Ratio notation and simplifying Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Ratio notation and simplifying questions. See exactly how to solve problems on simplifying ratios, common factors, highest common factor, writing a ratio.

simplifying ratioscommon factorshighest common factorwriting a ratioratio from a contextequivalent ratios
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Write the ratio 4:64 : 6 in its simplest form.

Worked solution

  1. Look for a common factor

    4:64 : 6

    Common factors of 44 and 66: 11, 22. The highest is 22.

  2. Divide both parts by the highest common factor

    4÷2=2,6÷2=34 \div 2 = 2, \quad 6 \div 2 = 3

    Dividing both parts of a ratio by the same number does not change the ratio.

  3. Write the simplified ratio

    4:6=2:34 : 6 = 2 : 3

    22 and 33 have no common factor left, so this is the simplest form.

Answer
2:32 : 3
Question 2
1 markeasy
Write the ratio 6:86 : 8 in its simplest form.

Worked solution

  1. Look for a common factor

    6:86 : 8

    Common factors of 66 and 88: 11, 22. The highest is 22.

  2. Divide both parts by the highest common factor

    6÷2=3,8÷2=46 \div 2 = 3, \quad 8 \div 2 = 4

    Dividing both parts of a ratio by the same number does not change the ratio.

  3. Write the simplified ratio

    6:8=3:46 : 8 = 3 : 4

    33 and 44 have no common factor left, so this is the simplest form.

Answer
3:43 : 4
Question 3
1 markeasy
Write the ratio 10:1510 : 15 in its simplest form.

Worked solution

  1. Look for a common factor

    10:1510 : 15

    Common factors of 1010 and 1515: 11, 55. The highest is 55.

  2. Divide both parts by the highest common factor

    10÷5=2,15÷5=310 \div 5 = 2, \quad 15 \div 5 = 3

    Dividing both parts of a ratio by the same number does not change the ratio.

  3. Write the simplified ratio

    10:15=2:310 : 15 = 2 : 3

    22 and 33 have no common factor left, so this is the simplest form.

Answer
2:32 : 3
Question 4
1 markeasy
Write the ratio 12:2012 : 20 in its simplest form.

Worked solution

  1. Look for a common factor

    12:2012 : 20

    Common factors of 1212 and 2020: 11, 22, 44. The highest is 44.

  2. Divide both parts by the highest common factor

    12÷4=3,20÷4=512 \div 4 = 3, \quad 20 \div 4 = 5

    Dividing both parts of a ratio by the same number does not change the ratio.

  3. Write the simplified ratio

    12:20=3:512 : 20 = 3 : 5

    33 and 55 have no common factor left, so this is the simplest form.

Answer
3:53 : 5
Question 5
1 markeasy
Write the ratio 14:3514 : 35 in its simplest form.

Worked solution

  1. Look for a common factor

    14:3514 : 35

    Common factors of 1414 and 3535: 11, 77. The highest is 77.

  2. Divide both parts by the highest common factor

    14÷7=2,35÷7=514 \div 7 = 2, \quad 35 \div 7 = 5

    Dividing both parts of a ratio by the same number does not change the ratio.

  3. Write the simplified ratio

    14:35=2:514 : 35 = 2 : 5

    22 and 55 have no common factor left, so this is the simplest form.

Answer
2:52 : 5

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