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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    

Creative Commons License
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.