0580 · 1.16Money

Money calculations and change

0:00Imagine buying a few things on holiday, then exchanging your remaining money before travelling home. You need to calculate the bill correctly and understand what the exchange rate means. A larger number in another currency does not automatically mean you have more purchasing power. In this video, we will make money calculations and currency conversions feel logical. You need the four operations and a basic understanding of decimals. Addition combines costs, subtraction finds money remaining, multiplication calculates the cost of identical items, and division can find a cost per item.

0:32The important extra step is keeping track of the currency. An amount without its currency can be unclear or misleading. One pound contains one hundred pence, so the decimal part of a pound measures hundredths. Two pounds and thirty-five pence can therefore be written as two point three five pounds. Five pence is zero point zero five pounds, not zero point five pounds. That zero matters because zero point five pounds represents fifty pence.

0:58Before combining amounts, express them in the same unit and currency. You can calculate entirely in pounds or entirely in pence, but do not mix the two. When adding or subtracting decimals, align the decimal points so corresponding place values match. For pounds, euros and dollars, final amounts are normally written with two decimal places. Our first exam-style example asks for the change when you buy three notebooks and one pen, paying with twenty pounds.

1:23Each notebook costs two pounds and thirty-five pence. Multiplying that price by three gives seven pounds and five pence. Adding the pen’s price of one pound and eighty pence gives a total of eight pounds and eighty-five pence. Subtract eight pounds and eighty-five pence from twenty pounds to obtain eleven pounds and fifteen pence in change. Subtraction works because the payment must equal the purchase cost plus the change. As a check, the bill is slightly below nine pounds.

1:49Your change should therefore be slightly above eleven pounds, which agrees with our answer.

Converting pounds to euros

1:54An exchange rate tells you how much of one currency is equivalent to a stated amount of another. Suppose one pound is equivalent to one point two four euros. Each pound exchanged produces one point two four euros at this rate. For these examples, assume that the stated rate applies without any exchange fees. Think of the rate as a matching pair rather than a command to multiply. To change pounds into euros, each pound becomes one point two four euros, so we multiply.

2:22To change euros back into pounds, we find how many groups of one point two four euros there are, so we divide. The direction follows from what the rate actually says, not from the names of the currencies. Our second exam-style example is to convert one hundred and eighty pounds into euros using this rate. Every pound gives one point two four euros. Multiply one hundred and eighty by one point two four to obtain two hundred and twenty-three point two euros.

2:46Write the final amount as two hundred and twenty-three euros and twenty cents. The multiplication is justified by the value of one pound. You have one hundred and eighty copies of the euro amount corresponding to that pound. The numerical answer is larger because each pound corresponds to more than one euro. That is a check for this particular rate, not a universal rule about currency conversion.

Converting euros back to pounds

3:08For our third exam-style example, you start with two hundred and twenty-three euros and twenty cents. You spend one hundred and twenty-eight euros and twenty cents, then convert the remainder into pounds at the same rate. Subtract the spending from the starting amount to obtain ninety-five euros. This first step keeps both amounts in euros. Each pound corresponds to one point two four euros, so divide ninety-five by one point two four.

3:33The result is seventy-six point six one two pounds and further digits. Round this to the nearest penny to obtain seventy-six pounds and sixty-one pence. Division reverses the multiplication because we are finding the number of pound-sized groups. Common mistakes include reversing the conversion and rounding too early. Avoid the first by writing what one unit of the starting currency is worth. Avoid the second by retaining the full calculator value until the final answer.

3:59Also, never subtract a cost in euros directly from a balance in pounds, because those amounts use different units. Paper two is non-calculator, so practise these methods using written decimal arithmetic and manageable exchange rates. Paper four allows a calculator, but you still need to choose the correct operation and show your working. Follow any stated accuracy instruction. Otherwise, give answers that are not exact to three significant figures, and money to two decimal places.

4:28Keep intermediate values unrounded. Money calculations are ordinary arithmetic with careful attention to units. Combine costs, subtract spending, and use multiplication or division according to the situation. For currency conversion, read the exchange rate as a statement of equivalent value. Keep the currency visible throughout your working, then check that your answer makes sense before rounding.