Number
The unitary method
Find the value of one thing first, then scale it to any number — and tell direct proportion from inverse.
If 6 books cost $270, you cannot get to the cost of 9 books in one jump. But you can get there in two: find what one book costs, then multiply by 9. Going through 'one' like that is called the unitary method, and it solves an enormous number of everyday problems.
Two kinds of proportion
In direct proportion, more of one means more of the other: more books, more cost. In inverse proportion, more of one means less of the other: more workers, fewer days. The unitary method works for both, but the second step is a multiplication for direct and a division for inverse.
Worked example
6 books cost $270. What do 9 books cost?
Find the cost of one book: 270 ÷ 6 = 45.
Dividing by the number you have gets you to a single unit, which is the only amount you can scale from safely.
Try it together
Now let us try one that runs the other way. 8 pipes fill a tank in 15 hours. How long do 12 pipes take?
Before working anything out, decide which way the answer should move. Getting that wrong is how a right method still gives a wrong answer.
1.Would 12 pipes take more time or less time than 8 pipes? Type 'more' or 'less'.
Have a go
Have a go on your own: if 4 chairs cost $2000, what do 6 chairs cost? Give just the number.
Hint: One chair first.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.