Academic Skills Advice
Fractions Refresher Sheet 3
Mixed Numbers & Improper Fractions:
An improper fraction is top heavy (𝑒𝑔
12
5
).
2
A mixed number has both a whole number and a fraction (𝑒𝑔 5 3 ).
You may be asked to convert from one to the other.
Changing from Improper to Mixed:
Divide the bottom number into the top then the remainder is written as the fraction.
Examples:
13
5
17
3
Whole ones
Fifths
How many 5’s in 13 (answer is 2) how many left over? (answer is 3) = 2
3
How many 3’s in 17 (answer is 5) how many left over? (answer is 2) = 5
2
5
3
Changing from Mixed to Improper:
Multiply the whole number by the bottom number of the fraction then add on the top
number of the fraction.
Examples:
4
2
3
4
3
7
4 x 3 = 12 then add the extra 2 on. You have 14 thirds =
14
3
3 x 7 = 21 then add the extra 4 on. You have 25 sevenths =
25
7
Try doing all the examples the other way round and see if you get back to where we
started.
1
H Jackson 2008 / Academic Skills
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Practice Questions:
Change the improper fractions to mixed numbers:
a)
e)
15
7
18
b)
f)
6
14
3
22
c)
g)
9
11
4
10
3
d)
h)
16
5
22
8
Change the mixed numbers to improper fractions:
a) 5
1
3
1
e) 9 2
H Jackson 2008 / Academic Skills
4
b) 3 7
2
f) 2 9
2
c) 8 5
5
g) 3 6
1
d) 4 4
5
h) 1 8
2