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Explain how to convert a percentage to a fraction without a denominator of 100

Lesson details

Learning outcome

I can convert a percentage to a fraction where the denominator is not 100

Key learning points

  1. Start by converting each percentage into a fraction with a denominator of 100
  2. Then, divide the denominator and numerator by a common factor.
  3. 25% is equal to one-quarter and 75% is equal to three-quarters.

Keywords

  • Convert - Convert means to change from one form to another.

  • Percent - Percent means the number of parts in each hundred.

  • Percentage - A percentage is a proportion of a whole.

Common misconception

Pupils may not convert percentages into fractions with denominators of 100 before attempting other conversions.

Encourage pupils to always write percentages as fractions with denominators of 100 before trying to find other fraction equivalents. Show them how missing this key step can lead to errors.

Teacher tip

Pupils need to have familiarity with converting and simplifying fractions before starting this lesson. Outside of the lesson, you may wish to develop speed of recall of percentages and their fraction equivalent (e.g. 25% and one-quarter).

Licence

This content is ยฉ Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
except where otherwise stated. See Oak's terms & conditions
(Collection 2).

Lesson video

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Prior knowledge starter quiz

6 Questions

Q1.
Match the fraction to the correct percentage.

Correct Answer:$$ {25} \over {100} $$,25%

25%

Correct Answer:$$ {99} \over {100} $$,99%

99%

Correct Answer:$$ {1} \over {100} $$,1%

1%

Correct Answer:$$ {67} \over {100} $$,67%

67%

Correct Answer:$$ {44} \over {100} $$,44%

44%

Q2.
Look at the number of squares that are shaded in this one-hundred square representation. Which statements are correct?

An image in a quiz
$$ {90} \over {100} $$ is shaded
Correct answer: 9% is shaded
Correct answer: $$ {9} \over {100} $$ is shaded
90% is shaded

Q3.
Complete the missing percentage. $$ {19} \over {100} $$ = %

Correct Answer: 19

Q4.
Match the percentage to the correct decimal number.

Correct Answer:40%,0.4

0.4

Correct Answer:10%,0.1

0.1

Correct Answer:80%,0.8

0.8

Correct Answer:50%,0.5

0.5

Correct Answer:90%,0.9

0.9

Q5.
Match the decimal number to the correct fraction or percentage.

Correct Answer:$$ {3} \over {100} $$,0.03

0.03

Correct Answer:57%,0.57

0.57

Correct Answer:$$ {12} \over {100} $$,0.12

0.12

Correct Answer:38%,0.38

0.38

Q6.
What does the representation show?

An image in a quiz
Correct answer: 68%
Correct answer: 0.68
0.86
Correct answer: $$ {68} \over {100} $$

6 Questions

Q1.
Match the fraction to the correct percentage.

Correct Answer:$$ {3} \over {10} $$,30%

30%

Correct Answer:$$ {8} \over {10} $$,80%

80%

Correct Answer:$$ {1} \over {10} $$,10%

10%

Correct Answer:$$ {4} \over {10} $$,40%

40%

Correct Answer:$$ {9} \over {10} $$,90%

90%

Q2.
Match the fractions that are equivalent.

Correct Answer:$$ {20} \over {100} $$,$$ {2} \over {10} $$

$$ {2} \over {10} $$

Correct Answer:$$ {40} \over {100} $$,$$ {4} \over {10} $$

$$ {4} \over {10} $$

Correct Answer:$$ {70} \over {100} $$,$$ {7} \over {10} $$

$$ {7} \over {10} $$

Correct Answer:$$ {90} \over {100} $$,$$ {9} \over {10} $$

$$ {9} \over {10} $$

Q3.
What does the representation show?

An image in a quiz
Correct answer: $$ {6} \over {10} $$
6%
$$ {6} \over {100} $$
Correct answer: $$ {60} \over {100} $$
Correct answer: 60%

Q4.
Look at the image. What fractions are equivalent to the ones shown?

An image in a quiz
Correct Answer:$$ {25} \over {100} $$ =,$$ {1} \over {4} $$

$$ {1} \over {4} $$

Correct Answer:$$ {50} \over {100} $$ =,$$ {1} \over {2} $$

$$ {1} \over {2} $$

Correct Answer:$$ {75} \over {100} $$ =,$$ {3} \over {4} $$

$$ {3} \over {4} $$

Q5.
What is the missing denominator in this fraction?

An image in a quiz
Correct Answer: 50

Q6.
40% of the one-hundred squares is shaded. Tick the fractions that are equivalent to 40%

An image in a quiz
Correct answer: $$ {40} \over {100} $$
$$ {4} \over {100} $$
Correct answer: $$ {4} \over {10} $$
$$ {4} \over {5} $$
Correct answer: $$ {2} \over {5} $$

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