Lessons

Math 6
Lessons
Number:
Equivalent Fractions
Equivalent Fractions
Fractions that equal the same number are called Equivalent Fractions. The model
shown below displays two fractions that are the same size and shape, but have
different names.
=
30
100
=
3
10
Since they represent the same area, they are equivalent fractions, meaning that
30 = 3 .
100 10
One way to create equivalent fractions is by dividing both the numerator and
denominator by the same divisor.
÷3
15
36
÷3
=
5
12
Both 15 and 36 are divisible by 3 so divide to get an
equivalent fraction.
You may also make equivalent fractions by multiplying both the numerator and
denominator by the same number.
5
7
•3
•3
=
15
21
Another way to visually represent fractions is by using fraction strips.
1 2
=
4 8
Looking at the fraction strips, you can see that taking the fraction strip
1
representing 4 and multiplying the number of sections by 2 gives you a
strip representing 2 . So the conversion of 1 = 2 is found by multiplying
8
4 8
the numerator and denominator by 2.
Math 6
1-1
Math 6
Lessons
Number:
Equivalent Fractions
When you learn to add and subtract fractions later it will be important to know
how to create equivalent fractions.
Example 1
a. Use a visual model to show that 2 = 8 and explain your
3 12
answer in words.
b. Replace the
with a number that makes the sentence true.
Explain in words how you found your answer.
3
=
7 21
2
c. Write three fractions equivalent to 5 .
Solution 1
a. Use a visual model to show that 2 = 8 and explain your
3 12
answer in words.
2
Using fraction strips, the 3 must be multiplied by 4 to obtain
the strip that will show 8 . The coloured parts of the strips are
12
the same size and showing that the fractions are equivalent.
b. Replace the
with a number that makes the sentence true.
Explain in words how you found your answer.
3
=
7 21
= 9. The denominator has been multiplied by 3 because
7 x 3 = 21 so the numerator needs to be multiplied by 3,
yielding 3 x 3 = 9.
1-2
Math 6
Lessons
Number:
Equivalent Fractions
2
c. Write three fractions equivalent to 5 .
x2
x3
x4
2 4
=
5 10
2 6
=
5 15
2
8
=
5 20
x2
x3
x4
For this you need to simply multiply both the numerator and denominator
of your fraction by the same number.
Let’s Practice
Using the given fraction strips, create an equivalent fraction to the
shaded model.
Given Model
Fraction
Equivalent Fraction Model
Fraction
3
4
1.
2.
3.
4.
Replace each
9
15
1.
5
3.
4
=
5 50
Math 6
=
with a number that will make the fractions equivalent.
15 3
2. 25 =
8
4. 11 = 77
1-3
Math 6
Lessons
5.
1
=
2 8
7.
3
=
8 24
9.
35
=
Equivalent Fractions
6.
6
7
11. 7 = 14
9
8.
10.
14.
7 14
15. 9 =
16.
35
=
6
=
20
24
1
=
3 27
16
=
3
4
12. 36 = 4
45
6
7
13.
1-4
Number:
16
=
3
4
36 4
=
45