Chapter Review
Frequently Asked Questions
Q: How can you multiply two mixed numbers?
A1: You can use an area model to multiply two mixed numbers.
For example, suppose that you wanted to calculate the area of
a rectangle that is 1 1 units long and 2 1 units wide. There are
3
4 5 squares, each with an area of
20
6
10
,
3
or
3 1.
3
2
1
So, the total area is
1
2
1
6
1
6
1
6
1
1
3
2
1
.
6
1
6
1
6
1
6
A2: You can write each mixed number as an improper fraction. Then
you multiply the numerators to get the numerator of the product
and multiply the denominators to get the denominator of the
product.
1
1
4
5
1 2 3
2
3
2
20
6
2
3
6
1
3
3
You can check if your answer is reasonable by estimating. Since
1 2 1 2 1, it is reasonable that the answer is a bit more
2
2
than 3.
328 Chapter 9
NEL
Q: How can you divide two fractions?
A1: You can determine the number of times the divisor fits into the
dividend using fraction strips and a common denominator.
2
5
8
5
2 3
6
3
6
16
5
6
6
16
1
, or 3 5
5
1
3
1
6
1
3
1
6
1
6
1
3
1
6
1
6
1
3
1
6
1
6
1
3
1
6
1
6
1
3
1
6
1
6
1
3
1
6
1
6
1
3
1
6
1
6
1
3
1
6
1
6
1
6
1
6
1
6
A2: You can multiply by the reciprocal. For example,
2
5
8
5
2 3
6
3
6
8
6
3
5
48
15
16
1
, or 3 5
5
Q: In what order do you perform a series of fraction calculations?
A: Use the rules for the order of operations:
Perform the operations in Brackets first.
Calculate Exponents next.
Divide and Multiply from left to right.
Add and Subtract from left to right.
For example,
3
2
1
3
1 2 2
2
5
5
8
8
3
3
2
1
1 2 2
2
5
5
2
3
3
2
1
1
2
2
5
5
4
3
3
1
2
2 2
4
3
3
1
2
2
2
3
2
1
3
( )
()
NEL
Fraction Operations
329
Practice Questions
(9.1)
(9.1)
1. Sketch a model and calculate.
3
2
a) 5
7
3
2
b) 5
7
3
5
3
4
2
3
3
2
and .
5
3
c) How much greater is the sum than the
difference?
(9.1)
1
2
d) 10
5
5
2
e) 9
7
7
2
f) 8
3
10. What is the value of each expression? (9.4)
3
(9.1) 4. Jake mowed about of the school lawn
5
yesterday. He mowed another 1 of the lawn
4
this morning. How much is left to mow?
(9.2)
5. Sketch a model, and calculate the answer.
1
3
a) 2 3
5
5
4
1
b) 2 3
5
2
(9.2)
a
b
1
c) 8 2
3
3
1
d) 7 2
10
4
a
b
b
a
7. Calculate.
1
1
a) 2 3
5
6
1
1
b) 5 3
2
3
330 Chapter 9
3
c) 8 1
5
1
5
d) 6 3
4
6
1
1
a) of 5
2
3
8
b) of 8
9
2
6
c) of 3
8
4
1
d) of 6
2
11. What is the missing fraction in each
sentence?
2 2
a) is of ■.
5 3
3 3
b) is of ■.
8 4
6. is a fraction. The sum of and is
close to 2. List two possible values for
(9.2)
9. a) Continue this addition pattern to get
(9.3)
three more terms in each row.
4
4
4
4
5
10
20
40
12
12
12
…
10
20
40
b) What is the 10th number in the 2nd row?
c) Why does it make sense that all the
numerators in the 2nd row are 12?
3. Calculate.
5
1
a) 8
3
3
5
b) 4
6
2
1
c) 5
7
cup of sugar. These are the only dry
ingredients. What is the total measure of
(9.2)
the dry ingredients?
2. a) Calculate the sum of and .
b) Calculate the difference of
2
3
8. A recipe calls for 1 cups of flour and
a
.
b
1
2
c) is of ■.
12 4
1
5
d) is of ■.
12 2
12. What is the missing fraction in each
sentence?
1
1
5
1
a)
■ of 2 is 8.
b)
■ of 6 is 1.
2
(9.4)
4
1
5
3
c)
■ of 9 is 3.
d)
■ of 7 is 7.
13. Sketch a model for this calculation.
6
3
2
20
4
5
(9.4)
(9.5)
NEL
(9.5)
1
2
14. Which products are greater than ?
3
5
A. 4
6
1
7
B. 6
8
(9.5)
3
8
C. 9
9
3
2
D. 5
3
same quotient as 4 3.
5
15. How much greater is the first product than
the second product?
()
()
(9.5)
17. About
3
4
5
2
d) 8
3
1
5
e) 5
7
3
2
f) 7
5
22. Calculate.
(9.7)
5
1
a) 6
6
5
1
b) 8
4
5
1
c) 6
4
3
2
d) 8
9
3
4
25. Choose two fractions to make each
statement true.
4
1
2
18. Eileen used to be on the phone 3 times
as much as her sister every day. As a New
Year’s resolution, she decided to cut down
to about 2 of the time she used to be on the
5
phone. About how many times as much as
her sister is Eileen now on the phone?
19. Calculate.
NEL
(9.7)
of cookies. How much of her sugar would
(9.8)
she need to make the whole batch?
of the students in the drama club
3
1
a) 3
7
2
2
3
b) 1 5
5
1
2
c) 1 1
3
3
3
6
5
2
3
Grade 8. What fraction of the students in
the drama club are Grade 8 girls?
(9.6)
4
6
24. Pia used of her sugar to make of a batch
are girls. About 3 of these girls are in
(9.6)
1
2
23. What fraction calculation can you use
to determine the number of quarters in
(9.7)
$4.50?
16. Calculate.
2
2
a) 9
7
2
3
b) 5
2 3
c) 3
1
3
21. Explain how you know that has the
3
5
1
5
a) than 4
6
4
6
3
5
3
1
b) than 4
6
4
2
(9.5)
5
6
20. Sketch a model to show 2 . (9.7)
5
12
d) 6
6
25
3
3
e) 2 3
4
4
1
3
f) 3 6
5
8
(9.8)
a) The sum is greater than the product.
b) The sum is less than the product.
c) The quotient is greater than the sum.
26. Use fractions to explain why 4.5 0.5
(9.9)
equals 2.25.
27. Which expression has the greatest value?
(9.10)
How do you know?
4
2
1
5
A. 5
3
5
8
4
2
1
5
B. 5
3
5
8
4
2
1
5
C. 5
3
5
8
(
(
)
)
28. Where can you place brackets to make this
(9.10)
equation true?
3
1
2
1
193
5
4
3
3
120
Fraction Operations
331