Sharing in a ratio

The Maths Habit

Amy and Ben buy some chocolate. Ben pays more. Which share is fair?

AAmyBenNot fair: Amy paid lessBAmyBenNot fair: Ben paid moreCAmyBen✓ Fair

Each box is one part. Write the ratio Amy : Ben.

AmyBen2 : 1
AmyBen1 : 4
AmyBen3 : 5

Ratio
It tells you how many parts each person gets.
2 : 3AmyBen
Part
One box of a bar. Every part is the same size.
Amy✓Ben
Share
The amount one person gets.
Benall of Ben’s bar

AmyBen
first+second=parts
total÷parts=one part
  1. 1Draw the bars.One bar for each person. One box for each part.
  2. 2Add the parts.This is all the parts.
  3. 3Find one part.Divide the total by all the parts.

Amy and Ben share £12 in the ratio 1 : 3. How much is one part?

1Draw the bars.
AmyBen
2Add the parts.
1+3=4
3Find one part.
12÷4=3

Cal and Dev share £20 in the ratio 1 : 4. How much is one part?

1Draw the bars.
CalDev
2Add the parts.
1+4=5
3Find one part.
20÷5=4

Amy and Ben share £12 in the ratio 1 : 3. How much is one part?

1Draw the bars.
AmyBen
2Add the parts.
1+3=4
3Find one part.
12÷4=3
12first+second=parts3total÷parts=one part

Eve and Fin share £10 in the ratio 3 : 2. How much is one part?

1Draw the bars.
EveFin
2Add the parts.
3+2=5
3Find one part.
10÷5=2

Amy and Ben share £12 in the ratio 1 : 3. How much is one part?

1Draw the bars.
AmyBen
2Add the parts.
1+3=4
3Find one part.
12÷4=3
12first+second=parts3total÷parts=one part

Gus and Ivy share £50 in the ratio 3 : 7. How much is one part?

1Draw the bars.
GusIvy
2Add the parts.
3+7=10
3Find one part.
50÷10=5

Amy and Ben share £12 in the ratio 1 : 3. How much is one part?

1Draw the bars.
AmyBen
2Add the parts.
1+3=4
3Find one part.
12÷4=3
12first+second=parts3total÷parts=one part

Jo and Kai share £15 in the ratio 4 : 1. How much is one part?

1Draw the bars.
JoKai
2Add the parts.
4+1=5
3Find one part.
15÷5=3

12first+second=parts3total÷parts=one part

1Lia and Max share £12 in the ratio 1 : 2. How much is one part?

1Draw the bars.
LiaMax
2Add the parts.
1+2=3
3Find one part.
12÷3=4

2Ned and Pip share £20 in the ratio 3 : 1. How much is one part?

1Draw the bars.
NedPip
2Add the parts.
3+1=4
3Find one part.
20÷4=5

3Raj and Sam share £35 in the ratio 2 : 3. How much is one part?

1Draw the bars.
RajSam
2Add the parts.
2+3=5
3Find one part.
35÷5=7

4Tom and Zoe share £16 in the ratio 5 : 3. How much is one part?

1Draw the bars.
TomZoe
2Add the parts.
5+3=8
3Find one part.
16÷8=2

One part is 4. How much is each bar worth?

48
412
420

Amy1 part1 partBen1 part1 part1 part
first+second=parts
total÷parts=one part
AmyshareBenshare
  1. 1Draw the bars.One bar for each person. One box for each part.
  2. 2Add the parts.This is all the parts.
  3. 3Find one part.Divide the total by all the parts.
  4. 4Find each share.Write one part in every box. Add up each bar.

Amy and Ben share £20 in the ratio 2 : 3. How much does each get?

1Draw the bars.
Amy44Ben444
2Add the parts.
2+3=5
3Find one part.
20÷5=4
4Find each share.
Amy£8Ben£12

Cal and Dev share £16 in the ratio 3 : 1. How much does each get?

1Draw the bars.
Cal444Dev4
2Add the parts.
3+1=4
3Find one part.
16÷4=4
4Find each share.
Cal£12Dev£4

Amy and Ben share £20 in the ratio 2 : 3. How much does each get?

1Draw the bars.
Amy44Ben444
2Add the parts.
2+3=5
3Find one part.
20÷5=4
4Find each share.
Amy£8Ben£12
12first+second=parts3total÷parts=one part4One part in every box. Add up each bar.

Eve and Fin share £30 in the ratio 1 : 4. How much does each get?

1Draw the bars.
Eve6Fin6666
2Add the parts.
1+4=5
3Find one part.
30÷5=6
4Find each share.
Eve£6Fin£24

Amy and Ben share £20 in the ratio 2 : 3. How much does each get?

1Draw the bars.
Amy44Ben444
2Add the parts.
2+3=5
3Find one part.
20÷5=4
4Find each share.
Amy£8Ben£12
12first+second=parts3total÷parts=one part4One part in every box. Add up each bar.

Gus and Ivy share £35 in the ratio 4 : 3. How much does each get?

1Draw the bars.
Gus5555Ivy555
2Add the parts.
4+3=7
3Find one part.
35÷7=5
4Find each share.
Gus£20Ivy£15

Amy and Ben share £20 in the ratio 2 : 3. How much does each get?

1Draw the bars.
Amy44Ben444
2Add the parts.
2+3=5
3Find one part.
20÷5=4
4Find each share.
Amy£8Ben£12
12first+second=parts3total÷parts=one part4One part in every box. Add up each bar.

Ola and Sam share £21 in the ratio 2 : 5. How much does each get?

1Draw the bars.
Ola33Sam33333
2Add the parts.
2+5=7
3Find one part.
21÷7=3
4Find each share.
Ola£6Sam£15

Sharing in a ratio worksheet, page 1

Sharing in a ratio worksheet, page 2

Answer sheet

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

  1. £20 in the ratio 1 : 3 is £5 and £15

    Right

  2. £30 in the ratio 2 : 3 is £15 and £10

    Wrong: divide by all the parts

  3. £12 in the ratio 1 : 2 is £8 and £4

    Wrong: the wrong way round

  4. £40 in the ratio 3 : 5 is £15 and £25

    Right

  5. £24 in the ratio 1 : 2 is £8 and £12

    Wrong: they do not add up to £24

  1. Share £36 in the ratio 1 : 2 : 3.

    £6, £12 and £18

  2. Amy and Ben share some sweets in the ratio 2 : 5. Ben gets 9 more than Amy. How many sweets are there?

    21 sweets

  3. Cal and Dev share some money in the ratio 3 : 4. Cal gets £15. How much does Dev get?

    £20

  1. Share £15 between Amy and Ben in the ratio 2 : 3.

    £6 and £9
    1Draw the bars.AmyBen2Add the parts.+=3Find one part.÷=4Find each share.AmyBen

  2. Share £30 between Cal and Dev in the ratio 1 : 5.

    £5 and £25
    1Draw the bars.CalDev2Add the parts.+=3Find one part.÷=4Find each share.CalDev

  3. Share £24 between Eve and Fin in the ratio 5 : 3.

    £15 and £9
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