Multiply going out and divide coming back
- Check the direction first by asking which currency the answer has to be in: an answer in pounds comes from dividing a foreign amount, an answer in foreign currency comes from multiplying a pound amount.
- Check the size second, because at 1.40 dollars to the pound a pound is worth more than a dollar, so the dollar figure must always be the bigger of the two numbers.
Example
- A UK student flying to New York has £250 of spending money and the rate is 1.40 dollars to the pound.
Step 1: convert the pounds into dollars by multiplying by the rate:
dollars received=£250×1.40=$350 \text{dollars received} = \pounds250 \times 1.40 = \text{\textdollar}350 dollars received=£250×1.40=$350- Coming home the student has 63 dollars left over and changes it back at the same rate.
Step 2: convert the dollars into pounds by dividing by the rate:
pounds received=$63÷1.40=£45 \text{pounds received} = \text{\textdollar}63 \div 1.40 = \pounds45 pounds received=$63÷1.40=£45- The £250 and the 350 dollars are the same money described in two currencies, so converting has made the student neither richer nor poorer.
- To turn pounds into that foreign currency, multiply the number of pounds by the rate, because every pound is worth 1.40 of them.
- To turn that foreign currency back into pounds, divide by the rate, because you are asking how many whole pounds the amount contains.
A change in the rate changes every price
Example
- A UK bakery buys an American dough mixer priced at 21,000 dollars, and the pound weakens from 1.50 dollars to 1.25 dollars.
Step 1: find the cost in pounds at the old rate, dividing because the price is set in dollars:
cost at the old rate=$21,000÷1.50=£14,000 \text{cost at the old rate} = \text{\textdollar}21{,}000 \div 1.50 = \pounds14{,}000 cost at the old rate=$21,000÷1.50=£14,000Step 2: find the cost in pounds at the new rate:
cost at the new rate=$21,000÷1.25=£16,800 \text{cost at the new rate} = \text{\textdollar}21{,}000 \div 1.25 = \pounds16{,}800 cost at the new rate=$21,000÷1.25=£16,800Step 3: subtract one from the other to find how much dearer the machine has become:
extra cost=£16,800−£14,000=£2,800 \text{extra cost} = \pounds16{,}800 - \pounds14{,}000 = \pounds2{,}800 extra cost=£16,800−£14,000=£2,800- The American seller never altered its price, yet the mixer costs the bakery £2,800 more purely because the pound is weaker.
- The trick is that the price in the seller's own currency does not change at all; what changes is what that unchanged price costs the buyer.
- A weaker pound buys less foreign currency, so anything priced abroad costs a UK buyer more pounds than before.
The same fall makes UK exports cheaper abroad
Example
- The same bakery sells a commercial oven abroad for £600, and the pound again weakens from 1.50 dollars to 1.25 dollars.
Step 1: find the price a US buyer pays at the old rate, multiplying because the price is set in pounds:
US price at the old rate=£600×1.50=$900 \text{US price at the old rate} = \pounds600 \times 1.50 = \text{\textdollar}900 US price at the old rate=£600×1.50=$900Step 2: find the price a US buyer pays at the new rate:
US price at the new rate=£600×1.25=$750 \text{US price at the new rate} = \pounds600 \times 1.25 = \text{\textdollar}750 US price at the new rate=£600×1.25=$750- The oven is 150 dollars cheaper to the American buyer even though the bakery still receives its £600 in full.
- A UK firm sets its price in pounds, so the foreign price is found by multiplying that pound price by the rate.
- When the pound weakens the same pound price converts into fewer dollars, so an American buyer sees a lower price without the UK firm changing anything.
Self review
- At 1.40 dollars to the pound, how many dollars do you get for £30?
- Which operation converts an amount of dollars back into pounds?
- A price is set in dollars and the pound weakens. Does it cost a UK buyer more or fewer pounds?
- A UK good is priced at £600. Give the two steps needed to find how a rate change alters its price abroad.
- Why does converting £250 into dollars leave you no better off?
