Dividing in a ratio Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Dividing in a ratio questions. See exactly how to solve problems on sharing in a ratio, total parts, two-part ratio, whole objects.

sharing in a ratiototal partstwo-part ratiowhole objectssmaller sharelengths
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Share £20 between Ali and Beth in the ratio 1:31 : 3. Work out Beth’s share.

Worked solution

  1. Add the parts of the ratio

    1+3=41 + 3 = 4

    The quantity is split into 44 equal parts altogether.

  2. Find the value of one part

    20÷4=520 \div 4 = 5

    Divide the total by the number of parts: one part is £5\pounds 5.

  3. Work out the share asked for

    3×5=153 \times 5 = 15

    That share is 33 of the 44 parts, so it is £15\pounds 15. Check: 5+15=205 + 15 = 20. ✓\checkmark

Answer
£15\pounds 15
Question 2
1 markeasy
Amy and Ben share 2424 sweets in the ratio 1:21 : 2. How many sweets does Ben get?

Worked solution

  1. Add the parts of the ratio

    1+2=31 + 2 = 3

    The quantity is split into 33 equal parts altogether.

  2. Find the value of one part

    24÷3=824 \div 3 = 8

    Divide the total by the number of parts: one part is 88.

  3. Work out the share asked for

    2×8=162 \times 8 = 16

    That share is 22 of the 33 parts, so it is 1616. Check: 8+16=248 + 16 = 24. ✓\checkmark

Answer
1616
Question 3
1 markeasy
Share £45 in the ratio 2:32 : 3. Work out the smaller share.

Worked solution

  1. Add the parts of the ratio

    2+3=52 + 3 = 5

    The quantity is split into 55 equal parts altogether.

  2. Find the value of one part

    45÷5=945 \div 5 = 9

    Divide the total by the number of parts: one part is £9\pounds 9.

  3. Work out the share asked for

    2×9=182 \times 9 = 18

    That share is 22 of the 55 parts, so it is £18\pounds 18. Check: 18+27=4518 + 27 = 45. ✓\checkmark

Answer
£18\pounds 18
Question 4
1 markeasy
A piece of string 3030 cm long is cut in the ratio 1:41 : 4. Work out the length of the shorter piece.

Worked solution

  1. Add the parts of the ratio

    1+4=51 + 4 = 5

    The quantity is split into 55 equal parts altogether.

  2. Find the value of one part

    30÷5=630 \div 5 = 6

    Divide the total by the number of parts: one part is 6 cm6 \text{ cm}.

  3. Work out the share asked for

    1×6=61 \times 6 = 6

    That share is 11 of the 55 parts, so it is 6 cm6 \text{ cm}. Check: 6+24=306 + 24 = 30. ✓\checkmark

Answer
6 cm6 \text{ cm}
Question 5
1 markeasy
Share 3535 marbles in the ratio 2:52 : 5. How many marbles are in the larger share?

Worked solution

  1. Add the parts of the ratio

    2+5=72 + 5 = 7

    The quantity is split into 77 equal parts altogether.

  2. Find the value of one part

    35÷7=535 \div 7 = 5

    Divide the total by the number of parts: one part is 55.

  3. Work out the share asked for

    5×5=255 \times 5 = 25

    That share is 55 of the 77 parts, so it is 2525. Check: 10+25=3510 + 25 = 35. ✓\checkmark

Answer
2525

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