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You will need
• fraction strips
• grid paper
• coloured pencils
9.5 Multiplying Fractions
GOAL
Multiply two fractions less than 1.
Learn about the Math
About 1 of Canadians who are 12 and older
10
downhill ski. About 2 of these skiers are between
5
the ages of 12 and 24.
fraction of the Canadian
? What
population between the ages
of 12 and 24 downhill ski?
Example 1: Using a fraction strip model
The fraction of Canadians between the ages of 12 and 24 who downhill
ski is 2 of 1. What fraction is this?
5
10
Jordan’s Solution
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
1
10
I used fraction strips to model 2 of 1.
5
I divided
1
10
10
into 5 equal sections and
coloured 2 of the sections.
I divided each 1 the same way to
10
determine the size of each section.
I made 5 10 50 sections. Only 2
sections were coloured.
So, 2 of 1 is 2.
5
2
50
10
50
1 since every 2 sections of 1
25
50
can be combined to make 1 section of 1.
1
2
2
of 10
50
5
1
25
About 1 of Canadians between the ages of 12 and 24 downhill ski.
25
25
300 Chapter 9
NEL
Example 2: Using a grid model to determine a fraction of a fraction
Calculate 2 1.
5
10
Sheree’s Solution
10
To calculate the area of a rectangle, you multiply the two
dimensions. The area of a rectangle 5 units wide and 10 units
long is 5 10. So, 2 1 must be the area of a rectangle that
5
5
Area 5 10
1
10
10
is 2 of a unit wide and 1 of a unit long.
10
5
I used a 5-by-10 grid to help me see the fifths and tenths.
There are 5 10 or 50 sections.
2
5
The purple rectangle is 1 wide and 2 long. It is 2 of the whole.
10
2
50
50
5
can be written in simplest form as 1.
25
2
1
21
5
10
5 10
2
50
1
25
Reflecting
2
5
1
10
2
5
1
10
1. Calculating of is the same as calculating . How does
Sheree’s solution show this?
2. How can you use a model to determine the numerator and
denominator of a product?
3. Write a rule for multiplying two fractions less than 1.
NEL
Fraction Operations
301
Work with the Math
Example 3: Multiplying fractions less than 1
About 2 of the students in Windham Ridge School are in Grades 7 and 8. About 5 of these
3
8
students are girls. What fraction of the students in the school are girls in Grades 7 and 8?
Solution A: Using fraction strips
Solution B: Using an area model
This model shows 5 of 2. Divide 2 into
8
3
Colour a 3-by-8 rectangle to show 5 by 2.
3
8
1
3
1
12
1
12
1
3
1
12
1
12
1
12
1
12
1
3
1
12
1
12
1
12
1
12
1
12
3
5
2
52
8
3
83
10
24
5
12
8 equivalent sections, and colour 5 of the
sections.
1
12
So, 5 of the students are girls in Grades 7
5
2
5
8
3
12
12
and 8.
So, 5 of the students are girls in Grades 7
12
and 8.
A
Checking
B
4. What multiplication expression does each
model represent?
a)
1
4
1
4
1
4
1
4
Practising
7. What multiplication expression does each
model represent?
a)
1
8
1 1 1 1 1 1 1 1 1 1 1 1
12 12 12 12 12 12 12 12 12 12 12 12
b)
1
4
1
4
1
8
1
8
1
4
1
8
1
8
1
4
1
8
1
8
1
8
b)
c)
3
4
2
5
5. Draw a model for . Use your model
to determine the product.
2
11
6. About of Canadian downhill skiers are
from British Columbia. Recall that about
1
10
of Canadians downhill ski. What
8. Draw a model for each multiplication
expression. Determine the product.
1
3
1
2
c) a) 2
8
6
5
4
1
3
2
b) d) 5
3
4
6
fraction of all Canadians are downhill
skiers from British Columbia?
302 Chapter 9
NEL
15. a) Recall that a2 a a and
a3 a a a.
Calculate each power for a 2.
9. Match each expression with its product.
7
5
a) 10
6
8
1
3
4
b) 15
6
8
9
3
7
2
9
c) 10 12
6
10
4
14
d) 7
15
3
i) a2
iii) a4
b) Why does a higher power of 2 result in
3
a lower product?
1
3
10. Matthew’s bed takes up of the width of
his bedroom and 3 of the length. What
5
fraction of the area of the floor does
Matthew’s bed take up?
2
3
ii) a3
16. How does the product of two fractions less
than 1 compare with the two fractions
being multiplied? Is the product greater
than, less than, or equal to each fraction?
How do you know?
17. a) Calculate 0.4 0.3.
b) Rename each decimal as a fraction, and
multiply. What do you notice?
5
8
11. Jessica is awake of the day. She spends of this time at home.
a) What fraction of the day is Jessica
awake at home?
b) How many hours is Jessica awake at
home?
C
Extending
3
4
18. More than of Americans eat ice cream at
least once a month. About 3 of these
10
12. a) Complete this pattern, and continue it
for three more products.
1
4 ■
2
1
2 ■
2
1
1 ■
2
1
1
■
2
2
b) How does this pattern explain the
product of
13. a)
1
2
1
?
2
Draw a picture to show that 2 3 6.
5
8
40
people eat vanilla ice cream.
a) What fraction of Americans eat vanilla
ice cream at least once a month?
b) According to recent statistics, there are
about 300 million Americans. About
how many of them eat vanilla ice
cream at least once a month?
19. a) What is the probability
of landing in the red
B
A section?
b) Why does it make
sense that the
2
3
2
7
40
c
d
■
■
14. Daniel said that . Complete the
missing fraction, and explain your thinking.
NEL
A
B
a
a2
2
9
20. What is the value of a in ?
product of 6.
a
b
B
A
probability is 1 1?
b) List two other pairs of fractions with a
A
21. What is the product of
1
2
2 3 4 … 99?
3
4
5
100
Fraction Operations
303