Calculating Exactly with Fractions
# Calculating Exactly with Fractions

GCSE(F) GCSE(H)

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. If fractions are involved, numbers should be left in fraction form unless indicated otherwise (for example, if a calculation has involved money).

## Examples

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?

Answer: 93p

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)

2. 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.

Explain why Misha is more accurate.

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.

Don used `frac(2)(3) = 0.667`, and multiplied that by 230 for an answer of 153.41.

Misha worked out the answer using fractions, and rounded the answer.

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