Direct proportion

The Maths Habit

3 pens cost one bag of coins. Which is a fair price for 6 pens?

3 pens=£6 pens=?
A£Too cheapB££✓ FairC£££Too much

Share the money equally. How much is in each part?

£8 in 2 equal parts£844£4 each
£15 in 3 equal parts£15555£5 each
£20 in 10 equal parts£202222222222£2 each

Direct proportion
When one amount is multiplied, the other amount is multiplied by the same number.
2 penscost4 penscost × 2
Equal parts
Parts that are all the same size.
Total
All the parts added together.
total

totalone part
total÷parts=one part
  1. 1Cut the bar.One part for each thing.
  2. 2Find one part.Divide the total by the number of parts.

5 tickets cost £20. How much does 1 ticket cost?

1Cut the bar.
5 tickets£2044444
2Find one part.
20÷5=4

3 cakes cost £15. How much does 1 cake cost?

1Cut the bar.
3 cakes£15555
2Find one part.
15÷3=5

5 tickets cost £20. How much does 1 ticket cost?

1Cut the bar.
5 tickets£2044444
2Find one part.
20÷5=4
1total2total÷parts=one part

4 pens cost £8. How much does 1 pen cost?

1Cut the bar.
4 pens£82222
2Find one part.
8÷4=2

5 tickets cost £20. How much does 1 ticket cost?

1Cut the bar.
5 tickets£2044444
2Find one part.
20÷5=4
1total2total÷parts=one part

10 stamps cost £30. How much does 1 stamp cost?

1Cut the bar.
10 stamps£303333333333
2Find one part.
30÷10=3

5 tickets cost £20. How much does 1 ticket cost?

1Cut the bar.
5 tickets£2044444
2Find one part.
20÷5=4
1total2total÷parts=one part

2 hats cost £18. How much does 1 hat cost?

1Cut the bar.
2 hats£1899
2Find one part.
18÷2=9

1total2total÷parts=one part

15 mugs cost £30. How much does 1 mug cost?

1Cut the bar.
5 mugs£3066666
2Find one part.
30÷5=6

24 bags cost £16. How much does 1 bag cost?

1Cut the bar.
4 bags£164444
2Find one part.
16÷4=4

310 cards cost £50. How much does 1 card cost?

1Cut the bar.
10 cards£505555555555
2Find one part.
50÷10=5

43 kites cost £21. How much does 1 kite cost?

1Cut the bar.
3 kites£21777
2Find one part.
21÷3=7

Each part is worth the same. What is the total?

?22224 × 2 = 8
?333335 × 3 = 15
?1010103 × 10 = 30

totalone part
total÷parts=one part
answer
one part×new parts=answer
  1. 1Cut the bar.One part for each thing.
  2. 2Find one part.Divide the total by the number of parts.
  3. 3Multiply.Cut a new bar. Multiply one part by the new number of parts.

4 pens cost £12. How much do 7 pens cost?

1Cut the bar.
4 pens£123333
2Find one part.
12÷4=3
3Multiply.
7 pens?£213333333
3×7=21

2 cakes cost £10. How much do 5 cakes cost?

1Cut the bar.
2 cakes£1055
2Find one part.
10÷2=5
3Multiply.
5 cakes?£2555555
5×5=25

4 pens cost £12. How much do 7 pens cost?

1Cut the bar.
4 pens£123333
2Find one part.
12÷4=3
3Multiply.
7 pens?£213333333
3×7=21
1total2total÷parts=one part3one part×new parts=answer

5 tickets cost £10. How much do 3 tickets cost?

1Cut the bar.
5 tickets£1022222
2Find one part.
10÷5=2
3Multiply.
3 tickets?£6222
2×3=6

4 pens cost £12. How much do 7 pens cost?

1Cut the bar.
4 pens£123333
2Find one part.
12÷4=3
3Multiply.
7 pens?£213333333
3×7=21
1total2total÷parts=one part3one part×new parts=answer

3 books cost £15. How much do 4 books cost?

1Cut the bar.
3 books£15555
2Find one part.
15÷3=5
3Multiply.
4 books?£205555
5×4=20

4 pens cost £12. How much do 7 pens cost?

1Cut the bar.
4 pens£123333
2Find one part.
12÷4=3
3Multiply.
7 pens?£213333333
3×7=21
1total2total÷parts=one part3one part×new parts=answer

2 bags of rice weigh 6 kg. How much do 5 bags weigh?

1Cut the bar.
2 bags6 kg33
2Find one part.
6÷2=3
3Multiply.
5 bags?15 kg33333
3×5=15

Direct proportion worksheet, page 1

Direct proportion worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 3 pens cost £6, so 6 pens cost £12

    Right

  2. 2 cakes cost £4, so 5 cakes cost £7

    Wrong: find one part, do not add on

  3. 4 mugs cost £20, so 1 mug costs £5

    Right

  4. 5 cards cost £10, so 1 card costs £50

    Wrong: divide, do not multiply

  5. 3 hats cost £9, so 4 hats cost £12

    Right

  1. 6 pens cost £4.20. How much do 4 pens cost?

    £2.80

  2. A recipe for 10 flapjacks uses 250 g of oats. How many grams of oats are needed for 25 flapjacks?

    625 g

  3. Shop A sells 3 cakes for £6.60. Shop B sells 5 cakes for £10.50. Which shop is cheaper for one cake?

    Shop B

  1. 3 cakes cost £12. How much do 5 cakes cost?

    £20
    1Cut the bar.£123 cakes2Find one part.÷=3Multiply.?5 cakes×=

  2. 4 pens cost £20. How much do 6 pens cost?

    £30
    1Cut the bar.£204 pens2Find one part.÷=3Multiply.?6 pens×=

  3. 5 tickets cost £35. How much do 2 tickets cost?

    £14
Exit tickets to print