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Year 8

Expressing one number as a percentage of another

I can describe one number as a percentage of another.

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New
New
Year 8

Expressing one number as a percentage of another

I can describe one number as a percentage of another.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Percentages can be written as a fraction out of 100
  2. One number can be written as a fraction of another.
  3. Using equivalent fractions this can be written as a fraction out of 100
  4. One number can be written as a percentage of another.
  5. Decimals can also be used to write one number as a percentage of another.

Common misconception

A single digit percentage is incorrectly worked out by dividing by 10 and not 100 e.g 3% = 0.3

Two responses can be used to remind students that to covert a percentage into a decimal; we divide by 100; using 3%, ask what 30% is as a decimal and 3% as a decimal. Pupils realise they cannot be the same. A place value chart also helps.

Keywords

  • Equivalent fractions - Two fractions are equivalent if they have the same value.

Using equivalent fractions, there are an infinite number of amounts which can be represented as 75%. Pupils can draw a spider diagram to illustrate this e.g 75 out of 100, 3 out of 4, 6 out of 8, 36 out of 48 etc.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
Two fractions are ____________ if they have the same value.
Correct answer: equivalent
improper
ordinary
proper
Q2.
What is 20% as a simplified fraction?
$$\frac{1}{20}$$
$$\frac{1}{4}$$
$$\frac{20}{100}$$
$$\frac{10}{50}$$
Correct answer: $$\frac{1}{5}$$
Q3.
What is 30% as a simplified fraction?
$$\frac{1}{30}$$
$$\frac{1}{3}$$
Correct answer: $$\frac{3}{10}$$
$$\frac{15}{50}$$
$$\frac{1}{20}$$
Q4.
What is 42% as a simplified fraction?
$$\frac{42}{100}$$
$$\frac{42}{20}$$
$$\frac{1}{42}$$
Correct answer: $$\frac{21}{50}$$
$$\frac{42}{50}$$
Q5.
Using short division or otherwise, work out the decimal answer to 25 ÷ 4.
Correct Answer: 6.25
Q6.
Using short division or otherwise, work out the decimal answer to 1 ÷ 6.
Correct answer: $$0.1 \dot 6$$
$$0.1 \dot 3$$
$$\frac{1}{6}$$
$$0.3$$
$$0.167$$

Exit quiz

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6 Questions

Q1.
$$\frac{7}{20}$$ as a percentage is %.
Correct Answer: 35, 35%, 35 %
Q2.
Which decimal is equivalent to 1%?
0.001
Correct answer: 0.01
0.1
1.0
10.0
Q3.
$$\frac{6}{25}$$ as a percentage is %.
Correct Answer: 24, 24%, 24 %
Q4.
Match each percentage to its decimal equivalent.
Correct Answer:23%,0.23

0.23

Correct Answer:45%,0.45

0.45

Correct Answer:49%,0.49

0.49

Correct Answer:3%,0.03

0.03

Correct Answer:30%,0.3

0.3

Correct Answer:0.3%,0.003

0.003

Q5.
$$\frac{3}{8}$$ as a decimal is .
Correct Answer: 0.375
Q6.
Using short division or otherwise, write $$\frac{7}{9}$$ as a percentage.
Correct answer: $$77.\dot 7$$%
$$0. \dot 7$$%
$$77. \dot 6$$%
77%
78%