How the Table of Joy Works for Basic Maths
The Table of Joy is an incredibly useful method for working out any kind of problem involving proportions – that is to say, if you double one of the numbers, the other automatically doubles. For example, the price of most things is proportional to how much you buy; two tins of beans cost twice as much as one tin of beans does.
Among other things, the Table of Joy in its basic form can be used for the following:
Currency conversion: If you need the exchange rate, or want to know how many pounds you get for a number of euros, turn to the Table of Joy.
Percentages: Whether you want to find one number as a percentage of another, the percentage increase or decrease, or an amount with or without tax . . . the Table of Joy is your friend.
Pie charts: If you want to know the angle, the value of a slice or the total value of a pie chart, you can use an easy sum . . . the Table of Joy reminds you of that sum.
Proportion: If you have two linked values where doubling or tripling one automatically triples the other, the values are proportional. And the Table of Joy deals with that.
Ratios: Whenever you see a colon, crack your knuckles and say ‘Here’s a Table of Joy question!’
Scaled maps and drawings: How far is that in real life? How far is that on the map? What’s the scale? Ask the Table of Joy and it will answer you truly.
Speed–distance–time calculations: Given any two of these three, you can work out the other using the Table of Joy.
Unit conversion: Apart from temperatures, which are a bit squiffy, you can use the Table of Joy to do just about any unit conversion in this book.
Glancing through an old numeracy test, you can use the Table of Joy in the answers of somewhere between a third and a half of the questions.
Introducing the Table of Joy
The Table of Joy – as its name suggests – is a table. You use the table to lay out the information you already have so you know precisely which sum you need to work out. The table doesn’t solve the sum for you – you still need to do that yourself – but the table takes all the guesswork out of deciding what to times and divide by what.
To create a Table of Joy, you draw a three-by-three grid like you play noughts and crosses on, label the rows and columns, decide where to put three numbers that you either have already or can easily work out, and then do a sum that has the same structure each time.
One of the many beauties of the Table of Joy is that it doesn’t matter which way around you label the rows and columns, as long as you put the numbers in a sensible place. The sum is exactly the same if you swap both of the rows with the columns or if you swap the two columns or the two rows over. You can’t swap a row with a column, though.
Seeing how the Table of Joy works
There are five steps to using the Table of Joy to solve a problem:
Draw a fairly big noughts-and-crosses grid.
It needs to be big enough so you can write labels in the rows and columns.
Label the rows and columns with the names of relevant information from the question.
Fill in the numbers relevant to each row and column, and a question mark for the square representing the answer you want.
Circle the number in the same column as the question mark and the number in the same row as the question mark.
Write these numbers with a times sign between them. Then write a divide sign followed by the remaining number.
Work out the answer!
The main trick of using the Table of Joy is working out what labels to use and which number to put where.
This Table of Joy solves the following question:
Larry and Curly split the loot in the ratio 3:7. Curly walks away with $350. How much loot does Larry receive?
Understanding what goes where
Labelling the rows and columns is a very important part of the Table of Joy. This labelling may seem like a chore, but it really helps you to keep track of which number goes where.
Write the things you're counting or measuring across the top. Down the side, put the different pieces of information you have or want.
For the example, the things you are counting are Larry’s money and Curly’s money. Down the side, you write the ratio and a question mark, because you want to know the total amount of money.
Labelling in this way makes the meaning of each number much more obvious. If you’ve just got a noughts-and-crosses grid, figuring out where to put Curly’s part of the ratio is really hard – but with the label ‘Curly’ at the top and ‘ratio’ at the side, things are more obvious.