Ratio and rate · Usually met around P6
Rates and unit prices
Find the amount for one unit first.
How to do it
Method
Find the amount for one unit first
3 for $27 → each $27 ÷ 3 = $9
Another way
Make the amounts equal
4 for $18 → 12 for $54; 6 for $24 → 12 for $48
In full
A rate is how much for each one unit: a unit price is the price of one item, or of 100 g; pages printed a minute and kilometres travelled an hour are rates too. To find a unit price, divide the total price by the amount: 3 pens for $27 cost $27 ÷ 3 = $9 each. With the unit price you can find the price of any amount: at $9 each, 7 cost $63. To find the better buy, change both to unit prices first: the lower unit price is the better buy. Or make the amounts the same and compare: 4 for $18 and 6 for $24, both made 12, are $54 and $48, so 6 for $24 is the better buy.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
3 notebooks cost $6 altogether. How much does each one cost, in dollars?
Show the answer and working
Answer: 2 dollars
Unit price = total ÷ how many: 6 ÷ 3 = 2.
Example 2
A 600 g bag of coffee beans costs $48. How much is that for each 100 g, in dollars?
Show the answer and working
Answer: 8 dollars
600 g is 6 lots of 100 g: 48 ÷ 6 = 8.
Example 3
The same notebook is sold in four packs. Which is the best buy?
- A. 4 for $32
- B. 4 for $56
- C. 5 for $65
- D. 2 for $14
Choose the right answer
Show the answer and working
Answer: D. 2 for $14
Change each to a unit price: the cheapest is $7 each.
Practise it in the game →Ratio and rate · Free to start, unlimited questions, no download