KS3 Maths · Year 7 · Chapter 13: Proportion · Lesson 1

Direct proportion

Year 7About 65 minutesCalculator allowed50 marks

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Quick questions to start.

A1
Needed today
Work out $1.35 \times 4$ .
[1 mark]
Answer
A2
Needed today
Work out $7.20 \div 6$ .
[1 mark]
Answer
A3
Last lesson
Work out $0.8 \div 0.02$ .
[1 mark]
Answer
A4
From chapter 11
A map has a scale of $1 : 50000$ . How many kilometres does $6$ cm on the map stand for?
[1 mark]
Answer

Example, then your turn

Year 7

Your teacher works through each example with you. Then try the one beside it.

Example 1

A lorry travels at a steady speed, so the distance is in direct proportion to the time. In $12$ minutes it travels $15$ km. Work out the missing distances in the table.

Hint Look at how the time changes from

12

minutes, then do the same to the distance.

B1
Water flows from a hose at a steady rate. In $6$ minutes, $45$ litres flow out. Work out the volumes that flow out in $2$ , $10$ and $18$ minutes.
[3 marks]
Answer $2$ min: $\dots\dots$ l $10$ min: $\dots\dots$ l $18$ min: $\dots\dots$ l

Example 2

$5$ kg of potatoes cost £ $3.40$ . The cost is in direct proportion to the mass. Work out the cost of $8$ kg of potatoes.

Hint

8

is not a whole-number multiple of

5

. Find the cost of

1

kg first.

B2
$7$ m of rope costs £ $9.80$ . The cost is in direct proportion to the length. Work out the cost of $12$ m of the rope.
[2 marks]
Answer£ $\dots\dots$

Example 3

$450$ g of cheese costs £ $5.40$ . How much cheese, in grams, can you buy for £ $8.40$ ?

Hint Work in pence. Find the cost of

1

g, then see how many grams £

8.40

pays for.

B3
$250$ ml of olive oil costs £ $3.50$ . How much oil, in ml, can you buy for £ $12.60$ ?
[2 marks]
Answer $\dots\dots$ ml

Example 4

An exchange rate is £ $20 =$ € $23$ . Change £ $70$ into euros. Change € $115$ into pounds.

Hint £

70

3.5

lots of £

20

. €

115

is how many lots of €

23

B4
An exchange rate is £ $15 = 18$ US dollars. Change £ $55$ into US dollars. Change $102$ US dollars into pounds.
[4 marks]
Answer $\dots\dots$ US dollars £ $\dots\dots$

Example 5

The table shows the cost of hiring a bike. Is the cost in direct proportion to the number of hours? Give a reason.

Hint Work out the cost for one hour each time. In direct proportion it is always the same.

B5
The table shows the cost of tickets for a show. Is the cost in direct proportion to the number of tickets? Give a reason.
[2 marks]
Answer

Practice

Year 7

C1
A tap drips at a steady rate: $75$ drips in $15$ minutes. How long does it take to drip $1000$ times? Give your answer in hours and minutes.
[2 marks]
Answer $\dots$ hours $\dots$ minutes
C2
A baker uses $1.4$ kg of flour to make $8$ rolls. How many rolls can the baker make from $5$ kg of flour?
[3 marks]
Answer $\dots\dots$ rolls

C3
$y$ is in direct proportion to $x$ . Work out the missing value $a$ .
[2 marks]
Answer $a = \dots\dots$
C4
$4$ litres is about the same as $7$ pints. How many pints is $1$ litre? How many litres is $1$ pint, to $2$ decimal places?
[2 marks]
Answer $\dots\dots$ pints $\dots\dots$ litres
C5
$12$ litres of petrol cost £ $17.64$ . Work out the cost of $31.4$ litres. Give your answer to the nearest penny.
[2 marks]
Answer£ $\dots\dots$

Exam-style questions

GCSE Foundation

D1
Here are the ingredients needed to make $10$ flapjacks. Harry has $500$ g of butter, $600$ g of oats and $300$ g of sugar. What is the greatest number of flapjacks Harry can make? You must show your working.
[4 marks]
Answer $\dots\dots$ flapjacks

D2
Sam says, "The fare is in direct proportion to the distance, because every extra $2$ miles costs £ $4$ more."
The table shows taxi fares. Is Sam correct? Give a reason for your answer.
[2 marks]
D3
A pair of trainers costs £ $72$ in London. The same trainers cost € $84$ in Paris. The exchange rate is £ $1 =$ € $1.15$ .
(a)
Work out the cost of the trainers in Paris in pounds. Give your answer to the nearest penny.
[2 marks]
Answer£ $\dots\dots$
(b)
In which city are the trainers cheaper, and by how much in pounds?
[2 marks]
Answer $\dots\dots$ by £ $\dots\dots$
Total for D3: 4 marks
D4
A van uses $18$ litres of diesel to travel $240$ km. The amount of diesel used is in direct proportion to the distance.
(a)
Work out the amount of diesel used to travel $400$ km.
[2 marks]
Answer $\dots\dots$ litres
(b)
Diesel costs £ $1.52$ per litre. Work out the cost of the diesel for a journey of $340$ km.
[3 marks]
Answer£ $\dots\dots$
Total for D4: 5 marks
D5
A printer prints $144$ pages in $4$ minutes, at a steady rate.
(a)
How many pages does it print in $30$ seconds?
[2 marks]
Answer $\dots\dots$ pages
(b)
Kim needs to print $2450$ pages. Will the job take more than one hour? Give a reason for your answer.
[2 marks]
Total for D5: 4 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
A shop sells cheese by mass. The cost is in direct proportion to the mass. $240$ g of the cheese costs £ $1.56$ more than $160$ g of the same cheese. Work out the cost of $1$ kg of the cheese.
[3 marks]
Hint 1 · What to try
What does the extra mass cost?
Hint 2 · The first line
$240 - 160 = 80$ g, so $80$ g of cheese costs £ $1.56$ .
Hint 3 · The full method
$1000 \div 80 = 12.5$ , so $1$ kg costs $1.56 \times 12.5 =$ £ $19.50$ .
Answer£ $\dots\dots$

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can tell from a table whether two quantities are in direct proportion.
I can find a missing amount by scaling or through the amount for one unit.
I can use a rate to convert both ways, such as between currencies.

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