Maths. The Truth about Mixed Numbers


It is a common misconception that one needs to convert mixed numbers into top heavy fractions to add or subtract them. Unlike with multiplication or division of mixed numbers we can leave them as mixed numbers.

Example 1

158 7/8 +23 23/24.

This means 158 + 7/8 + 23 + 23/24 so, of course we can add the whole number parts and fraction parts separately.

We get 181 + 44/24

= 181 + 11/6

= 182 5/6

It would have been very time consuming to have turned them into top heavy fractions, which not only would have been a waste of time in an exam but would also have increased the chance of making mistakes.

Example 2

68 1/4 - 25 1/3.

This means (68 + 1/4) - (25 + 1/3)

= 68 +1/4 - 25 - 1/3

= 43 + (3 - 4)/12

= 42 + (3 + 12 -4)/12

= 42 11/12

Again, we subtracted the whole number and fraction parts separately, but when the fraction part becomes negative we make the whole number part one less and add one back in terms of the lowest common denominator to keep the overall value the same.