Download Finding Common Denominators 20 72 28 36 15 6 45 24 Sample

Practice
Name
9-6
Finding Common
Denominators
In 1 through 8, find a common denominator for each pair of
fractions.
1.
5.
Sample answers are given.
3
5
5
2 and __
4
1 and __
4
7
__
2. __
and __
3. __
4. ___
and __
5
7 28
4 20
8
9 72
4
12
9 36
5
7 and __
1
1 and __
2
2 and __
4
7 and __
___
6. __
7. __
8. __
5 45
15
3 15
2
3 6
9
8
6 24
In 9 through 16, find a common denominator for each pair of
fractions. Then rename each fraction in the pair.
Sample
answers
are given.
3
3
1
2
1
2
___
__
__
__
__
__
9.
12
and
8
6 __
9
24; __
,
24 24
7 and __
1
13. __
9
6
10.
8
and 7
9
1 and __
1
12. __
5
3
7 and __
2
15. __
3
5
16. __
and __
11.
2
and
9 __
4
16
7 __
__
18;
,
,
56; __
18 18
56 56
3
1 and __
14. __
6
4
8
3
5 __
3
15; __
,
15 15
8
9
16
14 __
2 __
21 __
3
__
__
,
12;
,
24;
,
18; __
18 18
12 12
24 24
6
9 __
20
24; __
,
24 24
18. Andrew wants to rename _27 and
_3 using a common denominator.
4
Which of the following shows
these fractions renamed correctly?
17. Train A arrives at Central Station
on the hour and every 12 minutes.
Train B arrives on the hour and
every 15 minutes. When do both
trains arrive at the same time?
8
21
and ___
A ___
A On the hour and 30 minutes
past the hour
B On the hour and 15 minutes to
the hour
C On the hour and 27 minutes
past the hour
D On the hour only
28
28
3
2 and ___
B ___
28
28
6
4 and ___
C ___
28
28
3
2 and __
D __
7
7
11
19. Manuel says that you can use one of the denominators of _56 and __
when
30
renaming these fractions using a common denominator. Why is this true?
Sample answer: You can use 30 as the
common denominator since 30 is a
common multiple of 6 and 30.
P 9•6
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Practice
Name
9-7
Adding Fractions with
Unlike Denominators
Find each sum. Simplify if necessary.
2 + __
1
1. __
9
3
1 + __
2
4. __
4
3
5
1 + ___
7. __
6
12
3
1
10. __
+ __
9
4
5
__
9
11
___
12
7
___
12
31
___
36
3
1 + ___
2. __
7
21
4
1 + __
5. ___
12
6
1
4 + __
8. __
3
6
6
1
11. ___
+ __
12
3
2
__
7
3
__
4
2 + __
1
__
5
3
3.
1 + __
2
6. __
5
2
1
1 + __
1
9. __
5
8
5
__
6
13
___
15
9
___
10
13
___
40
1
4 + __
1
__
8
2
12.
Jeremy collected nickels for one week. He is making stacks of
his nickels to determine how many he has. The thickness of one
1
inch.
nickel is __
16
13. How tall is a stack of 16 nickels?
1 inch
14. What is the combined height of 3 nickels, 2 nickels,
and 1 nickel?
3
__
inch
8
5
4?
15. What is the sum of ___
+ __
30
5
A __
6
6
7
B __
9
9
D ___
2
C __
3
12
11
? What is the sum?
16. How do you rename _25 so you can add it to __
25
Use 25 as the common denominator.
Multiply the numerator and denominator
10
21 .
by 5 to get ___
. The sum is ___
25
25
P 9•7
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Practice
Name
9-8
Subtracting Fractions with
Unlike Denominators
Find the difference. Simplify if necessary.
10
1
1. ___
− __
12
4
7 − __
1
4. ___
12
4
4 − __
1
7. __
8
4
9
1
10. ___
− __
15
3
7
___
12
1
__
3
1
__
4
4
___
15
3
___
10
7
___
15
1
__
5
1
__
6
9
3
2. ___
− __
5
10
4 − __
1
5. __
5
3
4 − __
1
8. ___
5
10
4 − __
1
11. ___
12
6
7 − __
2
3. __
8
6
2 − __
1
6. __
3
6
9
2
9. __
− __
9
3
3
14 − __
12. ___
5
20
13. The pet shop owner told Jean to fill her new fish tank _34 full
9
full. What fraction of the tank does
with water. Jean filled it __
12
Jean still need to fill?
14. Paul’s dad made a turkey potpie for dinner on Wednesday.
The family ate _48 of the pie. On Thursday after school, Paul
2
of the pie for a snack. What fraction of the pie remained?
ate __
16
13
___
24
1
__
2
1
__
3
1
___
10
0
3
__
8
15. Gracie read 150 pages of a book. The book is 227 pages
long. Which equation shows the amount she still needs to
read to finish the story?
A 150 − n = 227
C n − 150 = 227
B 227 + 150 = n
D n + 150 = 227
16. Why do fractions need to have a common denominator
before you add or subtract them?
The denominator tells you how
many equal parts you are adding or
subtracting. The parts must be the
same when you add or subtract.
P 9•8
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Practice
Name
10-1
Improper Fractions and
Mixed Numbers
1. Draw a picture to show _86.
2. Draw a picture to show 3_56.
Check students’ drawings.
Write each improper fraction as a whole number or mixed number
in simplest form.
5
30
3. __
6
5_29
47
4. __
9
52
5. __
7
Write each mixed number as an improper fraction.
__
24
5
6. 4_45
__
55
4
7. 13_34
8. 9_58
7_37
__
77
8
__
32
9. Write 8 as an improper fraction with a
denominator of 4.
4
Which letter on the number line corresponds to each number?
F
4
27
10. __
5
A C
D
B
5
7
11. 4__
10
D
E
C
6
12. 4_35
A
13. Which number does the model represent?
12
A __
8
B 2_38
C 2_47
20
D __
8
14. Can you express _99 as a mixed number? Why or why not?
No, _99 can be expressed only as a
fraction or as a whole number (1).
P 10•1
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Practice
Name
10-4
Adding Mixed Numbers
In 1 through 6, find each sum. Simplify, if possible. Estimate for reasonableness.
5
2 + 8__
1. 7__
3
6
9
1
3. 11___
+ 3___
10
20
8
1
5. 5__
+ 3__
9
2
16_12
19
14__
20
7
9__
18
3
2
2. 4__
+ 2__
5
4
6
2
4. 7__
+ 5__
7
7
11 + 17__
2
6. 21___
12
3
3
7__
20
13_17
7
39__
12
7. Write two mixed numbers that have a sum of 3.
Sample answer: 1_14 + 1_34 = 3
8. What is the total
measure of an average
man’s brain and heart
in kilograms (kg)?
7
1__
kg
10
Vital Organ Measures
Average woman’s brain
3
1___
kg
4 lb
2__
5
Average man’s brain
2 kg
1__
5
3 lb
Average human heart
3
___
kg
10
7 lb
___
10
9. What is the total weight of an average
woman’s brain and heart in pounds (lb)?
10. What is the sum of the measures of an average
man’s brain and an average woman’s brain in
kilograms?
10
3_12 lb
7
2__
kg
10
11. Which is a good comparison of the estimated
11
?
sum and the actual sum of 7_78 + 2__
12
A Estimated < actual
C Actual > estimated
B Actual = estimated
D Estimated > actual
12. Can the sum of two mixed numbers be equal to 2? Explain why or why not.
No; Sample answer: It is impossible for
two mixed numbers to equal 2 because
every mixed number is greater than 1.
P 10•4
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Practice
Name
10-5
Subtracting Mixed Numbers
For 1 through 10, find each difference. Simplify, if possible.
3
10__
1.
3
7__
1
7
2.
4
1
− 7__
8
− 2___
1
3__
1
5___
4
1 − 3__
1
7. 6__
4
3
2 − 7__
1
9. 8__
7
3
13
2___
1
__
3
5
5__
12
8
1 − 3__
7
8. 5__
5
8
9
1
10. 2___
− 2__
10
The table shows the length and width
of several kinds of bird eggs.
1_12 in. longer
12. How much wider is the turtledove
egg than the robin egg?
3
1
2___
12
13
1___
40
17
___
30
Egg Sizes in Inches (in.)
11. How much longer is the Canada
goose egg than the raven egg?
3
__
10
3
− 12___
3
2
6. 4__
− 2__
4
3
18
11
2___
12
20
___
21
8
2
− 2__
21
5
5
− 6__
5. 9__
9
6
71
17__
4.
3
21
2
31
3.
Bird
Length
Width
Canada goose
2
3__
3
2___
Robin
3
__
3
__
4
5
Turtledove
1
1__
9
___
Raven
9
1___
3
1___
in. wider
5
10
5
10
10
10
15
13. Which is the difference of 21__
− 18_34 ?
16
7
A 2___
16
9
B 2___
16
3
C 3___
16
9
D 3___
16
14. Explain why it is necessary to rename 4_14 if you subtract _34 from it.
Sample answer: You cannot subtract _34
from _14 , so you must borrow 1 whole
from the 4 and rename 4_14 as 3_54 .
P 10•5
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