Mathematics · Professor Pi

Every card in Ratio and proportion, Year 7: more practice

The whole deck, in order — so you can read it through before your child ever sees it.

← Back to Ratio and proportion, Year 7: more practice

1 KS3-MATH-RAT-0072

A bag holds 8 red and 12 blue counters. Write the ratio of red to blue in its simplest form.

2 : 3

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

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.

2 KS3-MATH-RAT-0073

£35 is shared in the ratio 2 : 3. How many pounds is the larger share? (number only)

21

HintFind the total number of parts first.

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.

3 KS3-MATH-RAT-0074

Write the ratio 30 minutes : 2 hours in its simplest form.

1 : 4

HintPut both quantities into the same unit before you simplify.

Why2 hours is 120 minutes, so the ratio is 30 : 120. Dividing both by 30 gives 1 : 4.

4 KS3-MATH-RAT-0075

Counters are red and blue in the ratio 3 : 5. What fraction of all the counters are blue?

5/8

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

Why3 + 5 = 8 parts altogether, and 5 of them are blue, so 5/8 are blue. The red counters are 3/8.

5 KS3-MATH-RAT-0076

A drink is made from 1 part syrup to 4 parts water. What percentage of the drink is syrup?

20%

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

Why1 + 4 = 5 parts in total, so syrup is 1/5 of the drink, and 1/5 = 20%.

6 KS3-MATH-RAT-0077

In a proportion table, an input of 3 gives an output of 12 and an input of 7 gives 28. What output goes with an input of 5? (number only)

20

HintFind the number that turns each input into its output.

Why12 ÷ 3 = 4, and 28 ÷ 7 = 4, so every output is 4 times its input. Then 5 × 4 = 20.

7 KS3-MATH-RAT-0078

8 identical pencils cost £2.80. How much do 5 of them cost?

£1.75

HintFind the cost of a single pencil first.

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.

8 KS3-MATH-RAT-0079

Convert 350 centimetres into metres.

3.5 m

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

Why350 ÷ 100 = 3.5. Going from a smaller unit to a larger unit gives a smaller number.

9 KS3-MATH-RAT-0080

In a quiz, 35 out of 50 answers were correct. What percentage is that? (number only)

70

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

Why35/50 = 70/100, so the answer is 70%. Doubling both numbers makes the base 100.

10 KS3-MATH-RAT-0081

A map uses the scale 1 cm to 5 km. Two towns are 7.5 cm apart on the map. How far apart are they in real life?

37.5 km

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

Why7.5 × 5 = 37.5, so the towns are 37.5 km apart.

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