Ratio, proportion and percentages

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# 3.5.1 Try some yourself

## Activity 26

• (a) What is 40% as a fraction?

• (b) What is    as a percentage?

• (c) What is 1.26 as a percentage?

• (a)  40% =    =  .

• (b)    =   × 100% = 3 × 25% = 75%.

• (c) 1.26 = 1.26 × 100% = 126%.

## Activity 27

In an election 1248 votes out of 3000 are cast for the Gold party. What is this as a percentage? If in the previous election 35.1% voted Gold, what is the swing to Gold in percentage points?

× 100% = 41.6%.

The swing is 41.6 − 35.1 = 6.5 percentage points.

## Activity 28

A quote from a builder for some home improvements is £2200 plus VAT.

• (a) If VAT is %, what is the amount including VAT?

• (b) If the builder gives 10% reductions for prompt payment, what would the amount be then (including VAT)?

• (a) £2200 × = £2585.

• (b) £2585 × = £2326.50.

## Activity 29

An airline decides to increase its fares from London to Europe by 17% and its fares to North America by 15%. Before the increase a special offer European fare from London to Geneva was £165 and the North American fare from London to New York was £376. What would the new fares be for these trips after the increases?

The London to Geneva fare is increased by 17%. So it will now cost 117% of £165, i.e. 1.17 × £165 = £193.05.

The London to New York fare is increased by 15%. So it will now cost 115% of £376, i.e. 1.15 × £376 = £432.40.

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