Ratio and proportion, Year 7: more practice

2 : 3

HintDivide both numbers by the same amount, as far as you can.

The why8 : 12 simplifies by dividing both by 4 to give 2 : 3. The order matters: red comes first because the question asks for red to blue.

21

HintFind the total number of parts first.

The why2 + 3 = 5 parts, so one part is £35 ÷ 5 = £7. The larger share is 3 × £7 = £21, and the smaller is 2 × £7 = £14.

1 : 4

HintPut both quantities into the same unit before you simplify.

The why2 hours is 120 minutes, so the ratio is 30 : 120. Dividing both by 30 gives 1 : 4.

5/8

HintPart-to-part is not part-of-whole: add the parts to find the whole.

The why3 + 5 = 8 parts altogether, and 5 of them are blue, so 5/8 are blue. The red counters are 3/8.

20%

HintWork out how many parts there are in the whole drink first.

The why1 + 4 = 5 parts in total, so syrup is 1/5 of the drink, and 1/5 = 20%.

20

HintFind the number that turns each input into its output.

The why12 ÷ 3 = 4, and 28 ÷ 7 = 4, so every output is 4 times its input. Then 5 × 4 = 20.

£1.75

HintFind the cost of a single pencil first.

The why£2.80 ÷ 8 = £0.35 for one pencil, and 5 × £0.35 = £1.75. Going through the value of one is the unitary method.

3.5 m

HintThere are 100 centimetres in a metre, so which way does the number go?

The why350 ÷ 100 = 3.5. Going from a smaller unit to a larger unit gives a smaller number.

70

HintPer cent means out of 100, so scale the 50 up to 100.

The why35/50 = 70/100, so the answer is 70%. Doubling both numbers makes the base 100.

37.5 km

HintMultiply the map distance by the number of kilometres each centimetre stands for.

The why7.5 × 5 = 37.5, so the towns are 37.5 km apart.