You will need
9.4 Subtracting Fractions
• fraction strips
• number lines
with Models
GOAL
Subtract fractions less than 1 using fraction strips and number lines.
Learn about the Math
Yuki notices that 3 of the houses on Fox Street have garages and 1 have
4
6
sheds.
? How many more of the houses have garages than sheds?
A. Model 3 and 1 using fraction strips.
4
6
3
1
B. Determine the common denominator of and . Redraw your
4
6
models with this denominator.
C. How many parts of the new fraction strip represent the difference
3
1
between and ?
4
6
D. How many more houses have garages than sheds?
Reflecting
1. How could you have predicted that the answer in step D would be
2
greater than ?
4
3
4
1
6
2. What equivalent fractions did you use for and in step B?
3. How did using a common denominator help you make the fraction
strips in step C?
4. Explain how you can use fraction strips and a common denominator
to subtract fractions.
316 Chapter 9
NEL
Work with the Math
Example 1: Estimating and subtracting using fraction strips
Estimate and then subtract 2 1 using fraction strips.
3
5
Ryan’s Solution
I used fraction strips to show both fractions.
Then I figured out the difference between the longer coloured
part and the shorter coloured part.
It looks like the difference is about 1.
2
15 is a common denominator of 2 and 1 because 15 is a
3
5
common multiple of 3 and 5. So, I divided the fraction strips
into fifteenths.
0
25
The 2 strip becomes 10 because 2 , which is 1
.
3
15
35
3
15
3
13
The 1 strip becomes 3 because 1 , which is .
15
5
53
5
15
The difference is 10 3 7.
15
15
15
Example 2: Subtracting using a number line
Subtract 5 1 using a number line.
6
2
Yuki’s Solution
I used a number line showing twelfths, since
12 is a common denominator for 5 and 1.
6
5
52
6
62
10
12
2
1
16
2
26
6
12
I drew arrows to show 5 and 1.
6
2
I need to find the distance from 5 to 1.
6
2
There are four spaces between 1 and 5.
2
6
Since each space is 1, then 5 1 4.
12
NEL
6
2
12
Fraction Operations
317
Checking
5. a) How do you know that the difference
4
1
1
for is about ?
5
3
2
11. a) What fraction of the larger flag is red?
b) What fraction of the smaller flag is red?
c) How much more of the smaller flag is
red?
b) Use fraction strips to subtract 4 1.
5
3
6. Use a number line to model the difference
4
1
for . Show your work.
3
2
7. Suppose that 3 of the students in your class
5
1
6
have pets, and have more than one pet.
a) Use fraction strips or a number line to
calculate the fraction of the students
with only one pet.
b) How many students have no pets?
Practising
8. Use fraction strips to estimate and then
calculate each difference.
5
1
11
3
d) a) 8
4
8
4
1
1
7
3
b) e) 4
5
10
10
7
2
5
5
c) f) 6
3
3
4
9. Use number lines to calculate each
difference.
3
7
2
1
d) a) 5
4
3
10
5
3
1
3
b) e) 2
4
5
10
8
7
9
9
c) f) 3
9
4
8
10. Draw and colour a shape so that 5 is blue
8
1
and is yellow.
3
a) What fraction describes how much
more is blue than yellow?
b) What fraction describes the part of the
shape that is not blue or yellow?
318 Chapter 9
2
10
12. At Oakville School, of the students are
1
in Grades 7 and 8, and of the students
4
are in Grades 5 and 6.
a) Are there more Grade 5 and 6 students
or Grade 7 and 8 students?
b) What is the difference between the
sizes of the two groups of students?
Give your answer as a fraction of the
whole school.
1
13. Rosa does of her book report on Tuesday
2
and another 20% of her book report on
Wednesday. What fraction of the book
report is left to do?
1
14. Anne needs c. of sugar to make a dessert.
6
1
Ken says that she should fill a c.
2
measuring cup with sugar and then pour
1
out enough to fill a c. measuring cup.
3
1
He says that c. of sugar will be left in the
6
1
c. measuring cup. Do you agree? Explain.
2
NEL
15. Mohammed surveyed students in the school
about their favourite activities. The results
are shown in the following table. Use the
fractions to answer the questions.
Activity
swimming
tobogganing
skating
soccer
Fraction of students
who prefer activity
1
4
1
6
1
12
1
3
a) What fraction describes how many
more students prefer playing soccer to
swimming?
b) What fraction describes how many
more students prefer swimming to
skating?
c) What fraction describes how many
more students prefer tobogganing to
skating?
16. a) Subtract each pair of fractions. Look for
a pattern in the differences.
1
1
1
1
iii) i) 3
4
5
6
1
1
1
1
ii) iv) 4
5
6
7
b) Use the pattern you saw in part (a) to
1
1
help you calculate .
2
3
17. Addition is not the same as subtraction.
Yet, some of the steps for adding fractions
are the same as the steps for subtracting
fractions. Which steps are the same? Why
are they the same?
Extending
18. To subtract 4 3, Ann decides to add 1
3
4
4
to 1.
3
a) Model 4 and 3 on a number line.
3
4
b) Explain Ann’s method.
c) What is the difference for 4 3?
3
4
19. A travel agency is finding volunteers for
1
1
a travel group. Between and of the
4
2
group must be between the ages of 15 and
1
21, and at least of the group must be over
2
the age of 21.
a) What is the least fraction of the group
that can be under 15? Show your work.
b) What is the greatest fraction of the group
that can be under 15? Show your work.
20. Can the sum of two fractions equal the
difference between the same two fractions?
Explain.
21. What digit can you put in both boxes to
make the following equation true?
■ 2 11
7
■ 21
NEL
Fraction Operations
319