Academic Skills Advice
Fractions Refresher Sheet 2
Equivalent Fractions:
Some fractions are equivalent to (the same size as) others.
For example
1
2
is the same as
2
4
.
To make an equivalent fraction you can multiply the top number of a fraction by anything
as long as you do the same to the bottom number, and vice versa.
Examples:
2
3
X2
X4
=
X4
8
3
12
5
X10
=
X2
6
5
10
7
=
X10
50
70
The above pairs of fractions are equivalent because the top and bottom have been
multiplied by the same number every time. NB you should always work in PAIRS – think
to yourself “have I done the same to the top number as the bottom?”
Simplifying/Cancelling Fractions:
This is the same principle as above but you divide the top and bottom by the same
number instead of multiplying.
Examples:
÷5
15
20
÷7
=
÷5
3
14
4
21
÷3
=
÷7
2
12
3
15
=
÷3
4
5
To simplify a fraction you need to look for the number that will go into both the top and the
bottom number. When you can’t simplify any more then the fraction is in it’s simplest form.
You should write fractions in their simplest form wherever possible.
Creating Fractions from Real Scenarios:
If you are asked to write one number as a fraction of another just write the fraction then
simplify if possible. The number that you are writing the fraction of goes on the bottom,
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e.g. If I have £10 and spend £7 I have spent 7 out of 10 which is 10. (It is usually safe to
assume that the biggest number goes on the bottom but this is not always the case.)
Example:
Alex scored 20 out of 25 in a test. Write his score as a fraction in it’s lowest term.
Fraction:
20
25
© H Jackson 2008 / Academic Skills
simplifies to
4
5
(top and bottom divided by 5)
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Practice Questions:
Give a fraction that is equivalent to each of the following:
a)
1
2
b)
e)
3
7
f)
2
3
5
6
c)
3
8
g) 5
8
d)
2
5
h)
3
4
Cancel to the lowest term:
a)
2
4
b)
e)
12
15
f)
5
15
15
18
c)
9
12
d)
8
14
g)
10
14
h)
12
30
Express the following as fractions in their lowest term:
1) Mary scored 15 out of 20 in her algebra test. What fraction did she get correct?
2) 54 pupils are setting off on a school trip at 9am. 36 pupils have arrived by 8.30 – what
fraction have arrived?
3) I am flying abroad and my journey will be 4200 miles. What fraction of my journey
have I completed when I have travelled 600 miles?
4) Sam cuts a gateaux into 16 pieces and her friends eat 6 pieces – what fraction of the
gateaux is left?
5) If a maths lesson is 2½ hours long and 50 minutes is spent on problem solving – what
fraction of the lesson is this?
© H Jackson 2008 / Academic Skills
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