Level 2 – Fractions– Equivalence – 2-07b
*There are different ways of writing the same number - a fraction is
one way. Decimals and
percentages are other ways and will be looked at elsewhere.
*To make an equivalent fraction, multiply or divide the top and
bottom by the same number.
*We can use equivalences to solve problems, justifying the method
used.
Below are some questions that you can use to test your understanding
of how to calculate equivalent fractions and in what sort of contexts
they can be used.
Question 1
1
2
and
6
12
are two ways of representing how much of the rectangle is
coloured blue. Write down 2 more equivalent fractions that represents
how this rectangle can be split.
Question 2
Find the missing numbers in the following questions:
3 ?
? 9
? 10
a)
b) 
c) 

5 10
4 12
3 15
d)
3 ?

4 16
Question 3
Find the missing numbers in the following questions:
6 ?
? 2
? 5
4
?
b)
b)
c)
d)




8 4
25 5
30 6
22 11
Question 4
Find three fractions that are equivalent to
3
.
7
(More questions on the next page)
Questions in context
Question 5
You have a friend over for tea and you both want to order pizza.
You have a coupon for 2 large pizzas.
You cut one pizza into 3 equal pieces and you eat 2 slices.
Your friend cuts the other pizza into 12 equal pieces, how many
slices must they eat, to eat the same amount of pizza as you?
Question 6
Here are the ingredients for a fruit crumble. The quantity of each
ingredient is shown by weight and as a fraction of the total weight
of ingredients. Write these fractions as their smallest equivalent
fraction.
Original recipe
Fraction of total
12 oz fruit
12
20
2
20
5
20
4
20
2 oz margarine
4 oz self raising
flour
2 oz sugar
Smallest equivalent
fraction
Question 7 – Have a think!
In a class of 20, 8 of the students are girls. What fraction of the
class are girls?
In another class of 25 students 10 of them are girls. What fraction
are girls?
Do the two classes have an equivalent fraction of girls in their
classes?
Answers
Question 1
2
4
Another equivalent fraction is
and another one would be
3
6
Question 2
The missing numbers are:
a)
d) x2
3
10
x2
x5
2
9
=
4
c)
x3
3
6
=
5
b)
12
3
x3
=
x4
3
10
15
4
X5
=
12
16
x4
Question 3
The missing numbers are:
a)
d)
÷2
6
=
8
3
10
4
25
÷2
b)
c)
=
÷2
÷5
÷5
2
25
5
30
=
4
5
22
6
÷2
÷5
÷5
Question 4
There are many fractions equivalent to
(a) Start with
7
=
x2
3
. Two ways of finding some are shown.
7
3
and multiply by , 2 , 3, 4, etc
7
x2
3
x3
6
14
3
7
=
x3
x4
9
21
3
7
=
=
x4
12
28
2
11
(b)Keep doubling top and bottom
x2
3
=
7
x2
6
=
14
x2
12
28
24
=
56
Question 5
x22
x2
x2
?
You eat
of your pizza, your friend eats
, so
3
12
x4
2
3
=
8
Your friend eats 8 slices.
12
x4
Question 6
The factions written as their smallest equivalent fractions, are.
Original
Fraction
Working
Answer
recipe
of total
÷2
12 oz fruit
12
20
12
20
=
÷2
6
10
÷2
=
3
5
3
5
÷2
÷2
2 oz
margarine
2
20
2
20
=
1
10
1
10
÷2
÷5
4 oz self
raising
flour
5
20
5
20
=
1
4
1
4
÷5
÷4
2 oz
sugar
4
20
4
20
=
1
5
1
5
÷4
Question 7 – Have a think
In a class of 20, 8 of the students are girls. What fraction of the
class are girls?
In another class of 25 students 10 of them are girls. What fraction
are girls?
Do the two classes have an equivalent fraction of girls in their
classes?
8
10
are girls and in the second class
are
20
25
girls, and if these fractions are equivalent they should be able to
be expressed over the same denominator.
In the first class
First class simplified
simplified
Second class
÷5
10
÷4
8
20
=
2
25
5
=
2
5
÷5
÷4
Because they both reduce to 2 then they are equivalent. There is the same
5
fraction of girls in each class.