _
7×4
28
Multiply.
Multiply. Write in simplest form.
d.
_1 × _3
3
e.
7
_4 × _1
9
_5 × _3
f.
8
6
5
Multiply Mixed Numbers
_
_
4 Find 1 × 4 2 . Write in simplest form.
5
2
METHOD 1
2
_2
5
2
5
1
22
_
Rename 4 as an improper fraction,
.
5
5
Divide 2 and 22 by their GCF, 2.
22
_1 × 4_2 = _1 × _
2
_1 × 4 = 2
Rename the mixed number.
11
Simplifying
If you forget to simplify
before multiplying, you can
always simplify the final
answer. However, it is
usually easier to simplify
before multiplying.
Estimate
1 × 11
=_
Multiply.
1×5
1
11
=_
or 2_
Simplify.
5
5
METHOD 2
Use mental math.
2
2
is equal to 4 + _
.
The mixed number 4 _
5
(
5
)
1
2
1
2
× 4_
=_
4+_
. Use the Distributive Property to multiply,
So, _
2
5
2
5
then add mentally.
(
)
_1 4 + _2 = 2 + _1
2
5
5
1
= 2_
5
1
2
1
So, _
× 4_
= 2_
.
2
5
5
THINK Half of 4 is 2 and half of 2 fifths is 1 fifth.
Rewrite the sum as a mixed number.
1
Check for Reasonableness 2_ ≈ 2
5
✔
Multiply. Write in simplest form.
g.
_1 × 8_4
4
9
h. 5_ × 3
1
3
i. 1_ × 2_
7
8
2
5
Lesson 5-5 Multiplying Fractions and Mixed Numbers
253
Meaning of Multiplication
Recall that one meaning of
3 × 4 is three groups with
4 in each group. In
Example 5, there are
1 in
365 _41 groups with _
3
each group.
1
5 SLEEP Humans sleep about _
of each day. If each year is equal to
3
1
365_
days, determine the number of days in a year the average
4
human sleeps.
_
1
1
Humans sleep about _ of 365 days.
Words
3
4
Let d represent the number of days a human sleeps.
Variable
Equation
=
d
1
1
d=_
· 365_
_1 ·
3
365 _
4
1
Write the equation.
3
4
1,46 1
1 _
_
d= ·
3
4
Rename the mixed number as an improper fraction.
487
1,461
1 _
d=_
·
3
Divide 3 and 1,461 by their GCF, 3.
4
1
487
3
d=_
or 121_
4
4
Multiply. Then rename as a mixed number.
3
The average human sleeps 121_
days each year.
4
4
6 ANIMALS The house cat has an average lifespan that is _
of a lion’s.
5
If a lion’s lifespan is 15 years, find the average lifespan of a
house cat.
4
The lifespan of a house cat is _ of that of the lion.
Words
5
Let c represent the lifespan of a house cat.
Variable
Equation
4
c=_
· 15
Real-World Link
The average group of
lions, called a pride,
consists of about 15
2
lions with about of
3
the pride being female.
_
Source: African Wildlife Foundation
= _
5
4
c
·
15
Write the equation.
5
15
_
c= 4 ·_
5 1
Write the whole number 15 as an improper fraction.
3
4 _
c=_
· 15
5
1
Divide 5 and 15 by their GCF, 5.
1
12
c=_
or 12
Multiply, then simplify.
1
The average lifespan of a house cat is 12 years.
j. COOKING Sofia wishes to make _ of a recipe. If the original recipe
1
2
3
calls for 3_
cups of flour, how many cups should she use?
4
254
Chapter 5 Applying Fractions
Examples 1–4
(pp. 252–253)
Examples 5, 6
(p. 254)
HOMEWORK
For
Exercises
8–11
12–19
20–23
HELP
See
Examples
1, 2
3, 4
5, 6
Multiply. Write in simplest form.
1.
_2 × _1
2. 2 × _
4.
_1 × _8
5. 2_ × _
3
2
5
3
1
4
9
4
3.
_1 × 4
6
6. 1_ × 3_
5
6
2
3
3
5
7. WEIGHT The weight of an object on Mars is about _ its weight on
2
5
Earth. How much would an 80-pound dog weigh on Mars?
Multiply. Write in simplest form.
3
1
2
2
8. _ × _
9. _ × _
8
3
4
5
5
1
1
4
12. _ × _
13. _ × _
4
6
9
5
15
7
4
2
16. _ × _
17. _ × _
7
8
16
5
10.
1
9×_
11.
2
1
2
14. _ × _
4
3
10
3
18. _ × _
27
8
_4 × 6
5
3
1
15. _ × _
12
5
5
9
19. _ × _
6
10
20. DVDs Each DVD storage case is about _ inch thick. What will be the height
1
5
of 12 cases sold together in plastic wrapping?
21. PIZZA Mark left _ of a pizza in the refrigerator. On Friday, he ate _ of what
3
8
1
2
was left of the pizza. What fraction of the entire pizza did he eat on Friday?
22. MEASUREMENT The width of a vegetable garden is _ times its length. If the
3
length of the garden is 7_
feet, what is the width?
1
3
4
23. RECIPES A recipe to make one batch of blueberry muffins calls for 4_ cups
2
3
of flour. How many cups of flour are needed to make 3 batches of blueberry
muffins?
Multiply. Write in simplest form.
24. 4_ × _
25.
_5 × 2_1
26. 14 × 1_
27. 3_ × 8
28. 9 × 4_
29. 4 × 7_
30. 3_ × 2_
31. 5_ × 3_
2
3
4
7
8
2
5
6
2
3
1
7
1
4
2
3
3
4
1
3
3
4
32. MEASUREMENT The width of the fish
2
of its length. What is the width
tank is _
5
of the fish tank?
33. BICYCLING Philip rode his bicycle at 9_ miles
2
5
3
of an hour, how
per hour. If he rode for _
4
many miles did he cover?
30 in.
Lesson 5-5 Multiplying Fractions and Mixed Numbers
255
Evaluate each verbal expression.
34. one half of five eighths
35. four sevenths of two thirds
36. nine tenths of one fourth
37. one third of eleven sixteenths
MEASUREMENT Find the perimeter and area of each rectangle.
38.
39.
1
3 2 ft
2
1 3 yd
1
6 2 yd
1
5 4 ft
40. POOLS A community swimming pool is 90_ feet long and 55_ feet wide.
2
5
1
2
If Natalie swims the perimeter of the pool four times, what is the total
number of feet she will swim? Explain how you solved the problem.
MEASUREMENT For Exercises 41–44, use measurement conversions.
41. Find _ of _ of a gallon.
1
1
2
4
1
1
43. Find _ of _ of a kilometer.
100
1,000
42. What is _ of _ of a day?
1
1
60
24
1
1
44. What is _ of _ of a yard?
3
12
_
_
ALGEBRA Evaluate each expression if a = 4, b = 2 1 , and c = 5 3 .
2
45. a × b + c
Real-World Link
There are an
estimated 5 million
in-ground swimming
pools in the U.S.
46. b × c - a
4
47. 2bc
48. TELEVISION One evening, _ of the students in Rick’s class watched
2
3
3
1
of those students watched a reality show, of which _
television, and _
8
4
taped the show. What fraction of the students in Rick’s class watched and
taped a reality TV show?
Source: Pool & Spa Service
Industry News
49. FOOD Alano wants to make one and a
half recipes of the pasta salad recipe
shown at the right. How much of each
ingredient will Alano need? Explain how
you solved the problem.
50. FIND THE DATA Refer to the Data File on
pages 16–19. Choose some data and write
a real-world problem in which you would
multiply fractions.
Pasta Salad Recipe
Ingredient
broccoli
cooked pasta
salad dressing
cheese
Amount
_1
4
3
_
3 c
4
_2 c
3
1
_
1 c
1 c
3
Write and evaluate a multiplication expression to represent each model.
Explain how the models show the multiplication process.
51.
EXTRA
PRACTICE
See pages 680, 708.
256
Chapter 5 Applying Fractions
52.
H.O.T. Problems
53. CHALLENGE Two improper fractions are multiplied. Is the product
sometimes, always, or never less than 1? Explain your reasoning.
54. OPEN ENDED Write a word problem that involves finding the product
3
1
of _
and _
.
8
4
55.
WR ITING IN MATH Refer to Example 2. Explain how the model represents
the meaning of the multiplication process.
56. Of the dolls in Marjorie’s doll
57. Which description gives the
1
have red hair. Of these,
collection, _
5
3
_ have green eyes. What fraction of
relationship between a term and n,
its position in the sequence?
4
Marjorie’s doll collection has both red
hair and green eyes?
2
A _
9
4
C _
9
3
B _
19
D _
20
Position
1
2
3
4
5
Value of Term
_1
_1
_3
4
2
4
1
1_
n
1
4
F Subtract 4 from n.
1
G Add _
to n.
20
4
1
.
H Multiply n by _
1
J Divide n by _
.
4
4
58. MEASUREMENT Find which room dimensions would give an area of
3
125_
square feet. Use the eliminate possibilities strategy.
8
(Lesson 5-4)
3
1
A 11_
feet by 10_
feet
2
8
5
C 13_
feet by 9 feet
8
7
1
B 10_
feet by 12_
feet
3
1
D 14_
feet by 8_
feet
8
4
4
2
59. MEASUREMENT How much longer is a 2_ -inch-long piece of string than
2
a_
-inch-long piece of string?
5
1
2
(Lesson 5-3)
Replace each ● with <, >, or = to make a true sentence.
60.
5
2
_
●_
12
5
61.
(Lesson 4-9)
3
1
_
●_
16
62. 3_ ● 3_
7
6
8
6
5
63. PHONES A long-distance telephone company charges a flat monthly fee
of $4.95 and $0.06 per minute on all long-distance calls. Write and solve
an equation to find the number of monthly minutes spent talking
long-distance if the bill total was $22.95. (Lesson 3-5)
PREREQUISITE SKILL Solve each equation mentally.
64. x + 2 = 8
65. 9 + m = 12
(Lesson 1-7)
66. 7 - w = 2
Lesson 5-5 Multiplying Fractions and Mixed Numbers
257
5-6
Algebra: Solving Equations
MAIN IDEA
1
HOMEWORK Shawnda spends _
hour doing homework after school.
Solve equations with
rational number
solutions.
1
Then she spends another _
hour doing homework before bed.
2
2
1. Write a multiplication expression to find how much time
Shawnda spends doing homework. Then find the product.
New Vocabulary
2. Copy and complete the table below.
multiplicative inverse
reciprocal
_1 ×
_3 × _2 =
2
Math Online
_5 × _6 =
=1
5
3
5
×_=1
7
_2 × _6 =
2
6
_7 × _8 =
5
6
_7 × = 1
1
8
7
×8=1
glencoe.com
3. What is true about the numerators and denominators in the
• Extra Examples
• Personal Tutor
• Self-Check Quiz
fractions in Exercise 2?
Two numbers with a product of 1 are called multiplicative inverses,
or reciprocals.
Key Concept
Inverse Property of Multiplication
Words
Examples
The product of a number and its multiplicative inverse is 1.
Numbers
Algebra
_3 × _4 = 1
4
_a · _b = 1, for a, b ≠ 0
3
b
a
Find Multiplicative Inverses
_
1 Find the multiplicative inverse of 2 .
_2 · _5 = 1
5
2
5
5
2
Multiply _ by _ to get the product 1.
5
2
2 _
1
The multiplicative inverse of _
is 5 , or 2_
.
5
2
2
1
Find the multiplicative inverse of 2_
.
1
7
2_
=_
3
3
_7 · 3 = 1
3 7
_
2
3
Rename the mixed number as an improper fraction.
Multiply
_7 by _3 to get the product 1.
3
7
1 _
The multiplicative inverse of 2_
is 3 .
3
a.
258
Chapter 5 Applying Fractions
_5
6
b. 1_
1
2
7
c. 8
d.
_4
3
In Chapter 3, you learned to solve equations using the Addition,
Subtraction, and Division Properties of Equality. You can also solve
equations by multiplying each side by the same number. This is called
the Multiplication Property of Equality.
Key Concept
Multiplication Property of Equality
Words
If you multiply each side of an equation by the same nonzero
number, the two sides remain equal.
Examples
Numbers
_x = -3
5=5
Fractions
The fraction bar
indicates division. So, _2x
means x divided by 2.
Algebra
_2 x = 4
3
_3 · _2 x = _3 · 4
2
5·2=5·2
_x (2) = -3(2)
10 = 10
x = -6
2
2
3
2
x=6
Solve a Division Equation
_
3 Solve 7 = n . Check your solution.
4
n
7=_
4
n
_
7·4= ·4
4
28 = n
Check
n
7=_
4
28
7_
4
7=7 ✔
Write the equation.
Multiply each side of the equation by 4.
Simplify.
Write the original equation.
Replace n with 28.
Is this sentence true?
_
4 Solve d = 4.2.
3.5
d
_
= 4.2
3.5
Write the equation.
d
_
· 3.5 = 4.2 · 3.5
3.5
Multiply each side by 3.5.
d = 14.7
Simplify.
The solution is 14.7.
Check
d
_
= 4.2
Write the original equation.
3.5
14.7
_
4.2
3.5
Replace d with 14.7.
4.2 = 4.2 ✔
Is this sentence true?
Solve each equation. Check your solution.
e. 6 = _
m
8
f.
p
_
= 1.5
2.8
g.
k
_
= 2.3
4.7
Lesson 5-6 Algebra: Solving Equations
259
Solve a Multiplication Equation
_
_
5 Solve 3 x = 12 .
20
4
12
_3 x = _
20
4
3
4 _
12
· x= 4 ·_
3
3
20
4
(_)
Fractions as Coefficients
3 x can
The expression _
4 3
3
be read as _
of
x, _4
4
multiplied by x, 3x
x
divided by 4, or _
4
multiplied by 3.
Write the equation.
(_)
1
1
1
4
3
4
3
20
Multiply each side by the reciprocal of _, _.
3 4
4 3
12
_4 · _3 x = _4 · _
1
1
1
Divide by common factors.
5
4
x=_
Simplify.
5
Solve each equation. Check your solution.
h.
_1 x = 8
i.
2
_3 x = 9
21
_7 x = _
j.
4
8
64
_
6 Valerie needs 2 yard of fabric to make each hat for the school play.
3
How many hats can she make with 6 yards of fabric?
A 12
C 8
B 9
D 4
Read the Item
2
Each hat needs _
yard of fabric. Given the number of hats, you
3 2
would multiply by _ to find the number of yards of fabric needed.
3
Solve the Item
Verify Your Answer
It is a good idea to
verify your answer by
checking the other
answer choices. By
doing so, you can
greatly reduce your
chances of making
an error.
Write and solve a multiplication equation.
_2 n = 6
3
3
3
_
· 2n =
·6
2
2
3
(_)
(_ )
n=9
Write the equation.
_3
Multiply each side by .
2
Simplify.
So, the answer is B.
k. Wilson has 9 pounds of trail mix. How many _ -pound bags of
260
Chapter 5 Applying Fractions
3
4
trail mix can he make?
F 3
H 9
G 6
J
12
Examples 1, 2
(p. 258)
Examples 3–5
(p. 259–260)
Example 5
(p. 260)
Find the multiplicative inverse of each number.
1.
_8
2.
5
_2
3. 5_
4
5
9
4. 9
Solve each equation. Check your solution.
5.
k
_
=2
8.
h
0.5 = _
y
3
6. 4 = _
16
9.
3.6
7.
12
_3 a = _
8
b
_
= 2.5
8.2
10. 6 = _x
4
7
40
11. FRUIT Three fourths of the fruit in a refrigerator are apples. There are
24 apples in the refrigerator. The number of pieces of fruit is given by the
3
equation _
f = 24. How many pieces of fruit are in the refrigerator?
4
Example 6
(p. 260)
HOMEWORK
For
Exercises
13–20
21–26
33–34
27–32
51–52
HELP
See
Examples
1, 2
3, 4
5
6
12. MULTIPLE CHOICE Dillon deposited _ of
3
4
his paycheck into the bank. The deposit
slip shows how much he deposited.
What was the amount of his paycheck?
A $15
C $60
B $33.75
D $75
Dillon Gates
Find the multiplicative inverse of each number.
13.
_5
6
17. 3
14.
11
_
2
18. 14
15.
_1
19.
1
5_
1
_
16.
6
10
2
20. 6_
3
8
Solve each equation. Check your solution.
21.
x
_
=3
24.
w
5=_
12
4.9
2
12
_
27. t = _
5
25
8
2
_
_
30.
= b
3
3
22. 28 = _
d
4
25.
h
0.8 = _
3.6
3
24
_
_
28.
= a
16
4
1
1
_
31. g = 3_
2
3
23.
b
_
=6
26.
m
_
= 2.8
29.
_7 k = _5
32.
_3 c = 6_1
2.4
4.6
8
5
6
4
33. DISTANCE The distance d Toya travels in her car while driving
d
60 miles per hour for 3.25 hours is given by the equation _
= 60.
3.25
How far did she travel?
34. ANIMALS An adult Fitch ferret weighs about 1.8 kilograms. To find its
p
weight in pounds p, you can use the equation _ = 2.2. How many pounds
1.8
does an adult Fitch ferret weigh?
Lesson 5-6 Algebra: Solving Equations
261
Solve each equation. Check your solution.
35.
a
_
= 15
36. -8 = _
38.
_5 x = -1.5
39.
37. 34.5 = _m
5
6
r
-2
-5
7
_1 t = _3
40.
8
4
_3 m = 1_1
8
2
For Exercises 41–46, define a variable and write an equation. Then solve.
41. CAVES The self-guided Mammoth Cave Discovery Tour includes an
7
elevation change of 140 feet. This is _
of the elevation change on the Wild
15
Cave Tour. What is the elevation change on the Wild Cave Tour?
42. MUSEUMS Twenty-four students brought their permission slips to attend
Real-World Link
Kentucky’s Mammoth
Cave is the longest
recorded cave system
in the world, with
more than 360 miles
explored and
mapped. The Wild
Cave Tour requires
visitors to crawl
through an opening
only 9 inches high.
Source: National Park Service
4
the class field trip to the local art museum. If this represented _
of the class,
5
how many students are in the class?
43. MEASUREMENT If one serving of cooked rice is _ cup, how many servings
3
4
1
will 16_
cups of rice yield?
2
44. HIKING After Alana hiked 2_ miles along a hiking trail, she realized that
5
8
3
she was only _
of the way to the end of the trail. How long is the trail?
4
45. SLEEP The average person spends _ of his life asleep. According to this, if a
1
3
person has spent 26 years asleep, how old is he?
46. ANALYZE TABLES Tierra recorded the
EXTRA
PRACTICE
See pages 681, 708.
H.O.T. Problems
Distance Ran in One Week
distance she ran each day last week.
5
If she ran _
of her weekly running goal,
6
what was her running goal?
Day
47. REASONING Complete the statement: If 8 = _,
then m - 12 =
. Explain your reasoning.
m
4
Distance (mi)
Monday
1
Wednesday
2
_3
4
_1
2
1
_
2
Friday
1
Saturday
4
48. Which One Doesn’t Belong? Identify the pair of numbers that does not belong
with the other three. Explain.
6
9 _
_
,
6 9
1
4, _
4
_3 , 5
_2 , _7
5
7 2
49. CHALLENGE The formula for the area of a
b1
1
trapezoid is A = _
h(b1 + b2), where b1 and b2
2
are both bases and h is the height. Find the
value of h in terms of A, b1, and b2. Justify
your answer.
h
b2
50.
WR ITING IN MATH Explain the Multiplication
Property of Equality. Then give an example of
an equation in which you would use this
property to solve the equation.
262
Chapter 5 Applying Fractions
51. Audrey drove 200 miles in 3.5 hours.
52. The table shows the results of a survey.
Which equation can you use to find
the rate r at which Audrey was
traveling?
Music Preference
Type
Fraction of Students
pop
_5
B 200 · 3.5 = r
jazz
_1
r
C _
= 200
rap
_1
A 200 = 3.5r
8
8
4
3.5
D 200r = 3.5
If there are 420 students surveyed,
which equation can be used to find the
number of students s who prefer rap?
1
F _
s = 420
1
H s+_
= 420
4
4
1
1
· 420 J 420 + s = _
G s=_
4
4
Multiply. Write in simplest form.
3
4
53. _ × _
8
9
(Lesson 5-5)
1
54. 1_ × 6
2
55. 2_ × _
2
5
56. 1_ × 1_
1
6
1
2
7
9
57. COOKING Lawana had 4_ cups of chopped walnuts. She used 1_ cups in
2
3
1
4
a recipe. How many cups of chopped walnuts are left?
Write each percent as a decimal.
58. 25%
(Lesson 5-3)
(Lesson 4-7)
59. 8%
60. 25.6%
61. 123%
62. MEASUREMENT A farmer has a rectangular pumpkin field with a perimeter
of 3,800 feet. If the width of the pumpkin field is 800 feet, what is the
length of the field? (Lesson 3-6)
ALGEBRA Solve each equation. Check your solution.
63. 7 = x + 8
64. k - 3 = -14
66. ALGEBRA The table below shows the
time needed to complete 4 art projects.
If the pattern continues, how much
time is needed to complete the fifth
art project? (Lesson 2-7)
PREREQUISITE SKILL Estimate.
67. 18_ ÷ 3
1
6
(Lesson 3-2)
Project
1
2
3
4
Time (min)
8
25
42
59
70.
9
6
_
÷_
5
(Lesson 5-1)
68. 24_ ÷ 11_
3
8
65. -2 = m + 6
7
9
69.
2
11
_
÷_
11
12
10
7
Lesson 5-6 Algebra: Solving Equations
263
Meaning of Division
You know that one meaning of division is to put objects into equal
groups. But there are other meanings too. Look for these meanings
when you’re solving a word problem.
To share
Zach and his friend are going to share 3 apples
equally. How many apples will each boy have?
To take away equal amounts
Isabel is making bookmarks from a piece of
ribbon. Each bookmark is 6.5 centimeters long.
How many bookmarks can she make from a
piece of ribbon that is 27 centimeters long?
26 cm
6.5 cm
6.5 cm
6.5 cm
6.5 cm
To find how many times greater
The Nile River, the longest river on Earth,
is 4,160 miles long. The Rio Grande River
is 1,900 miles long. About how many times
longer is the Nile than the Rio Grande?
Nile River 4,160 mi
Rio Grande 1,900 mi Rio Grande 1,900 mi
1. Solve each problem above.
Identify the meaning of division shown in each problem.
Then solve the problem.
2. A landscape architect wants to make a border along one side of a
garden using bricks that are 0.25 meter long. If the garden is 11.25
meters long, how many bricks does she need?
3. The Jackson family wants to buy a flat-screen television that costs
$1,200. They plan to pay in six equal payments. What will be the
amount of each payment?
4. A full-grown blue whale can weigh 150 tons. An adult African
elephant weighs about 5 tons. How many times greater does a blue
whale weigh than an African elephant?
5. Each story in an office building is about 4 meters tall. The Eiffel Tower
in Paris, France, is 300 meters tall. How many stories tall is the Eiffel
Tower?
264
Chapter 5 Applying Fractions
5-7
Dividing Fractions
and Mixed Numbers
MAIN IDEA
Cut two paper plates into four equal
pieces each to show 2 ÷ 1 .
_
Divide fractions and
mixed numbers.
4
1.
Math Online
4
2. How would you model 3 ÷ _?
glencoe.com
• Concepts In Motion
• Extra Examples
• Personal Tutor
• Self-Check Quiz
1
4
1
4
1
How many _
’s are in 2 plates?
1
2
1
4
1
4
1
4
1
4
1
4
1
4
3. What is true about 3 ÷ _ and 3 × 2?
1
2
1
Dividing 8 by 2 gives the same result as multiplying 8 by _
, which
2
1
is the same as
is the reciprocal of 2. In the same way, dividing 4 by _
3
1
, or 3.
multiplying 4 by the reciprocal of _
3
reciprocals
_
8· 1 =4
2
8÷2=4
_
reciprocals
4 ÷ 1 = 12
3
same result
4 · 3 = 12
same result
Is this pattern true for any division expression?
_7
3
8
7
Consider _
÷_
, which can be rewritten as _
.
8
_7
_7 × _4
_3
_3 × _4
_3
4
4
Multiply the numerator and denominator
3
4
by the reciprocal of , which is .
3
8
_8 = _
4
_
_
4
3
4
_7 × _4
3
_3 × _4 = 1
8
3
=_
4
1
3
7
4
=_
×_
8
3
3
7
7
4
÷_
=_
×_
. These examples suggest the following rule.
So, _
8
4
8
3
Key Concept
Divide by Fractions
Words
Examples
To divide by a fraction, multiply by its multiplicative inverse,
or reciprocal.
Numbers
_7 ÷ _3 = _7 · _4
8
4
8
3
Algebra
_a ÷ _c = _a · _d , where b, c, d ≠ 0
b
d
b
c
Lesson 5-7 Dividing Fractions and Mixed Numbers
265
Divide by a Fraction
_ _
1 Find 3 ÷ 1 . Write in simplest form.
2
4
Estimate 1 ÷
_1 =
2
Think: How many groups of
_3 ÷ _1 = _3 · _2
2
4
2
2
_1
_2
Multiply by the reciprocal of , which is .
2
1
4
_1 are in 1? 1 ÷ _1 = 2
1
1
3 _
=_
·2
4
Divide 4 and 2 by their GCF, 2.
1
2
3
1
=_
or 1_
2
Multiply.
2
1
1_
≈2 ✔
Check for Reasonableness
2
Divide. Write in simplest form.
a.
_3 ÷ _1
4
b.
4
_4 ÷ _8
5
c.
9
_5 ÷ _2
6
3
To divide by a mixed number, first rename the mixed number as an
improper fraction. Then multiply the first fraction by the reciprocal,
or multiplicative inverse, of the second fraction.
Divide by Mixed Numbers
_ _
2 Find 2 ÷ 3 1 . Write in simplest form.
3
Estimate
3
_1 ÷ 3 = _1 × _1 or _1
2
2
10
_2 ÷ 3_1 = _2 ÷ _
3
3
3
3
3
2
=_·_
3 10
1
1
3
10
2 _
=_
· 3
1
1
=_
5
3
3
266
_1
Rename 3 as an improper fraction.
3
Multiply by the reciprocal of
10
3
_
, which is _.
3
10
Divide out common factors.
5
Multiply.
Check for Reasonableness
Dividing by a Whole
Number
Remember that a whole
number can be written
as a fraction with a 1 in
the denominator.
1
So, 2 _ ÷ 5 can be
3
5
1
rewritten as 2 _ ÷ _.
6
_1 is close to _1 . ✔
5
6
Divide. Write in simplest form.
d. 5 ÷ 1_
1
3
e. - _ ÷ 1_
3
4
1
2
f. 2_ ÷ 5
1
3
g. NUTS In planning for a party, 5_ pounds of cashews will
1
Chapter 5 Applying Fractions
1
4
3
be divided into _
-pound bags. How many such bags can
4
be made?
3 WOODWORKING Students in a
woodworking class are making
butterfly houses. The side pieces of
the house need to be 8 1 inches long.
4
How many side pieces can be cut from
_
_
1
a board measuring 49 1 inches long?
8 4 in.
2
To find how many side pieces can be cut,
1
1
by 8_
.
divide 49_
2
4
48 ÷ 8 = 6
Estimate Use compatible numbers.
99
33
1
1
49_
÷ 8_
=_
÷_
2
4
Rename the mixed numbers as improper fractions.
2
4
99
4
=_·_
2 33
3
2
2
33
Multiply by the reciprocal of
99 _
=_
· 4
1
33
4
_
, which is _.
4
33
Divide out common factors.
1
6
=_
or 6
Multiply.
1
So, 6 side pieces can be cut.
Check for Reasonableness The answer matches the estimate.
✔
h. FOOD Suppose a small box of cereal contains 12_ cups of cereal.
1
-cup servings are in the box?
How many 1_
2
3
3
i. MEASUREMENT The area of a rectangular bedroom is 146_ square
7
8
3
feet. If the width of the bedroom is 11_
feet, find the length.
4
Examples 1–3
(pp. 266–267)
Divide. Write in simplest form.
1.
_1 ÷ _1
8
3
1
1
_
5.
÷ 7_
2
2
Example 2
(p. 266)
Example 3
(p. 267)
2.
_3 ÷ _1
5
4
4
2
_
6.
÷ 1_
7
7
3. 3 ÷ _
6
7
7.
4.
3
2
5_
÷ 4_
5
3
_3 ÷ 6
4
8. 6_ ÷ 3_
1
2
5
7
9. FOOD Deandre has 7 apples, and each apple is divided
evenly into eighths. How many apple slices does
Deandre have?
10. WALKING On Saturday, Lindsay walked 3_ miles
2
hours. What was her walking pace,
in 1_
1
2
5
in miles per hour?
Lesson 5-7 Dividing Fractions and Mixed Numbers
267
HOMEWORK
For
Exercises
11–14
15–32
HELP
See
Examples
1
2, 3
Divide. Write in simplest form.
11.
_3 ÷ _6
12.
8
7
1
15. 6 ÷ _
2
_5 ÷ _5
13.
9
6
4
16. _ ÷ 2
9
_2 ÷ _1
3
_7 ÷ _3
14.
2
8
4
1
18. 5 ÷ 1_
3
17. 2_ ÷ 4
2
3
19. FOOD Mason has 8 cups of popcorn kernels to divide into _ -cup portions.
2
3
How many portions will there be?
20. MOVIES Cheryl is organizing her movie collection. If each movie case is
_3 inch wide, how many movies can fit on a shelf 5 feet wide?
4
Divide. Write in simplest form.
21.
_2 ÷ 2_1
3
2
25. 3_ ÷ 1_
4
5
1
3
22.
_8 ÷ 5_1
9
3
26. 9_ ÷ 2_
5
6
1
2
23. 4_ ÷ 6_
24. 5_ ÷ 2_
3
1
2
4
1
2
_
_
27. 5 ÷
5
3
2
1
7
7
3
7
_
_
28. 6 ÷
8
4
29. ICE CREAM Vinh bought 4_ gallons of ice cream to serve at his birthday
1
2
1
of a gallon, how many pint-sized servings can be made?
party. If a pint is _
8
30. BEVERAGES William has 8_ cups of fruit juice. If he divides the juice
1
4
3
-cup servings, how many servings will he have?
into _
4
BIRDS For Exercises 31 and 32, use the table
that gives information about several types
of birds of prey found at the Woodland Park
Zoo in Seattle, Washington.
31. How many times as heavy is the Golden
Eagle as the Red-tailed Hawk?
32. How many times as heavy is the Golden
Eagle as the Northern Bald Eagle?
Bird
Golden Eagle
Northern
Bald Eagle
Red-Tailed Hawk
Maximum
Weight (lb)
_9
10
9
_
9
10
1
3_
13
2
Source: Woodland Park Zoo
Draw a model of each verbal expression and then evaluate the expression.
Explain how the model shows the division process.
Real-World Link
Red-tailed hawks are
large, stocky birds
with long, broad
wings and short,
broad tails. Females
are larger than males
and can weigh up to
1
3_ pounds.
2
Source: Woodland Park Zoo
268
33. one half divided by two fifths
34. five eighths divided by one fourth
35. one and three eighths divided by one half
36. two and one sixth divided by two thirds
37. PIZZA A concession stand sells three
types of pizza. The diagram shows
how much pizza of each type is left
after the concession stand was open
for one hour. If the pizza is sold in
1
slices that are _
of a whole pizza,
8
how many more slices can be sold?
Chapter 5 Applying Fractions
Sausage
Cheese
Supreme
_
_
_
ALGEBRA Evaluate each expression if g = 1 , h = 1 , and j = 3 2 .
38. j ÷ h
6
39. g ÷ j
2
3
40. 3g ÷ h
41. h ÷
(_12 j)
42. SHOPPING A supermarket sells pretzels in _ -ounce snack-sized bags or
3
4
1
-ounce regular-sized bags. How many times larger is the regular-sized
12_
2
bag than the snack-sized bag?
43. MEASUREMENT A recipe calls for 2_ cups of brown sugar and _ cup of
2
3
2
3
confectioner’s sugar. How many times greater is the number of cups of
brown sugar in the recipe than of confectioner’s sugar?
SCHOOL For Exercises 44 and 45, use the
table that shows the number of hours
students spend studying each week
during the school year.
Weekly Study Hours
Fraction of
Students
Hours
_1
50
_2
25
11
_
50
17
_
100
_1
5
_1
5
_3
none
44. How many times greater was the
1–2
number of students who spent over
10 hours each week studying than
those who spent only 1–2 hours each
week studying?
3–5
6–7
8–10
45. How many times greater was the number
of students who spent 3 or more hours
each week studying than those who spent
less than 3 hours each week studying?
Over 10
Not sure
25
Source: Time Magazine
46. SCHOOL SUPPLIES Tara bought a dozen folders. She took _ of the dozen
1
3
and then divided the remaining folders equally among her four friends.
What fraction of the dozen did each of her four friends receive and how
many folders was this per person?
47. WEATHER A meteorologist has issued a thunderstorm warning. So far, the
EXTRA
PRACTICE
See pages 681, 708.
H.O.T. Problems
1
storm has traveled 35 miles in _
hour. If it is currently 5:00 p.m., and the
2
storm is 105 miles away from you, at what time will the storm reach you?
Explain how you solved the problem.
48. CHALLENGE If _ is divided by a certain fraction _, the result is _. What is
5
6
a
b
the fraction _a ?
1
4
b
49. SELECT A TOOL Reynaldo cut a rope to make
the running knot shown. The rope used to
3
1
feet long and was _
of
make the knot was 1_
2
4
the original rope length. Which of the following
tools could be used to determine the rope’s
original length? Justify your selection(s).
Then use your tool(s) to find the length.
paper and pencil
model
calculator
real object
Lesson 5-7 Dividing Fractions and Mixed Numbers
269
50. FIND THE ERROR Evan and José are finding _ ÷ _. Who is correct? Explain
4
5
your reasoning.
_4 ÷ _6 = _4 · _7
5
5 6
7
14
_
= 28 or _
_4 ÷ _6 = _5 · _6
5
7
6
7
4 7
30
1
_
= 28 or 1_
14
15
30
Evan
51.
José
WR ITING IN MATH If you divide a proper fraction by another proper
fraction, is it possible to get a mixed number as an answer? Explain
your reasoning.
53. How many 1_ -pound boxes of
1
8
52. The Corbett family owns 300 acres of
3
pounds
peanuts can be made using 6_
4
of peanuts?
land that they plan to rent to people
1
for their horses. How many 7_
-acre
2
lots can they make using the 300 acres?
F 4
H 6
1
C 40_
2
1
D 292_
2
G 5
J
A 21
B 40
Find the multiplicative inverse of each number.
6
54. _
7
4
55. _
13
7
(Lesson 5-6)
57. 5_
1
4
56. 8
58. Find _ × _. Write in simplest form. (Lesson 5-5)
1
10
5
8
59. MEASUREMENT Find the length of a rectangular flower bed if the
perimeter is 12 feet and the width is 1.5 feet.
(Lesson 3-6)
60. ANIMALS An elephant herd can move 50 miles in a day. At this rate, about
how many miles can an elephant herd move each hour?
(Lesson 1-1)
in Geography
A Traveling We Will Go It’s time to complete your project. Use the data you have gathered about
schedules and costs to prepare a travel brochure for your vacation destination. Be sure to include a
paragraph describing why you chose your vacation spot.
Unit Project at glencoe.com
g
270
Chapter 5 Applying Fractions
5
Math Online
Study Guide
and Review
glencoe.com
•
• Vocabulary Review
Key Vocabulary
compatible numbers
Be sure the following
Big Ideas are noted
in your Foldable.
multiplicative inverse (p. 258)
(p. 232)
reciprocal (p. 258)
like fractions (p. 236)
Fractions
Estimating with Fractions
unlike fractions (p. 237)
Mix
Numbeed
rs
(Lesson 5-1)
• When the numerator is much smaller than the
denominator, round the fraction to 0.
• When the numerator is about half of the
1
denominator, round the fraction to _.
2
• When the numerator is almost as large as the
denominator, round the fraction to 1.
Adding and Subtracting Fractions
(Lessons 5-2 and 5-3)
Vocabulary Check
Choose the correct term or number to
complete each sentence.
1. To add like fractions, add the (numerators,
denominators).
2. The symbol ≈ means (approximately,
exactly) equal to.
• To add or subtract like fractions, add or subtract
the numerators and write the result over the
denominator.
3. When dividing by a fraction, multiply by
• To add or subtract unlike fractions, rename the
fractions using the LCD. Then add or subtract as
with like fractions.
a fraction is much smaller than the
1
denominator, round the fraction to 0, _
.
• To add or subtract mixed numbers, first add or
subtract the fractions. If necessary, rename them
using the LCD. Then add or subtract the whole
numbers and simplify if necessary.
Multiplying and Dividing Fractions
(Lessons 5-5 and 5-7)
• To multiply fractions, multiply the numerators
and multiply the denominators.
• The product of a number and its multiplicative
inverse is 1.
• To divide by a fraction, multiply by its
multiplicative inverse, or reciprocal.
its (value, reciprocal).
4. When estimating, if the numerator of
2
5. Fractions with different denominators are
called (like, unlike) fractions.
6. The multiplicative inverse of _ is
5
6
(_65 , -_56 ).
7. The mixed number 2 _ can be renamed
(
4
7
)
7 _
as 2 _
, 1 11 .
7
7
8. When multiplying fractions, multiply the
numerators and (multiply, keep) the
denominators.
9. The reciprocal of _ is (-3, 3).
1
3
10. The fractions _ and _ are (like, unlike)
fractions.
4
16
2
4
11. Another word for multiplicative inverse
is (reciprocal, denominator).
Solving Equations
(Lesson 5-6)
If you multiply each side of an equation by the
same nonzero number, the two sides remain equal.
12. The fraction _ can be read x multiplied by
( )
1
2, _
.
2
x
2
Chapter 5 Study Guide and Review
271
5
Study Guide and Review
Lesson-by-Lesson Review
5-1
Estimating with Fractions
(pp. 230–235)
Example 1
Estimate.
13. 2_ ÷ 1_
14. 6_ - 5_
9
1
8
10
13
1
_
_
15.
×
5
15
1
17. _ · 25
2
2
9
16.
_1 + _3
1
7
_
12
5
5 is almost as large as 6, so 2_
≈ 3.
2
8
6
1
18. 15_ ÷ 7_
7
3
6
12
5
18_
feet and the width of her living
8
1
feet. About how many
room is 9_
2
square feet of carpet would be needed
for her living room?
20. FOOTBALL Jamil practiced football for
3
2
1_
hours on Saturday and 2_
hours on
3
4
Sunday. About how many more hours
did he practice on Sunday than on
Saturday?
The sum is about 8.
21.
22.
6
6
1
_
_
23.
+5
9
9
5
_
_
25.
- 5
8
12
Example 2
9
_3 + _
7
≈ 1.
7 is almost as large as 8, so _
8
4
1
≈_
.
4 is about half of 7, so _
8
7
2
2
2
Example 3
_ _
Find 1 + 2 .
6
3
_1
6
2
+_
3
____
_5
6
4
How much rain fell between 8 a.m.
and 4 p.m.?
28. PIZZA Owen ate _ of a pizza Tuesday
night. The next day, he ate an
1
of the pizza. What fraction
additional _
2
of the pizza has he eaten?
Chapter 5 Applying Fractions
2
1
The difference is about _
.
_1 inch. By 4 p.m., the gauge read _3 inch.
272
7
_7 - _4 ≈ 1 - _1 or _1
27. RAIN At 8 a.m., Della’s rain gauge read
1
8
7
8
Use a model.
7
14
9
3
_
24.
-_
10
10
3
7
26. _ + _
20
4
8
_ _
Estimate 7 - 4 .
(pp. 236–241)
Add or subtract. Write in simplest form.
_2 - _1
6
5
1
5_
+ 2_
≈ 5 + 3 or 8
her living room. It has a length of
Adding and Subtracting Fractions
6
12
1
≈ 5.
1 is much smaller than 12, so 5_
19. MEASUREMENT Gina wishes to carpet
5-2
_
Estimate 5 1 + 2 5 .
Example 4
_ _
Find 3 - 1 .
10
3
6
5
1
_
-_
=_
-_
10
4
20
1
=_
20
20
4
Rename the fractions
using the LCD, 20.
Subtract the
numerators.
Mixed Problem Solving
For mixed problem-solving practice,
see page 708.
5-3
Adding and Subtracting Mixed Numbers
(pp. 242–246)
Example 5
29. 3_ + 6_
3
2
1
4
+ 3_
= 5_
+ 3_
5_
30. 4_ - 2_
9
2
15
15
6
2
31. 8_ + 1_
7
7
3
1
_
_
33. 7 - 5
5
3
5
1
_
35. 3 + 11_
8
2
1
2
3
3
3
11
_
32. 7
- 4_
12
12
3
1
34. 5_ + 1_
6
4
3
4
_
36. 4
- 2_
5
10
37. BABYSITTING Lucas watched his little
1
2
sister for 2_
hours on Friday, 3_
hours
2
3
3
hours on Sunday.
on Saturday, and 1_
3
6
6
6
Add the whole
numbers and add
the fractions.
1
= 9_
8 = 8 + 1 or 9
_7
5
_1
6
_
6
5
3
_
=1
5
5
_1
6
_
Find 4 1 - 2 3 .
3
6
3
1
- 2_
= 3_
- 2_
4_
5
2
Rename the fractions.
7
= 8_
Example 6
4
PSI: Eliminate Possibilities
2
_
3
6
How many hours did Lucas watch his
little sister?
5-4
_
Find 5 2 + 3 1 .
Add or subtract. Write in simplest form.
5
5
_1
_6
Rename 4 as 3 .
5
5
Subtract the whole
numbers and subtract
the fractions.
(pp. 248–249)
Solve by eliminating possibilities.
38. SCHOOL It takes Beth 15 minutes to
Example 7 A group of friends went to a
theme park. Six of the friends rode the
_
1
walk to school, _
mile away. What is
2
her walking pace?
Ferris wheel. If this was 2 of the group,
3
how many friends were in the group?
A 2 miles per hour
A 3
B 1 mile per hour
B 6
C 7.5 miles per hour
C 9
D 30 miles per hour
D 12
39. COOKING Which of the following
would yield a larger batch of bagels?
1
F Multiply a recipe by _
.
1
.
G Divide a recipe by _
2
2
3
.
H Multiply a recipe by _
4
J
Divide a recipe by 3.
Since 6 friends rode the Ferris wheel
2
and this was _
of the total number of
3
friends in the group, the number of
friends in the group must be greater
than 6. So, eliminate choices A and B.
If there were 12 friends in the group,
the 6 that rode the Ferris wheel would
1
represent _
of the group. So, eliminate
2
choice D.
Choice C is the only remaining possibility.
6
2
Since 6 out of 9 is _
or _
, C is correct.
9
3
Chapter 5 Study Guide and Review
273
5
Study Guide and Review
5-5
Multiplying Fractions and Mixed Numbers
(pp. 252–257)
40.
_3 × _2
41.
42.
10
_3 × _
43. 4 × _
44.
3
1
2_
×_
45. 4_ × 2_
5
7
5
21
3
5
4
_
×_
12
1
2
4
9
13
20
_ _
Find 5 × 2 .
Example 8
Multiply. Write in simplest form.
9
5×2
_5 × _2 = _
9
9×3
3
10
=_
1
12
Simplify.
27
_ _
Find 3 1 × 2 3 .
Example 9
46. FOOD An average slice of American
1
inch thick. What is
cheese is about _
8
the height of a package containing
20 slices?
2
3
1
7
11
× 2_
=_
×_
3_
2
2
4
3
Multiply the numerators
and multiply the
denominators.
4
_1
_3
Rename 3 and 2 .
4
2
4
Multiply the numerators
and multiply the
denominators.
7 × 11
=_
2×4
5
77
=_
or 9_
Simplify.
8
5-6
Algebra: Solving Equations
(pp. 258–263)
Example 10 Find the multiplicative
inverse of 9 .
Find the multiplicative inverse of each
number.
47.
7
_
_
49. 3_
1
3
48. 5
12
_9 · _5 = 1
5
The product of
9
_9 and _5 is 1.
5
9
Solve each equation. Check your
solution.
50. 8 = _
Example 11
52.
n
-7.6 = _
3
51.
_4 b = 12
53.
x
_
= 2.5
5
_4 · _3 g = _4 · 2
3
4
mysteries. If there are 10 mystery books,
how many books are on the shelf?
Dividing Fractions and Mixed Numbers
Divide. Write in simplest form.
_3 ÷ _6
5
7
57. 2_ ÷ _
3
5
6
4
3
1
_
59. 4
÷ 2_
5
10
56. 4 ÷ _
2
3
58. -_ ÷ 3
2
5
8
2
_
60. - ÷ _
21
7
1
61. MEASUREMENT How many _ -inch
8
3
_
lengths are in 6 inches?
4
Chapter 5 Applying Fractions
4
Write the equation.
Multiply each side by
4
0.3
2
3
55.
_
Solve 3 g = 2.
_3 g = 2
54. BOOKS Of the books on a shelf, _ are
274
5
9 _
The multiplicative inverse of _
is 5 .
5
9
w
2
5-7
8
_3
the reciprocal of .
3
8
2
g=_
or 2_
3
3
4
Simplify.
(pp. 265–270)
Example 12
_ _
Find 2 4 ÷ 7 .
4
7
14
7
÷_
=_
÷_
2_
5
10
5
10
5
10
_4
Rename 2 .
5
2
2
Multiply by the
5
7
reciprocal of
14 _
=_
· 10
1
1
4
=_
or 4
1
Simplify.
_7 .
10
5
Practice Test
1.
7
2
5_
- 1_
3.
13
_3 × _
9
• Chapter Test
13
15
2.
5
1
3_
+ 6_
received a check from his grandmother.
Of this amount, the table shows how he
spent or saved the money.
7
12
2
4
4. 5_ ÷ 1_
3
5
Fraction of
Check
5. BAKING A restaurant uses 2_ pounds of
3
4
8.
10.
12.
14.
8
4
_
+_
15
15
_5 × _2
8
5
5
1
_
4 - 2_
12
12
5
4
8_
- 1_
7
14
_8 ÷ 5_1
9
3
7.
9.
11.
13.
15.
_1
spent on a CD
7
_
20
deposited into
savings account
2
Two weeks later, he withdrew _
of the
7
1
_
-_
3
6
8
_
6×
21
5
7
_
6 + 3_
9
12
5
2
4_
× 1_
6
3
_1 ÷ 5
6
10
amount he had deposited into his savings
account. What fraction of the original check
did he withdraw from his savings account?
2
F _
7
H _
3
9
G _
23
16. MULTIPLE CHOICE Seth drove 5_ miles to the
3
4
1
16
3
pounds?
How many ounces are in 8_
4
6
miles to the park. What is the total distance
Seth drove?
J
30
7
_
40
20. MEASUREMENT An ounce is _ of a pound.
5
1
bank, 6_
miles to the post office, and 4_
3
spent on
baseball cards
4
Add, subtract, multiply, or divide. Write in
simplest form.
How Spent or
Saved
5
_2
flour to make a batch of dinner rolls. About
how many pounds of flour are needed if
3 batches of dinner rolls are to be made?
6.
glencoe.com
19. MULTIPLE CHOICE For his birthday, Keith
Estimate.
7
Math Online
9
A 15_
miles
ALGEBRA Solve each equation. Check your
solution.
7
miles
B _
12
21.
13
11
miles
C _
12
y
_
= 8.1
3.7
3
5
_
23.
=_
x
8
4
22. 6 = _m
2
5
24. 3_ = _p
1
6
2
3
11
miles
D 16_
12
17. SPORTS Tyler’s football practice lasted
1
1
hours. If _
of the time was spent catching
2_
2
4
passes, how many hours were spent
catching passes?
18. MEASUREMENT The floor of a moving van
5
1
feet long and 7_
feet wide. Find
is 11_
3
12
the area of the moving van floor.
25. MULTIPLE CHOICE Maria is making a mural
2
that is 9_
feet long. She wants to divide the
3
5
mural into sections that are each _
foot.
8
Which equation can be used to find n, the
number of sections in Maria’s mural?
5
2
A _
n = 9_
8
3
2
_
_
B 9 n= 5
3
8
5
2
C _
+ n = 9_
8
3
5
2
D n-_
= 9_
8
3
Chapter 5 Practice Test
275
5
Math Online
Test
Practice
Cumulative, Chapters 1–5
glencoe.com
• Test Practice
4. The fraction _ is found between which pair
5
6
of fractions on a number line?
Read each question. Then fill in the correct
answer on the answer sheet provided by your
teacher or on a sheet of paper.
1. Mrs. Brown needs to make two different
desserts for a dinner party. The first recipe
1
requires 2_
cups of flour, and the second
4
3
cup less than the first.
recipe requires _
4
Which equation can be used to find n, the
number of cups of flour needed for the
second recipe?
3
1
-_
A n = 2_
4
4
1 _
B n = 2_
·3
4 4
3
1
C n = 2_
+_
4
4
3
1
D n = 2_
÷_
4
4
5
1
F _
and _
8
4
1
4
G _
and _
3
9
31
11
H _
and _
36
12
7
17
and _
J _
12
18
5. The table shows the distance Kelly swam
over a four-day period. What was the total
distance, in miles, Kelly swam?
Kelly’s Swimming
Day
Distance (miles)
2. Which of the following is true concerning
the least common multiple of 6 and 9?
Monday
1.5
F It is greater than the least common
multiple of 8 and 12.
Tuesday
2
G It is greater than the least common
multiple of 5 and 15.
Wednesday
2.3
Thursday
3
H It is less than the least common multiple
of 4 and 6.
J It is less than the least common multiple
of 3 and 4.
_3
4
_1
2
A 10.5 miles
1
C 10_
miles
1
miles
B 10_
4
D 9 miles
20
3. Kyle’s hockey team has 6 sixth graders,
9 seventh graders, and 5 eighth graders.
Which statement below is true?
6. Which of the following gives the correct
5
1
meaning of the expression _
÷_
?
8
A One fourth of the team members are
sixth graders.
5
8
3
1
F _
÷_
=_
×_
8
3
5
1
B More than half of the team members are
seventh graders.
5
5
3
1
G _
÷_
=_
×_
C 25% of the team members are eighth
graders.
5+1
5
1
H _
÷_
=_
D 30% of the team members are seventh
graders.
5
5
1
1
J _
÷_
=_
×_
276
Chapter 5 Applying Fractions
8
8
8
3
3
3
8
1
8+3
8
3
3
Preparing for Standardized Tests
For test-taking strategies and practice,
see pages 716–733.
7. What is the value of the expression
(3 + 4)2 ÷ 7 - 2 × 6?
A -9
C 30
B -5
D 1
Record your answers on the answer sheet
provided by your teacher or on a sheet of
paper.
10. Write an equation using two variables to
8. Which line contains the ordered
show the relationship between the position
x and the value of a term y.
pair (-1, 2)?
y
k
O
l
x
Position (x)
1
2
3
4
5
Value of
Term (y)
5
9
13
17
21
n
n
11. Evan runs 2_ miles each week. He runs
3
8
m
_3 mile on Mondays and _3 mile on Tuesdays.
4
F Line k
4
How far does he run, in miles, if the only
other day he runs each week is Thursday?
G Line l
H Line m
12. Find 15 ÷ (-5).
J Line n
9. A pizza shop tried 45 new types of pizza
during the past year and 20% of them
became popular. Which best represents the
fraction of pizzas that did not become
popular?
Record your answers on the answer sheet
provided by your teacher or on a sheet of
paper. Show your work.
1
A _
13. A box of laundry detergent contains 35 cups.
3
C _
5
_
B 4
9
5
1
It takes 1_
cups per load of laundry.
4
D _
5
4
a. Write an equation to represent how many
loads you can wash with one box.
b. How many loads can you wash with
Question 9 Be sure to pay attention
to emphasized words, or words that
are italicized. In Question 9, you
are asked to find which answer is
not correct.
one box?
c. How many loads can you wash with
3 boxes?
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Chapters 1–5 Test Practice
277