
Unit 7: Numeracy skills
Fractions
Improper fractions
An improper fraction is one where the numerator is larger than the denominator, for example,10 / 3
To convert this to a mixed number (one combining a whole number and a fraction), think of 10 / 3 in the following way:
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
- | - | - | - | - | - | - | - | - | - |
3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
3 x 1 / 3 = 1, so out of the ten 1 / 3’s, nine can be grouped into three whole units, leaving only 1 / 3 left over. Hence, 10 / 3 = 3 1 / 3
Similarly, 12 / 5 = 2 2 / 5
16 / 11 = 1 5 / 11
21 / 15 = 1 6 / 15 = 1 2 / 5 (by cancelling)
We can also go from mixed numbers to improper fractions:
2 1/8 | = | (2 | x | 8) | + | 1 | = | 1 | 6 | + | 1 | = | 1 | 7 |
--------- | - | ----- | - | ----- | ||||||||||
8 | 8 | 8 | 8 | 8 |
3 1/4 | = | (3 | x | 4) | + | 1 | = | 1 | 2 | + | 1 | = | 1 | 3 | ||
---------- | - | ----- | - | ----- | ||||||||||||
4 | 4 | 4 | 4 | 4 |
SMILE - Numeracy skills by Tom Frank, Eric Williams and Clare Wright, University of Birmingham Careers Centre adapted by Marion Kelt Glasgow Caledonian University is licensed under a Creative Commons Attribution 3.0 Unported License.