Rate: find the rate, the total or the number of units

A rate tells you how much of one thing goes with ONE of another: 12 litres per minute, $2.50 per litre, 45 pages per minute. Everything in this topic is a single relationship — total = rate × number of units — turned whichever way the question needs. If the total and the units are given, divide to get the rate. If the rate and the units are given, multiply to get the total. If the total and the rate are given, divide to find how many units. The one habit that makes all three easy is finding the amount for ONE unit first, which is the same move you already use for fractions of a set. Two rates in one question, like a tap filling while a leak drains, combine into a single net rate before anything else happens — and two prices can only be compared once both are the price for 1 kg.

Worked example

Problem A printer prints 480 pages in 8 minutes. At the same rate, how long will it take to print 1200 pages?

Find the amount for ONE minute first — that is what a rate is: 480 ÷ 8 = 60, so the printer prints 60 pages a minute.
Now the question turns the relationship round: the total is known and the number of minutes is not.
Ask how many lots of 60 fit into 1200: 1200 ÷ 60 = 20 minutes.
Tip Write the rate down as its own line — "60 pages per minute" — before you answer anything. Almost every lost mark in this topic comes from skipping straight to a multiplication.
Watch out When two rates act at the same time, combine them into ONE rate for one minute before you divide. Dividing the tank by just one of the two taps is the classic error.
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