Ratio and proportion, Year 7: proportion tables and scale drawings：全部卡片
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- 3 pens cost 90p. What do 5 pens cost?
£1.50
提示Find the cost of one pen first.
为什么One pen costs 90 ÷ 3 = 30p, so five cost 5 × 30 = 150p.
- A proportion table shows 4 → 10 and 6 → 15. What number multiplies each input to give its output?
2.5
提示Divide an output by the input that made it.
为什么10 ÷ 4 = 2.5 and 15 ÷ 6 = 2.5. In a proportion table every pair is linked by the same multiplier.
- A recipe uses 200 g of flour for 8 biscuits. How much flour is needed for 20 biscuits?
500 g
提示Work out the flour for one biscuit.
为什么200 ÷ 8 = 25 g for each biscuit, and 20 × 25 = 500 g. Or notice that 20 is 2.5 times 8.
- 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
提示Check the price of 1 kg in each column.
为什么2 kg for £3 and 4 kg for £6 are both £1.50 per kilogram. At that rate 6 kg should cost £9.
- 5 tickets cost £40. How many tickets can you buy for £64? (number only)
8
提示Find the price of a single ticket.
为什么One ticket costs 40 ÷ 5 = £8, and 64 ÷ 8 = 8 tickets.
- 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
提示Each centimetre on paper stands for the same real length.
为什么4 cm on the plan is 4 lots of 2 m, which is 8 m.
- 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
提示The number stays; only the unit changes.
为什么Each metre becomes one centimetre, so 3.5 m is drawn as 3.5 cm, which is 35 mm on the ruler.
- Write the scale '1 cm represents 1 m' as a ratio.
1 : 100
提示Put both lengths into centimetres.
为什么1 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.
- A scale drawing uses 1 cm to 5 m. A garden is 30 m long. How long is it on the drawing?
6 cm
提示This time you are going from real life down to paper, so divide.
为什么30 ÷ 5 = 6, so the garden is drawn 6 cm long.
- 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
提示Multiply, then change the unit.
为什么2 × 50 = 100 cm, and 100 cm is 1 m.
1★ KS3-MATH-RAT-0046
2★ KS3-MATH-RAT-0047
3★ KS3-MATH-RAT-0048
4★ KS3-MATH-RAT-0049
5★ KS3-MATH-RAT-0050
6★ KS3-MATH-RAT-0051
7★ KS3-MATH-RAT-0052
8★ KS3-MATH-RAT-0053
9★ KS3-MATH-RAT-0054
10★ KS3-MATH-RAT-0055