WJEC MATHEMATICS
INTERMEDIATE
FRACTIONS, DECIMALS, AND
PERCENTAGES
EQUIVALENT FRACTIONS
1
Contents
Simplifying Fractions
Mixed and Improper Fractions
Equivalent Fractions
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
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Simplifying Fractions
Key Point:
If you multiply (or divide) the numerator and denominator
of a fraction by the same number, the fraction is
unchanged.
Any question that involves fractions may require you to simplify
To simplify a fraction you need to divide the top and bottom number
of the fraction by the same number
Example
Simplify
12
36
So, we need a number that we can divide 12 and 36 by. They are
both even, so we can divide the top and bottom number by 2
6
18
Again, both of these are even, so we can divide them both by 2 and
we get
3
9
We cannot divide these numbers by 2. But we can divide them both
by 3
1
=
3
(You may have noticed that 12 and 36 are both in the 12 times table,
so you could have divided them both by 12 at the start and you
1
would get 3 much sooner. It does not matter how many steps you
take to get the answer.)
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Example 2
Simplify
42
56
Both numbers are in the 2 times table so divide by 2
21
28
Both numbers are in the 7 times table, so divide by 7
3
4
42
3
So, 56 = 4
Exercise N44
Simplify the following
a. 20
18
d. 56
49
g.240
35
e. 60
25
h.142
44
f. 72
b. 40
c. 48
64
90
24
12
i. 45
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Mixed and Improper Fractions
A mixed number consists of a large number (whole parts) and a
fraction (fractional part). The numerator of the fraction will always be
smaller than the denominator
2
E.g. 3 5
An Improper Fraction is a 'top heavy' fraction. (The numerator is
bigger than the denominator)
E.g.
17
5
Mixed to Improper
When given a mixed number, and you need to convert it to be an
improper fraction, follow these steps;
1. Multiply the large number by the denominator
2. Add the numerator to this
This gives you the new numerator. The denominator
stays the same!
Example
4
65 =
34
6 multiplied by 5 is 30, then
add the 4
5
Denominator stays the
same!
5
Exercise N45
Change the following to improper fractions
a. 4 3
2
d. 5 10
4
e. 8 11
7
f. 8 7
b. 5 5
c. 7 9
1
3
g. 5 2
4
h. 5 11
2
i. 11 12
4
11
Improper to Mixed
To convert from an improper fraction to a mixed number, follow these
steps
1. Find out how many times the denominator goes into the
numerator and what the remainder is.
The number of times becomes the large number
The remainder becomes the numerator.
The denominator does not change!
Example
42
5
How many 5's are in 42?
𝟐
𝟖
𝟓
8 with 2 left over
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Exercise N46
Convert the following improper fractions to mixed numbers
a.
55
b.
30
c.
60
6
4
7
d.
90
e.
100
f.
8
3
54
5
g.
84
h.
99
i.
9
5
50
8
7
Equivalent Fractions
Simplifying fractions is all about dividing the top and bottom number.
However, you can also multiply the top and bottom number to find
equivalent fractions.
For example, start with any fraction;
2
3
Now, multiply the top and bottom by 2
4
6
We could have chosen to multiply the top and bottom by 3
6
9
All of these fractions are equivalent (the same)
2 4 6
= = =⋯
3 6 9
See the pattern?
The top numbers are the 2 times table and the bottom numbers are
the 3 times tables.
We can use this information to write all the equivalent fractions of;
5 10 15 20 25
=
=
=
=
=⋯
7 14 21 28 35
Exercise N47
Write the first 6 equivalent fractions of
1
a. 4
3
b.8
3
e. 12
4
f. 14
c. 5
d. 9
11
7
8
Example Question
3
2
Which is bigger; 7 or 5
To compare fractions, you need to make sure the denominators
(bottom numbers) are the same. Keep writing their equivalent
fractions until you have a fraction in each list with the same
denominator.
3
6
9
12 15
=
=
=
=
7 14 21 28 35
2
4
6
8
10 12 14
=
=
=
=
=
=
5 10 15 20 25 30 35
So now we can compare!
15
14
Which is larger, 35 or 35
It's clear that
15
35
is larger so our answer is
3
7
Exercise N48
Which is the larger fraction
3
5
3
8
3
5
5
8
a. 4 𝑜𝑟
b. 7 𝑜𝑟
c. 7 𝑜𝑟
11
7
8
8
12
40
d. 13 𝑜𝑟
e. 9 𝑜𝑟
3
f. 5 𝑜𝑟
45
4
7
6
13
𝑜𝑟
9
Exam Questions N26
1.
2.
3.
4.
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