Calculating Exactly with Fractions

## Calculating Exactly with Fractions

Fraction calculations do not always give an exact answer. For example, multiplying 20 by frac(1)(2) gives an exact answer of 10, but multiplying 20 by frac(1)(3) gives an answer of 6.dot6, or 6.6666...

Calculations should always be carried out as accurately as possible, with any rounding taking place at the very end of the calculation. Where fractions are involved, numbers should be left in fraction form, unless told otherwise. If the answer involves money, then give the answer with two decimal places eg £3.45.

## Example 1

Apples are normally sold at £2.80 per kilo at the local store. They are currently reduced to two thirds of their normal price. If I buy half a kilo, how much would that cost me?

Work in pence. The final cost is normal price x discount x purchase amount

= 280 x frac(2)(3) x frac(1)(2)

= 280 x frac(1)(3) (cancelling the twos)

= 93.333

= 93.33 pence (round to the nearest penny)

Don worked out 230 xx frac(2)(3) as 153.41. Misha worked on the same calculation for an answer of 153.33, which she rounded to 2 decimal places.
Don used frac(2)(3) = 0.667, and multiplied that by 230 for an answer of 153.41.
Answer: Don first approximated frac(2)(3) as 0.667, and the approximation was multiplied 230 times. Misha made her approximation only with the final answer.