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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
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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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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.

Keywords

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

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.


To help you plan your year 8 maths lesson on: Expressing one number as a percentage of another, download all teaching resources for free and adapt to suit your pupils' needs...

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.
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Lesson video

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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: $$0.1 \dot 6$$
$$0.1 \dot 3$$
$$\frac{1}{6}$$
$$0.3$$
$$0.167$$

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
tick

0.23

Correct Answer:45%,0.45
tick

0.45

Correct Answer:49%,0.49
tick

0.49

Correct Answer:3%,0.03
tick

0.03

Correct Answer:30%,0.3
tick

0.3

Correct Answer:0.3%,0.003
tick

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%