Mathematics · Professor Pi

Every card in Ratio and proportion, Year 7: proportion tables and scale drawings

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1 KS3-MATH-RAT-0046

3 pens cost 90p. What do 5 pens cost?

£1.50

HintFind the cost of one pen first.

WhyOne pen costs 90 ÷ 3 = 30p, so five cost 5 × 30 = 150p.

2 KS3-MATH-RAT-0047

A proportion table shows 4 → 10 and 6 → 15. What number multiplies each input to give its output?

2.5

HintDivide an output by the input that made it.

Why10 ÷ 4 = 2.5 and 15 ÷ 6 = 2.5. In a proportion table every pair is linked by the same multiplier.

3 KS3-MATH-RAT-0048

A recipe uses 200 g of flour for 8 biscuits. How much flour is needed for 20 biscuits?

500 g

HintWork out the flour for one biscuit.

Why200 ÷ 8 = 25 g for each biscuit, and 20 × 25 = 500 g. Or notice that 20 is 2.5 times 8.

4 KS3-MATH-RAT-0049

In a price table, 2 kg costs £3, 4 kg costs £6 and 6 kg costs £10. Which entry breaks the proportion?

6 kg for £10

HintCheck the price of 1 kg in each column.

Why2 kg for £3 and 4 kg for £6 are both £1.50 per kilogram. At that rate 6 kg should cost £9.

5 KS3-MATH-RAT-0050

5 tickets cost £40. How many tickets can you buy for £64? (number only)

8

HintFind the price of a single ticket.

WhyOne ticket costs 40 ÷ 5 = £8, and 64 ÷ 8 = 8 tickets.

6 KS3-MATH-RAT-0051

A plan uses a scale of 1 cm to 2 m. A wall is 4 cm long on the plan. How long is the real wall?

8 m

HintEach centimetre on paper stands for the same real length.

Why4 cm on the plan is 4 lots of 2 m, which is 8 m.

7 KS3-MATH-RAT-0052

On a scale drawing where 1 cm represents 1 m, how long should you draw a room that is 3.5 m long?

3.5 cm

HintThe number stays; only the unit changes.

WhyEach metre becomes one centimetre, so 3.5 m is drawn as 3.5 cm, which is 35 mm on the ruler.

8 KS3-MATH-RAT-0053

Write the scale '1 cm represents 1 m' as a ratio.

1 : 100

HintPut both lengths into centimetres.

Why1 m is 100 cm, so 1 cm on the paper stands for 100 cm in real life. A ratio scale has no units because both sides use the same one.

9 KS3-MATH-RAT-0054

A scale drawing uses 1 cm to 5 m. A garden is 30 m long. How long is it on the drawing?

6 cm

HintThis time you are going from real life down to paper, so divide.

Why30 ÷ 5 = 6, so the garden is drawn 6 cm long.

10 KS3-MATH-RAT-0055

A plan has the scale 1 : 50. A door is 2 cm wide on the plan. How wide is the real door, in metres?

1 m

HintMultiply, then change the unit.

Why2 × 50 = 100 cm, and 100 cm is 1 m.

Keep what you learn

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