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SATs practice · Year 6Chapter 5 · Ratio and proportion
Year 6 Arithmetic (SATs) · Ratio and proportion · Lesson 5.3

Year 6 Arithmetic (SATs): Sharing and grouping in a ratio

Part of the Year 6 Arithmetic (SATs) ratio and proportion chapter. Chapter overview · whole chapter on one page

5.3

Sharing and grouping in a ratio

Year 6
Solve problems of unequal sharing and grouping using knowledge of fractions and multiples (Year 6)
Story. Ali and Ben earn a prize of £60 for the school quiz. They agree to share it in the ratio 2 : 3, because Ali answered fewer questions. Ruby then wants to share the same method among three friends.

Rule

To share in a ratio, add the parts, find the value of one part, then multiply each number in the ratio by that value.

Check the shares add up to the total. With three friends, add all three parts of the ratio.

Key ideas

  • Share in a ratio by finding the value of one part.
  • The total must be shared into all the parts of the ratio.
  • The shares must add up to the total.
Worked example 5.3.1
Share £60 between Ali and Ben in the ratio 2 : 3. How much does each get?

Method. Find the total parts, the value of one part, then each share.

  1. Add the parts of the ratio. 2 + 3 = 5, so the total is shared into 5 equal parts.
    2 + 3 = 5 parts
  2. Find the value of one part. Share the total into 5 equal parts.
    60 ÷ 5 = 12
  3. Find each share. Multiply the value of one part by each number in the ratio.
    2 × 12 = 24 and 3 × 12 = 36
  4. Write the answer.
    Ali £24, Ben £36

Check. £24 + £36 = £60. ✓

Worked example 5.3.2
Share 84 sweets in the ratio 3 : 4. How many sweets does each part get?

Method. Find one part by dividing by 7.

  1. Add the parts of the ratio. 3 + 4 = 7, so the total is shared into 7 equal parts.
    3 + 4 = 7 parts
  2. Find the value of one part. Share the total into 7 equal parts.
    84 ÷ 7 = 12
  3. Find each share. Multiply the value of one part by each number in the ratio.
    3 × 12 = 36 and 4 × 12 = 48
  4. Write the answer.
    36 and 48

Check. 36 + 48 = 84. ✓

Worked example 5.3.3
Share 120 in the ratio 2 : 3 : 5 between three children. How much does the child with 5 parts get?

Method. Add all three parts, then find the value of one part.

  1. Add the parts. 2 + 3 + 5 = 10 parts.
    10 parts
  2. Find one part. 120 ÷ 10 = 12.
    12
  3. Find the 5-part share. 5 × 12 = 60.
    60
  4. Write the answer.
    60

Check. 24 + 36 + 60 = 120. ✓

Exercise 5C  Practice: sharing and grouping in a ratio

Non-calculator
1
FShare 48 in the ratio 1 : 3. Write both shares.
2
FShare 75 in the ratio 2 : 3. Write both shares.
3
FShare 90 in the ratio 4 : 5. Write both shares.
4
FShare 120 in the ratio 3 : 5. Write both shares.
5
FShare 63 in the ratio 4 : 5. Write both shares.
6
FShare 54 in the ratio 1 : 8. Write both shares.
7
FShare 25 in the ratio 2 : 3. Write both shares.
8
PSA prize of £250 is shared between Ali and Ben in the ratio 3 : 2. How much does Ali get?
9
PS96 counters are sorted into red and blue in the ratio 5 : 7. How many are red?
10
PSThree children share 120 in the ratio 2 : 3 : 5. How much does the child with 2 parts get?
11
PSA bag has 36 marbles in the ratio 1 : 2 : 3 of three colours. How many marbles are the most common colour?
12
RBen says that if 40 is shared in the ratio 3 : 2, each person gets 20. Is he right? Explain.
13
R72 pupils are put into two groups in the ratio 1 : 2. How many pupils are in the bigger group?

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