Name _____________________________________________________________________________________________________
Adding Fractions and Mixed Numbers:
Like Denominators
R 8-1
If fractions have the same denominator, you can add them by adding the
numerators.
2
!!
6
Find
#
#
3
!!.
6
2
!!
6
3
!!
6
5
!!
6
1
!!
6
Add the numerators: 2 # 3 " 5.
Use the common denominator.
Simplify, if possible.
2
!!
6
Find 1!3! # 2!3!.
4
#
3
!!
6
"
5
!!
6
4
Step 1
Step 2
Step 3
Add the
fractions.
Add the whole
numbers.
Simplify the sum,
if possible.
3
4
3
# 2 !!
4
6
!!
4
1 !!
1 !!
3
4
1
3
!!
4
# 2 !3!
#2
3
!!
4
6
4
3
6
!!
4
4
3 !!
" 3 # 1 !2! " 4
4
2
!!
4
"4
1
!!
2
Simplify.
4
2. 4!! " 6!3!
3
11
5. 4!! " 5!5!
5
1. 1!! " 2!3!
3
4. 3!! " 5!4!
4
7
3. 3!! " 4!4!
4
7
6
6. 9!! " 10!9!
9
11
Add. Write each answer in simplest form.
2
6
4
6
1
8
7. !! # !! "
3
6
4
6
2
3
9. 1!! # 2!! "
© Scott Foresman, Gr. 5
4
8
8. !! # !! "
2
3
10. 1!! # 1!! "
(249)
Use with Chapter 8, Lesson 1.
Name _____________________________________________________________________________________________________
Adding Fractions and Mixed Numbers:
Like Denominators
H 8-1
Add. Write each answer in simplest form.
3
7
"
2
3
3
6. !! " !! #
10
10
3
2
9. !! " !! #
6
6
3
6
14.
"
4
!!
10
9
!!
10
3
18.
" 5!35!
!!
4!68!
" 1!38!
!!!
5
7
5
12. 5!! " 2!! #
8
8
15.
"
!!
3!35!
1
2
11. 1!4! " 3!4! #
2
!!
5
1
!!
5
1
7
8. !! " !! #
9
9
!
17.
1
5. !! " !! #
6
6
10. !! " !! #
8
8
13.
3. !! " 1!! #
8
8
1
7. 2!! " 1!! #
3
3
4
5
2. !! " !! #
8
8
4. !! " 1!! #
9
9
1
3
6
1. !! " !! #
10
10
7
!!
12
7
!!
12
19.
7
!
"!
10
12
7
!
" 3!
12
!!
1
!
2!
10
1!11!
16.
!!!
20.
!!!
"
3
!!
13
11
!!
13
!!!
Test Prep Circle the correct letter for each answer.
21. Albert’s family ordered an 8-slice pizza for dinner. Albert ate 2 slices for dinner. The
next day, Albert ate 2 more slices for lunch. What fraction of the pizza did Albert eat?
2
A !8!
2
B !4!
1
C !4!
1
D !2!
22. Breakwater School has two newspapers, The Bugle and The Bulletin.
The Bugle comes out on Tuesday and Friday. The Bulletin comes out on
Thursday. On what fraction of the school week does a paper come out
at Breakwater? (Hint: There is no school on Saturday or Sunday.)
2
F !7!
© Scott Foresman, Gr. 5
2
G !5!
(250)
1
H !5!
3
J !5!
Use with Chapter 8, Lesson 1.
Name _____________________________________________________________________________________________________
Subtracting Fractions and Mixed Numbers:
Like Denominators
R 8-2
If fractions have the same denominator, you can subtract them by subtracting
the numerators.
Find
7
!!
9
"
5
!!.
9
"
7
!!
9
5
!!
9
2
!!
9
Subtract the numerators: 7 " 5 # 2.
Use the common denominator.
Simplify, if possible.
7
!!
9
"
5
!!
9
#
2
!!
9
When you subtract mixed numbers, you may have to rename the numbers.
Rename 3!1! to show 9 more ninths.
9
3!1!
9
# 2$1$
# 2$
9
!!
9
$
1
!!
9
1
!!
9
# 2!10!
Now, find
3!1!
9
"
9
4
1!!.
9
Step 1
Step 2
Step 3
4
!!
9
Subtract the fractions. Then
subtract the whole numbers.
Simplify,
if possible.
% !1!, so you will need to
9
rename 3!1! to show more ninths.
9
3!1! # 2!9! $
"
9
1!4!
9
9
1
!!
9
# 2!10!
"
2!10!
9
1!4!
9
"
2!10!
9
1!4!
9
"
1!6!
9
1!4!
9
1!6!
9
# 1!2!
9
3
Find each missing numerator.
1
3
3
1. 2!! = 1!!
1
2. 6!! = 5!7!
7
3
!
3. 3!! = 2!
10
10
Subtract. Write each answer in simplest form.
4
6
3
6
7
8
4. !! " !!
© Scott Foresman, Gr. 5
5
8
5. !! " !!
(252)
3
8
5
8
6. 2 !! " 1!!
1
3
2
3
7. 4 !! " 1!!
Use with Chapter 8, Lesson 2.
Name _____________________________________________________________________________________________________
Subtracting Fractions and Mixed Numbers:
Like Denominators
H 8-2
Subtract. Write each answer in simplest form.
5
9
3
9
1. ! " !
2.
4
!
6
1
3
3!
" 2!
8
8
"
2
!
6
9
10
5
10
6.
6
10
1
10
10.
4
2!
"
8
14.
4
!
3!
10
5. ! " !
9. ! " !
13.
"
2
!!
5
1
!!
5
6
!
8
3.
7
!
8
7.
1
2
2!
" 1!
3
3
6
!
8
4.
4
1!
"1
5
8.
3
!
9
11.
1
3
5!
"!
4
4
12.
15.
7
!
4!
12
16.
7
!
"!
10
!
"
7
!
"!
12
!!
!!
"
2
!
9
1
5
5!
" 2!
8
8
"
4
!!
12
3
!!
12
!!
7
! of a dozen eggs in the refrigerator.
17. Jenna had !
12
She used !5! of a dozen eggs for a recipe. How many
12
eggs were left after she used the eggs for her recipe?
Test Prep Circle the correct letter for each answer.
2
8
18. After a class picnic, Mitchica wrapped up 4!! leftover pizzas. For dinner, she
and her brother ate 1!6! pizza. How many pizzas were left after their dinner?
8
1
8
A 3!!
6
8
B 1!!
1
2
C 2!!
1
2
D 3!!
6
12
9
12
19. Alma’s bakery made 6!! dozen blueberry muffins. They spread frosting on 3!!
dozen. How many muffins were not frosted?
3
4
1
2
F 3!! dozen
© Scott Foresman, Gr. 5
G 3!! dozen
(253)
1
2
H 2!! dozen
3
4
J 2!! dozen
Use with Chapter 8, Lesson 2.
Name _____________________________________________________________________________________________________
Problem-Solving Skill
R 8-3
Too Much or Too Little Information
Here is an example of a problem with too much information.
Jim is 9 years old. He lives in a 3-story house on 24th Street.
He has 3 hamsters. How old will Jim be next year?
To answer the question, you need to know how old Jim is now.
Jim is 9 years old. Next year he will be 10 years old. All the other
information is not needed.
Here is an example of a problem with too little information.
Sheila is 8 years old. She lives at 35 West Street with her older sister Pam.
How much older is Pam than Sheila?
To answer the question, you need to know how old Pam is.
The problem doesn’t say.
Greg mowed 4 lawns last week and earned a total of $45. This Monday he mowed and
earned $14. On the same day, Greg got a new customer and this will improve the
amount of money he earns. Greg wants to compare the amount of money he earns this
week with what he earned last week.
1. What information is needed to compare the amount of money Greg earns?
a. The amount of money Greg earned last week.
b. The amount of money Greg will earn this week.
c. The amount of money Greg earned on Monday.
2. What information is not needed to compare the amount of money earned?
a. The amount Greg earned mowing lawns last week.
b. Greg mowed 4 lawns last week.
c. The amount of money Greg mowing lawns this week.
3. The new customer will pay Greg $10 to mow his yard. Which inequality shows the correct
comparison of wages Greg earned last week with the wages he will earn this week?
a. $45 ! $55
b. $45 " $14
c. $45 # $45
© Scott Foresman, Gr. 5
(255)
Use with Chapter 8, Lesson 3.
Name _____________________________________________________________________________________________________
Problem-Solving Skill
H 8-3
Too Much or Too Little Information
Here is a recipe for cole
slaw. The ingredients cost
about $6.00. You can
prepare and mix the
vegetables in 15 minutes,
then you must refrigerate the
finished cole slaw for 3 to 4
hours before serving.
Recipe
1
!!
4
1
!!
2
Cole Slaw
5 cups shredded
cabbage
cup sour cream
cup mayonnaise
1 tablespoon vinegar
shredded carrots
1 teaspoon sugar
1
!!
4
cup shredded red
cabbage
1
!!
4
cup French dressing
1. Which fact is needed to find how much sour cream to put in the recipe?
a. Refrigerate the finished cole slaw 3 to 4 hours before serving.
1
4
1
2
b. Use !! cup sour cream.
c. Use !! cup mayonnaise.
2. Which of the following information is missing?
a. the amount of shredded carrots
b. the amount of sugar
c. how long to refrigerate the finished cole slaw
3. Which fact is not necessary to make the cole slaw?
a. It costs about $6.00 to make.
1
4
b. It uses !! cup shredded red cabbage.
1
4
c. It uses !! cup French dressing.
4. Suppose you want to double the recipe. Which number sentence represents how
much sour cream you would need?
1
4
7
4
1
4
a. 2 " !! # !!
9
4
b. 2 $ !! # !!
1
4
1
4
2
4
c. !! $ !! # !!
5. Can you tell how many people the recipe serves? Explain.
6. Suppose you begin preparing the cole slaw at 2:00 P.M.. Is there enough information to
decide if it will be ready to serve by 6:00 P.M.? Explain.
© Scott Foresman, Gr. 5
(256)
Use with Chapter 8, Lesson 3.
Name _____________________________________________________________________________________________________
Estimating Sums and Differences
of Mixed Numbers
R 8-4
To estimate sums and differences of mixed numbers, round each number
to the nearest whole number. If the fraction is greater than or equal to !1!,
2
round up to the nearest whole number. Otherwise round down.
Round:
3!3! "! 4
4
3
!!
4
>
1
!!
2
so round 3!3! to 4
3!3! "! 3
4
8
3
!!
8
<
1
!!
2
so round 3!3! to 3
8
Estimate each sum or difference.
2!5! "!
8
1!3! "!
8
"
3
"1
5
!!
8
3
!!
8
$
%
1
!!
2
1
!!
2
so round 2!5! to 3
so round
8
1!3!
8
to 1
4
6!5! "!
#
12
4!7! "!
12
6
#5
5
!!
12
7
!!
12
<
>
1
!!
2
1
!!
2
so round 6!5! to 6
so round
12
4!7!
12
to 5
1
Estimate each sum or difference.
3!2!
1.
"
5
2!3!
5
6!3!
4.
#
7
2!2!
7
"!
1!5! "!
2.
"!
"
"!
"!
8
2!3! "!
8
"
4!3! "!
5.
#
6!7! "!
3.
6!7! "!
6.
8
2!7! "!
8
#
6
12
2!5! "!
12
16
4!5! "!
16
6
7. 4!8!
7
8. 1!9!
4
!
9. 18!
18
!
10. 4!
12
" 5!18!
" 8!19!
11
!
# 5!
18
7
!
# 2!
12
© Scott Foresman, Gr. 5
(258)
Use with Chapter 8, Lesson 4.
Name _____________________________________________________________________________________________________
Estimating Sums and Differences
of Mixed Numbers
H 8-4
Estimate each sum or difference.
1.
3!34!
2.
4!13!
2
6.
" 4!14!
5.
3.
4!69!
7.
6
!
# 2!
10
" 2!14!
2
4
6
3
!
3!
10
1
6
3
8
4.
8!34!
8.
7
!
" 3!
12
# 1!29!
9. 5!!" 2!! $
7
!
1!
12
"
5
8
10. 4!! # 2!! $
3
!!
4
4
!
3!
12
3
!
# 1!
12
6
# 2!23!
5
12
11. 2 " 3!! $
7
9
1
9
12. 2!! # 1! $
Decide if you need an estimate or an exact answer. Tell why.
1
3
13. Eli is making his own fruit soda. He uses 2!! cups of fruit juice. He blends this with
1!34! cups of fizzy soda water. Estimate the amount of fruit soda this will make.
1
8
14. Celeste is baking bread. The recipe calls for 7 cups of flour. Celeste has 2!! cups of
white flour and 3!58! cups of whole wheat flour. Estimate the amount of flour she has
for the recipe.
15. Will Celeste have enough flour for the recipe? Explain.
Test Prep Circle the correct letter for each answer.
1
4
16. 3!! " 2!6! is
6
A about 6
5
12
B less than 5
C about 5
D equal to 4
G about 1
H greater than 3
J equal to 2
7
12
17. 6!! # 4!! is
F equal to 1
© Scott Foresman, Gr. 5
(259)
Use with Chapter 8, Lesson 4.
Name _____________________________________________________________________________________________________
Adding Fractions: Unlike Denominators
R 8-5
To add fractions with unlike denominators, you need to find the least common
denominator (LCD).
Find
5
!!
8
+
1
!!.
6
Step 1
Find the LCD.
The LCD is the least common
multiple of 6 and 8.
#
5
!!
8
1
!!
6
Multiples of 8: 8, 16, 24…
Multiples of 6: 6, 12, 18, 24…
Step 2
Write the equivalent
fractions using the LCD.
#
5
!!
8
"
(5 $ 3)
!!
(8 $ 3)
"
15
!!
24
1
!!
6
"
(1 $ 4)
!!
(6 $ 4)
" #
4
!!
24
Step 3
Add. Simplify the sum,
if possible.
#
5
!!
8
1
!!
6
"
"#
15
!!
24
4
!!
24
19
!!
24
Add. Simplify each sum, if possible.
1.
1
!!
4
"
2.
!!
12
# !13! " # !14!
2
_____
_____
4.
3
!!
8
"
1
!!
8
"
5.
!!
9
!!
3.
5
!!
6
"
!!
8.
2
!!
3
"
!!
3
! " # !!
#!
10
_____
_____
# !23! " # !!
_____
_____
(261)
2
!!
5
"
4
!!
!
# !12! " # !
10
_____
_____
6.
# !17! " # !!
_____
_____
!!
© Scott Foresman, Gr. 5
"
# !16! " # !4!
_____
_____
# !25! " # !!
_____
_____
7.
3
!!
8
2
!!
3
"
!!
# !15! " # !!
_____
_____
9.
7
!!
8
"
!!
1
! " # !!
#!
10
_____
_____
Use with Chapter 8, Lesson 5.
Name _____________________________________________________________________________________________________
Adding Fractions: Unlike Denominators
H 8-5
Add. Simplify each sum, if possible.
1.
!
5.
!
1
8
3
##
8
1
##
4
2.
!
7
##
9
1
##
3
6.
!
1
4
1
2
3
##
5
2
##
3
3.
!
1
##
3
5
##
6
7.
!
1
3
10. # ! # "
9. # ! # "
2
##
8
1
##
2
4.
!
2
##
6
1
##
3
1
4
8.
!
7
12
2
3
11. # ! # "
3
##
4
1
##
8
1
##
3
2
##
9
2
7
12. # ! # "
13. Heidi likes to create different fruit juice combinations. In a large glass,
she pours #31# cup of pineapple juice, #41# cup of pear juice, #41# cup of apple
juice, and #61# cup of lime juice. How much juice is in the glass?
14. Heidi decided to switch to other juices. In another large
glass, she pours #83# cup of tomato juice, #41# cup carrot juice, #81# cup of
1
# cup of lemon juice. How much juice is in the glass?
beet juice, and #
16
2
9
1
4
1
3
15. Next Heidi mixed ## cup of raspberry juice, ## cup cranberry juice, ##
cup grape juice, and #61# cup peach juice. How much juice is in the glass?
Test Prep Circle the correct letter for each answer.
2
5
5
#
16. #3# ! #6# ! #
12
1
11
#
C 2#
12
1
#
D 1#
12
#
A 1#
12
1
B 1#4#
1
3
1
17. #2# ! #8# ! #4# is:
5
9
F less than #8# ! #
2#
4.
5
9
G equal to #8# ! #
2#
4.
© Scott Foresman, Gr. 5
(262)
3
5
H greater than #4# ! #8# .
3
5
J less than #4# ! #8# .
Use with Chapter 8, Lesson 5.
Name _____________________________________________________________________________________________________
Subtracting Fractions: Unlike Denominators
R 8-6
To subtract fractions with unlike denominators, you need to find the least
common denominator (LCD).
Find 5!6! " 1!8!.
Step 1
Find the LCD.
"
5
!6!
1
!8!
Multiples of 6: 6, 12, 18, 24…
Multiples of 8: 8, 16, 24…
Step 2
Write the equivalent
fractions using the LCD.
5
!6!
#
–
1
!!
8
#
"
5
!6!
1
!!
8
Step 3
Subtract. Simplify the
difference, if possible.
20
!!
24
(!
1 $!
3)
3
!
(8 $ 3) #" !
24
(!
5 $ 4)
(6 $!
4)
#
#
#
"
20
!!
24
3
!!
24
17
!!
24
Subtract. Simplify, if possible.
1.
4.
7.
2
!3!
!1
6!
#
9
!
1!
0
2
!
" 3!
#
1
!2!
2
!9!
#
!!
2.
6
1
" # " !6!
!!
!
!!
5.
" !!
! # !!
!!
8.
" # " !!
!!
!
© Scott Foresman, Gr. 5
(264)
1
!2!
1
!5!
#
7
!8!
1
!3!
#
5
!!
2
" # "!!
!!
!
!!
" # " !!
!!
!
3
!4!
2
!5!
#
!!
" # " !!
!!
!
3.
7
!8!
3
!5!
#
2
!3!
2
!5!
#
35
!!
"
" !40!
! # !!
6.
9.
!!
" # " !!
!!
!
3
!4!
3
!
1!
0
#
!!
" !!
"
! # !!
Use with Chapter 8, Lesson 6.
Name _____________________________________________________________________________________________________
Subtracting Fractions: Unlike Denominators
H 8-6
Subtract. Simplify each difference, if possible.
1.
"
5
!!
9
1
!!
3
2.
"
!
5
!!
6
3
!!
5
3.
"
!
1
2
6. !! " !! #
5
6
2
3
10. !! " !! #
9. !! " !! #
4.
"
!
3
4
5. !! " !! #
4
!!
5
1
!!
2
3
5
1
2
1
3
3
10
7
9
!
2
5
7. !! " !! #
9
10
1
!!
2
1
!!
6
2
5
11. !! " !! #
5
8
1
2
5
9
1
3
8. !! " !! #
12. !! " !! #
13. Ramon and his sister Gabi are coloring a
stack of posters to advertise their school’s
talent show. In one afternoon, Ramon
colored !14! of the posters, while Gabi
colored !38! of the posters. How much more
of the posters has Gabi colored?
14. Gabi bought a box of crayons to color in
the posters. Ramon was using !25! of the
crayons, and Gabi was using !13! of the
crayons. What fraction of the crayons are
still in the box?
Test Prep Circle the correct letter for each answer.
1
3
15. What is the difference of !2! and !8!?
1
A !
1!
6
3
B !
1!
6
11
1
C !8!
7
D !8!
7
H !
1!
2
2
J !3!
1
16. What is the difference of !
1!
2 and !4!?
1
G !8!
1
F !
1!
2
© Scott Foresman, Gr. 5
(265)
Use with Chapter 8, Lesson 6.
Name _____________________________________________________________________________________________________
Adding Mixed Numbers
R 8-7
4!2! # 3!3!.
Find
3
4
Step 1
4!2! Multiples of 3: 3, 6, 9, 12…
Find the LCD.
#
3
3!3!
4
Multiples of 4: 4, 8, 12…
Step 2
4!2!
Write the equivalent
fractions using the LCD.
#
3
3!3!
4
4!8!
"
"
#
12
3!9!
12
Step 3
4!2!
Add. Simplify the sum,
if possible.
#
3
3!3!
4
4!8!
"
"
#
12
3!9!
12
7!17!
12
"7#
12
!!
12
#
5
!!
12
" 8!5!
12
Estimate to check: 5 # 4 " 9.
Find the sum and simplify, if possible. Check by estimating.
1.
3!1! "
5
3!!
10
# 2!1! " # 2!!
2
4.
2!1! "
5
10
2!!
# 3!2! " # 3!!
3
© Scott Foresman, Gr. 5
(267)
2.
1!2! "
3
1!8!
# 2!1! " # 2!3!
4
5.
4!2! "
7
4!!
+ 1!1! " # 1!!
2
3.
1!26! "
10
1!!
12
# 5!25! " # 5!!
6.
5!12! "
5 !!
# 7!29! " # 7!!
Use with Chapter 8, Lesson 7.
Name _____________________________________________________________________________________________________
Adding Mixed Numbers
H 8-7
Find the sum and simplify, if possible.
1.
2!13!
2.
4!14!
6.
5!15!
10.
" 6!16!
9.
3.
4!14!
7.
3!45!
11.
" 6!12!
" 3!16!
5.
4!23!
4.
4!18!
8.
1
!
" 2!
16
" 2!12!
7!49!
" 3!12!
3
!
3!
10
12.
" 2!35!
1
2!35!
+ 12!23!
" 1!12!
" 3!13!
1
!
" 3!
10
5!15!
2!34!
" 5!13!
1
13. It takes Susan 2!2! hours to prepare a soup recipe, and 1!3! hours to prepare a bread
recipe. How much time does Susan spend preparing both recipes?
Test Prep Circle the correct letter for each answer.
1
4
14. Darlene is making up fruit baskets for the senior citizen’s home. She’s using 1!!
pound of apples, 1!2! pound oranges, 2!1! pound of dates, and
3
2
each basket. How much will each basket weigh?
1
2
1
B 5!!
2
1
3
1
D 6!!
6
A 4!! pounds
C 6!! pounds
pounds
pounds
7
8
3
!!
4
pound of walnuts in
1
4
15. Caleb’s meat loaf recipe calls for 1!! pounds ground beef, 2!! pounds ground veal,
and 1!3! pounds of ground turkey. How many pounds of meat are in the meat loaf?
5
F 4!!
8
1
G 5!!
8
4
pounds
pounds
© Scott Foresman, Gr. 5
(268)
7
8
5!1!
4
H 5!! pounds
J
pounds
Use with Chapter 8, Lesson 7.
Name _____________________________________________________________________________________________________
Subtracting Mixed Numbers
Find
R 8-8
13!3! " 11!5!.
8
12
3
Step 1
13!8! $
Write equivalent fractions
with the LCD.
5
3
10
!!
24
#
9
! !,
24
have to rename
13!8! $
you will
13!9!
24
10
!!
– 11!1!
2 $ " 11 24
Step 2
Because
9
13!2!
4
5
9
24
!!
13!2!
4 $ 12 24 %
10
33
$ 12!2!
4
10
!!
– 11!1!
2 $ – 11 24
to
9
!!
24
"11!2!
4
show more twenty-fourths.
33
Step 3
12!2!
4
Subtract the fractions and
the whole numbers. Simplify
the difference, if possible.
10
– 11!2!
4
23
!
1!
24
Estimate to check: 13 – 11 $ 2.
Find each difference and simplify, if possible. Check by estimating.
1!2! $
1.
"
5
1
1!!
10
1!10!
"
"
$ " 1!10!
4!1!
4.
5.
4
2!3!
8
© Scott Foresman, Gr. 5
(270)
3!3! $
2.
5
2!1!
2
3!3!
10
–1!1!
2
3!6!
3.
$ "2!5!
7!56! $
7!!
" 3!49! $ "3!!
6.
3
!
5!
15
6
!
–2!
10
Use with Chapter 8, Lesson 8.
Name _____________________________________________________________________________________________________
Subtracting Mixed Numbers
H 8-8
Find each difference and simplify, if possible.
1.
7!12!
2.
"4!14!
3!13!
2
5. 5 !5!
6.
3
!
"2!
10
7!13!
1
10.
2!14!
"1!56!
"1!18!
!!
!!
1
!
"9!
10
!!!
!!
15!12!
11.
15!15!
8.
"3!11!
6
!!
9. 5!2!
!!
5!34!
7.
"5!59!
!!!
"2!34!
!!!
!!
6!38!
4.
"11!12!
"1!56!
!!
12!34!
3.
6!38!
12.
"2!56!
"6!13!
!!
!!!
13. Two cooks are in the kitchen of the Splendid Soup Shop this afternoon.
Antonio has been working for 3 !14! hours. Nanetta has been at work for
1!12! hours. How many more hours has Antonio worked than Nanetta?
1
2
14. Before breakfast started, the cooks in the Sunview Hotel had 5!! dozen
eggs. So far they have used 2!34! dozen eggs to make breakfast for their
customers. How many dozen eggs are left?
Test Prep Circle the correct letter for each answer.
1
3
2
9
15. 13!! " 2!! #
1
3
1
9
A 11!!
1
2
B 11!!
1
9
C 10!!
2
9
D 10!!
3
4
16. 7!! " 5!! #
3
4
1
4
G 2!!
F !!
© Scott Foresman, Gr. 5
(271)
3
4
H 2!!
3
4
J 1!!
Use with Chapter 8, Lesson 8.
Name _____________________________________________________________________________________________________
Problem-Solving Strategy
R 8-9
Solve a Simpler Problem
Robin is stacking boxes of sugar cubes in the stable at the horse farm where
she works. There are labels on the top and front side of each box. If Robin stacks
the boxes 5 high with 3 boxes in each level, how many labels can she see?
Understand
You need to find the number of labels that can be seen if the
boxes are stacked in a 5 ! 3 array.
Plan
You can solve a simpler problem.
Think about how many labels could be seen if the boxes are
stacked in a 1 ! 3 array, then in a 2 ! 3 array, then in a
3 ! 3 array. Look for a pattern and use it to solve the
problem for a 5 ! 3 array.
Solve
In a 1 ! 3 array, 6 labels show.
L
L
In a 2 ! 3 array, 9 labels show.
L
L
L
L
L
L
L
L
L
L
L
L
L
L
In a 3 ! 3 array, 12 labels show.
L
L
L
L
L
L
L
L
L
L
L
Each time 3 more labels can be seen.
So Robin can see 18 labels in the 5 ! 3 array.
Look Back
Did you count only the number of labels that show?
Use a simpler problem to help you solve each problem.
1. The stable stocks 6 different kinds of
horse foods. Robin feeds the horses two
kinds of food each day. In how many
ways can Robin choose 2 different kinds
of foods from the 6 foods stocked
in the stable?
2. Robin is setting up six rows of horses
for a horse show. There is 1 horse in
the first row. There are 4 horses in the
2nd row, 7 horses in the third row, and
so on. How many horses are there in
the show?
3. There were 4 horses at the stable when Robin began working there. At the end of her
first year, 2 more horses had been added. At the end of the 2nd year, there were 4 more
horses than the year before. At the end of the next year there were 6 more horses than
the year before. If this pattern continues, how many horses will there be at the end of the
6th year?
© Scott Foresman, Gr. 5
(273)
Use with Chapter 8, Lesson 9.
Name _____________________________________________________________________________________________________
Problem-Solving Strategy
H 8-9
Solve a Simpler Problem
Use a simpler problem to help you solve each problem.
1. There are 7 rows of vegetables at a farm stand. In the first row, there are 2 vegetables.
In the second row there are 3 vegetables. In the next row there are 4 vegetables, and
so on. How many vegetables are in the 7 rows?
2. Sandra can make 5 different types of fruit drinks. She drinks two types of fruit drinks
each day. In how many ways can she choose 2 different fruit drinks from the 5 she
can make?
3. The vegetable stand owner is setting up a display. He needs to cut a rope into
36 pieces to complete his display. How many cuts does he need to make?
4. Boxes of raspberries are labeled on each of the four sides of a box. How many labels
can you see if 9 boxes are lined up next to one another?
5. Thomas planted a peach tree. It grew 4
branches during the first year. It then grows
3 new branches every year. How many
branches will it have after it has been
growing for 12 years?
6. In a picnic area there are small tables like the
one shown at the right. Ten of these tables
are placed end to end to make one long table.
How many people can sit at this long table?
7. Jeffrey bought 3 bags of dried fruit for every 2 days he will be on vacation. If he will
be on vacation for 14 days, how many bags of dried fruit did he buy?
© Scott Foresman, Gr. 5
(274)
Use with Chapter 8, Lesson 9.
Name _____________________________________________________________________________________________________
Multiplying by a Fraction
R 8-10
To multiply a fraction by a fraction, multiply the numerators and then the
denominators. Simplify the product if necessary.
To find
3
!!
4
of
3
!!,
8
multiply
3
!!
4
"
3
!!.
8
3"3
!!
4"8
Multiply the numerators.
#
9
!!
32
#
30
!!
8
Then multiply the denominators.
9
!!
32
Simplify the product, if necessary.
To find
5
!!
8
of 6, write 6 as a fraction,
6
!!.
1
Multiply the numerators.
5"6
!!
8"1
Then multiply the denominators.
30
!!
8
Simplify the product, if necessary.
# 3!3!
4
A reciprocal of a fraction is found by reversing the numerator and the
denominator. The reciprocal of !1! is !n!.
n
1
Remember: The product of a number and its reciprocal is 1.
Multiply. Simplify the product, if possible.
3
4
1
2
1. !! " !! #
3
7
3. !! " 3 #
2
9
1
2
(3 "
!
!) # !!
2. !! " !! #
(3 "
!
!) = !! = 1!27!
4. !! " 2 =
(4 "
(7 "
)
)
5
12
2
3
7
9
6. !! " !!
4
5
1
2
3
5
8. !! " 9
5. !! " !!
(5 " )
!
!
= !! # !5!
(
" 1)
6
7
12
2
3
7. !! " !!
1
4
5
12
9. !! " 11
© Scott Foresman, Gr. 5
(2 " )
!
! = !18! # !19!
( " 2)
12
5
10. !! " !!
(276)
Use with Chapter 8, Lesson 10.
Name _____________________________________________________________________________________________________
Multiplying by a Fraction
H 8-10
Multiply. Simplify the product, if possible.
2
3
3
4
2. !! " !! #
5
6
1
20
4. !! " !! #
5
6
2
3
6. !! " !! #
1. !! " !! #
3. !! " !! #
5. !! " !! #
1
3
1
4
3
4
3
8
7
8
6
7
1
6
7. !! " 33 #
3
1
6
8. !! " 20 #
4
6
9. !4! " !3! #
11
! #
10. !7! " !
12
3
5
11. There are 25 students in Ms. Ruiz’s fifth grade class. If !! of them
bring lunch to school, how many of the students bring lunch?
2
3
12. There are 36 students in a cooking class. !! of the students have never taken
a cooking class. How many students have never taken a cooking class?
Test Prep Circle the correct letter for each answer.
3
4
13. In a cooking class of 36 students, !! of the students
enjoy making deserts. How many students do not
enjoy making deserts?
A 12
C 48
B 27
D 9
14. Ms. Ruiz baked 48 muffins . She brought them to school
for the bake sale. Within the first !1! hour, !5! of the muffins
2
6
were sold. How many muffins were not yet sold?
F 24
H 5
G 8
J 40
© Scott Foresman, Gr. 5
(277)
Use with Chapter 8, Lesson 10.
Name _____________________________________________________________________________________________________
Dividing Fractions
R 8-11
To divide by a fraction, multiply by the reciprocal of the fraction.
Example 1
To find 3 " !58!, multiply
3 by the reciprocal of !58!.
3"
5
!!
8
# 3 $ !85!.
3$8
!!
5$1
Example 2
To find !58! " !23!, multiply
by the reciprocal of !23!.
5
!!
8
"
2
!!
3
#
5
!!
8
Multiply the numerators,
then multiply the
denominators.
5
!!
8
$ !32!.
#
24
!!
5
24
!!
5
Multiply the numerators,
then multiply the
denominators.
5$3
!!
8$2
#
Simplify the product.
# 4!45!
The product is already
simplified.
15
!!
16
Divide. Simplify the quotient if possible.
4
1
4
3
4$3
3
2
3
3
3$
3
1
3
12
1
! # !! # 1!!
1. !9! " !! # !9! $ !! # !
9$1
3
3
! #
2. !5! " !3! # !5! $ !! # !
5$2
3. !4! " !2! # !4! $
7
2
4. !9! " !3! #
2
3
6. !9! " !4! #
3$2
! #
#!
4$1
# 1!12!
2
7
5
2
$
#
5. !3! ÷ !9! =
$
#
7. !7! " !5! #
© Scott Foresman, Gr. 5
(279)
$
$
#
#
Use with Chapter 8, Lesson 11.
Name _____________________________________________________________________________________________________
Dividing Fractions
H 8-11
Divide. Simplify the quotient, if possible.
2
3
1. !3! " !4! #
1
1
2. !6! " !4! #
4
1
3. !9! " !8! #
5
1
4. !6! " !
2!
0 #
1
1
5. !
1!
0 " !9! #
5
2
6 !6! " !3! #
7
1
7. !8! " !7! #
3
1
8. !5! " !3! #
3
3
9. !4! " !8! #
7
6
10. !8! " !7! #
2
1
11. !
1!
3 " !
1!
0 #
12. 3 " !3! #
1
13. Mental Math How many portions can be cut from
6 large sandwiches if each portion is
!1!
8
of a sandwich?
14. Math Reasoning What fraction of a pound is 4 ounces? Explain how you can use
division by a fraction to figure out how many 4 ounce pieces of beef are in 3 pounds.
Test Prep Circle the correct letter for each answer.
15. Which of the following has a quotient different from the others?
2
3
A !3! " !4!
5
4!
C !9! " !
10
4
4
B !9! " !8!
5
5
D !9! " !8!
16. Which of the following has a quotient different from the others?
1
1
F !2! " !6!
3
1
H !2! " !2!
2
2
G !3! " !9!
3
5
J !4! " !6!
© Scott Foresman, Gr. 5
(280)
Use with Chapter 8, Lesson 11.
Name _____________________________________________________________________________________________________
Multiplying and Dividing Mixed Numbers
R 8-12
To multiply or divide mixed numbers, you need to rewrite each mixed number as
an improper fraction.
Example 1
Find 21!3! " 31!2!.
21!3! " 31!2! #
#
#
7
!3! " 7
!2!
(!
7 " 7)
(3 "!
2)
4
9
!6! # 81
!6!
Write the numbers as improper fractions.
Multiply.
Simplify.
Example 2
Find 41!5! $ 31!3!.
41!5! $ 31!3! #
#
#
#
2
!51
!
2
!51
!
$
"
1
!30
!
3
!
1!
0
(21 " 3)
!!
(5 " 10)
13
63
!! # 1!!
50
50
Write the numbers as improper fractions.
Multiply by the reciprocal of the divisor.
Simplify.
Multiply or divide. Simplify, if possible.
3
1
23
11
3
! # 10!!
1. 4!5! " 2!5! # !! " !! # !
25
1
1
13
2. 1!3! " 4!3! # !3! " !! # !9! # 5!9!
1
7
3. 3!2! " 6 # !! " !! # !! #
3
1
4
18
3
54
!
4. 3!5! $ 1!3! # !5! $ !! # !5! " !! # !! # 2!
10
2
1
12
60
5. 2!5! $ 1!5! #!! $ !5! # !5! " !6! # !! #
2
3
3
11
4
! #
6. 1!9! $ !4! # !9! $ !! # !! " !! # !
27
© Scott Foresman, Gr. 5
(282)
Use with Chapter 8, Lesson 12.
Name _____________________________________________________________________________________________________
Multiplying and Dividing Mixed Numbers
H 8-12
Multiply or divide. Simplify, if possible.
3
1
1. !5! " 2!3! #
1
5
3
2. !9! " 4!4! #
2
3. 8!2! " !3! #
5
1
1
2
3
4. 3!4! " 4!2! #
2
5. 1!9! " 4!7! #
6. 3!3! " 1!5! #
2
1
8. 3!2! $ !9! #
1
3
1
10. 2!4! $ 2!4! #
7. 2!3! $ !4! #
9. 6!5! $ !2! #
2
3
3
2
3
1
2
12. 5!5! $ 6!9! #
1
1
14. 4!7! $ !9! #
11. 4!9! $ 1!3! #
2
13. 2!2! " 4!4! #
4
2
3
15. Laurence bicycled 19!
1!
0 miles in 2!3! hours. What was his average speed?
7
16. Laurence brought 3!8! pounds of trail mix for the ride. He shared it equally with 7
friends. Was each friend’s share greater than or less than
1
1
!2!
pound? Explain.
2
17. The entire bike ride lasted 8!2! hours. It drizzled rain for !3! of the ride.
How long did the cyclists ride in the rain?
Test Prep Circle the correct letter for each answer.
2
3
18. Which of the following has the same product or quotient as 4!3! " 6!8!?
18
3
A !3! " 6!8!
14
51
B !3! $ !8!
14
8
C !2! " !
5!
1
14
8
D !3! $ !
5!
1
1
1
19. Which of the following has the same product or quotient as 2!3! $ 1!2!?
3
2
F !7! $ !3!
© Scott Foresman, Gr. 5
7
2
G !3! " !3!
(283)
3
3
H !7! " !2!
3
2
J !7! " !3!
Use with Chapter 8, Lesson 12.
Name _____________________________________________________________________________________________________
Problem-Solving Application
R 8-13
Finding Fraction Patterns
You can solve a problem by finding a pattern.
The band director is arranging musicians in rows. The first row
is as wide as the bandstand. The second row is !12! as wide as the
bandstand. The third row is !13! as wide as the bandstand.
How wide will the sixth row be?
Understand
You need to find out how wide the sixth row will
be. You know how wide the first three rows are.
Plan
You can look for a pattern of how the fractions
change with each row. Then you can continue the
pattern for three more rows.
Solve
Row 1: !11!
Row 2: !12!
Row 3: !13!
Continue the pattern.
Row 4: !14!
Row 5: !15!
So, Row 6 will be
Look Back
1
!!
6
Row 6: !16!
as wide as the bandstand.
Check the pattern. Do the fractions increase
or decrease in a way that makes sense?
Look at a pattern to solve these problems.
The musicians will sit on steps that decrease in height from top to bottom.
The first steps will decrease by the following fractions: !56!, !46!, !36!.
1. What number is the same in all the fractions?
2. What numbers change as the fractions decrease?
3. Is the pattern in the numerator or denominator of the fractions? Explain.
4. By what fractions will the height of the next two steps decrease?
© Scott Foresman, Gr. 5
(285)
Use with Chapter 8, Lesson 13.
Name _____________________________________________________________________________________________________
Problem-Solving Application
H 8-13
Finding Fraction Patterns
Look for a pattern to solve these problems.
1. Some circus clowns arrange themselves so that the second clown
is !59! the height of first clown, the third clown is !69! the height of the
first clown, and so on. What fraction of the height of the first clown
is the height of the fifth clown? the sixth clown?
2. The set crew is hanging photographs of various sizes around the stage.
The second photo is !12! the height of the first, the third photo is !13! the height
of the second, the fourth photo is !14! the height of the third. What size will the
sixth photo be?
3. The height of a series of boxes used in a clown act will decrease by the
9 7 5
!, !!, !!. By what fractions will the height of the boxes
following fractions: !
10 10 10
decrease over the next two boxes?
4. One clown juggles balls that decrease by the following fractions of the first
ball:
1 1 1
!!, !!, !!.
12 10 8
What are the next three fractions in the pattern?
5. The clowns wear oversize wigs, each larger than the next. The first clown’s
wig is 1!45! cm long, the next clown’s wig is 3!35! cm long, and the third clown’s
wig is 5!25! cm long. If the pattern remains the same, what is the length of
the hair on the next three clowns’ wigs?
17
!
6. Clowns can get covered with pie. One clown has !
20 of his costume covered.
The second clown has !1250! of his costume covered. The third clown has !1220! of his
costume covered. How much of the fifth clown’s costume will be covered?
© Scott Foresman, Gr. 5
(286)
Use with Chapter 8, Lesson 13.
Name _____________________________________________________________________________________________________
Evaluating Expressions with Fractions
R 8-14
Evaluating expressions with fractions is similar to evaluating expressions with
decimals or whole numbers.
Example 1
Evaluate
x!
2
"3"
2
"3"
Example 2
# x when
1
"6".
x!
#x!
!
!
2
"3"
4
"6"
5
"6"
#
#
5
"6"
1
"6"
1
"6"
Evaluate
5
"9"
5
"9"
–x !
!
$ x when
5
"6" $ 3
"8"
2
0
9
"
2"
4 $ "
2"
4
1
1
"
2"
4
Example 4
x when
4
"5".
x
5
"6"
3
"8".
!
Example 3
x!
Evaluate
Evaluate x % 6 when
x ! 4"9".
!
5
"9"
!
5 &4
""
9&5
!
& 4"5"
2
0
"
4"
5
!
!
4
"9"
4
"9"
!
4
""
54
x%6!
4
"9"
% 6"1"
& 1"6"
!
2
""
27
Evaluate each expression for x ! 1"2", x ! 1"4", and x ! 1"8"
1
1. "3" # x
"
2. x $ "
16
3
3. "4" x
4. x % "3"
1
1
Evaluate each expression for x ! 2"3", x ! 3"4", and x ! 7"8".
1
5. 3"2" # x
4
6. 4"5" $ x
1
7. 1"3" x
1
8. 7"8" % x
© Scott Foresman, Gr. 5
(288)
Use with Chapter 8, Lesson 14.
Name _____________________________________________________________________________________________________
Evaluating Expressions with Fractions
Evaluate n !
1
3
""
4
and 1"56" # n for each given value of n.
3
2
2. n $ 1"4"
1. n $ "3"
Evaluate "57"n and n %
1
""
4
H 8-14
3. n $ "7"
for each given value of n.
3
2
4. n $ "8"
1
5. n $ 2"3"
1
6. n $ 1"6"
1
7. Terrell’s coin collection is "4" pennies and "5" quarters. If the number of coins in the
collection is c, write an expression that describes the number of pennies. Write a
second expression to describe the number of quarters.
a. If Terrell has 260 coins in his collection, how many are pennies?
How many are quarters?
b. Write an expression to describe what fraction Terrell’s total collection
is neither pennies nor quarters? Explain.
c. There are half as many nickels as there are quarters in the collection.
What fraction of the collection are nickels? Explain.
Test Prep Circle the correct letter for each answer.
1
3
8. Which expression is the correct translation for “x is "3" of "5"”?
3
1
A "5"x $ "3"
1
3
B "3"x $ "5"
1
3
C x $ "3" & "5"
1
3
D x $ "3" ÷ "5"
9. Which expression is the correct translation for “the difference between
33"4" and a number x”?
3
3
F x # 3"4"
© Scott Foresman, Gr. 5
G 3"4" % x
(289)
15
H "4"x
3
J 3"4" # x
Use with Chapter 8, Lesson 14.