When you are asked to do a currency conversion, you will usually be given an exchange rate first, as in this question:
“George changes some pounds into Euros. The exchange rate is £1=€1.18. If he changes £350 into Euros, how many Euros will he receive?”
Draw a simple Ratio Grid and give headings of £ and €. Put the numbers 1 and 1.18 in the correct columns. Then, the final number from the question, £350, goes in the £ column under the 1. Putting the numbers into their correct places is easy if you have headings! Put a ring around the empty space – that is where your answer will go.
In this grid, the 2 multiplying numbers are the “1.18” and the “350”, and you will divide by 1. So the sum will be 1.18×350÷1.
The answer is 413, and it is clearly in the Euros column, so give your answer as €413.
It’s easy if you get the headings right!
If you want lots of practice, Mr Corbett has a great set of currency conversion questions.
Ratio Grids can be used whenever you have a problem that starts with 3 numbers, and you have to times and divide. They are a clear way of laying out your working, and knowing which order to do the calculation.
You will need a calculator to do the practice questions, but first, here are 2 videos. The first shows you how to solve a small ratio grid, the second deals with the larger ones:
I invented “Ratio Grids” to help students who struggle with Proportional Reasoning. The philosophy includes:
All proportional reasoning sums are essentially the same – times 2 numbers and divide by a third. If one of the numbers is one, then it’s just a multiply or a divide.
Students who get used to working a problem “forwards” often struggle to work backwards, but mathematically there is no difference!
Skills gained working with ratios can be applied to shopping, percentages, similar shapes, stratified sampling, speed, density, and other “per” problems, Direct and Inverse proportion, currency conversions, unit conversions and the Sine Rule, without learning shed loads of new stuff.
Students often get in a muddle because they do sums and lose hold of the units of numbers so although they get a correct answer they don’t realise what it means! Ratio hold the units of numbers as well as the numbers themselves.
Students sometimes try to mix different units inappropriately in their working. With ratio grids this is much less likely.