How to Apply the Table of Joy to Ratio Questions
You can use the Table of Joy to solve typical ratio questions on most numeracy tests. A ratio describes how many times bigger one share of something is than another share.
A typical ratio question might tell you that someone splits their time between Project A and Project B in a ratio of 5:3. If he spends 15 hours this week on Project B, how long does he spend on Project A?
In this question, you have three key pieces of information: the two sides of the ratio (5 and 3) and the time for Project B (15). You can put these numbers into the Table of Joy.
Here’s what you do:
Draw a noughts-and-crosses grid.
Leave plenty of space for the labels.
Figure out what the two sides of the ratio represent.
In the example, the two sides of the ratio represent Project A and Project B. These labels go in the top row.
On the left, write ‘ratio’ in one row and whatever you want to measure in the other – in this case, ‘time’.
Fill in the ratio in the middle row (remember to keep it the right way around) and put the time you know in the correct column.
Here, the time goes in the column marked ‘Project B’. Put a question mark in the remaining square.
Write out the Table of Joy sum.
Take the number in the same column as the question mark, times by the number in the same row as the question mark, divide by the number opposite. For the example, you do 5 x 15 ÷ 3.
Work out the sum.
In the example, the answer is 25.
You’d be a little bit lucky to get a question as simple as this one in an exam. More often than not, you have to work with the total and one side of the ratio.
The good news is this isn’t any more difficult – you simply need an extra layer of thought before you do the Table of Joy sum.
Take a moment to read the question and decide whether you’re interested in the two parts or a part and a total. The example looks at the two-parts version.
By contrast, with the part-and-a-total version, you replace the missing part of the ratio with the total of the ratio – just add the numbers either side of the colon.
After that, you follow exactly the same process, but change one of the column labels to ‘total’ and the numbers in that column as appropriate. The figure answers the following question:
Alice and Bob share 12 biscuits in the ratio 3:1. How many does Alice eat?