Use knowledge of common equivalents to compare fractions and decimals | Maths

Starter quiz

What is 100 divided into four equal parts? Each part is equal to ______

'25' ✓
What is 1,000 divided into five equal parts? Each part is equal to ______

'200' ✓
What is 10 divided into five equal parts? Each part is equal to ______

'2' ✓
10 divided into five equal parts is the same as saying ___

Five times ten

One fifth of 10 ✓

10 divided by 5 ✓

One fifth divided by 10

One fifth multiplied by 10 ✓
Which equation would you use to calculate 1,000 divided into four equal parts?

${1}\over{4}$ ÷ 1,000

${1}\over{4}$ × 1,000 ✓

${1}\over{5}$ ÷ 1,000

${1}\over{5}$ × 1,000
Match the statements to the equations they represent.

${1}\over{5}$ × 10

⇔

One fifth of 10 ✓

${1}\over{4}$ × 10

⇔

One quarter of 10 ✓

${1}\over{2}$ × 10

⇔

One half of 10 ✓

${1}\over{10}$ × 10

⇔

One tenth of 10 ✓

Exit quiz

How could you write this decimal as a fraction? The decimal is 0.04

${1}\over{10}$

${1}\over{100}$

${2}\over{100}$

${4}\over{100}$ ✓

${2}\over{50}$ ✓
How could you write this decimal as a fraction? The decimal is 0.75

${75}\over{100}$ ✓

${7}\over{10}$

${3}\over{4}$ ✓

${5}\over{100}$
Match the fraction with the equivalent decimal.

${3} \over {100}$

⇔

0.03 ✓

${3} \over {4}$

⇔

0.75 ✓

${3} \over {5}$

⇔

0.6 ✓

${3} \over {10}$

⇔

0.3 ✓
Why is ${1}\over{3}$ more difficult to convert to a decimal?

It is because 3 is not a factor of 10 or 100 ✓

It is because 3 is a prime number.
Which pair of fractions and decimals is equivalent?
$Which symbol would go between this fraction and decimal?$

Which symbol would go between this fraction and decimal?

<

=

> ✓

Worksheet

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Lesson Details

Key learning points

0.1 is equal to 1/10
0.2 is equal to 1/5
0.25 is equal to 1/4
0.5 is equal to 1/2
0.75 is equal to 3/4

Common misconception

The numbers in a decimal can be rewritten as a fraction so one-fifth becomes 1.5 as a decimal and that fractions and decimals do not represent equivalent values.

Read decimals as a number of tenths and hundredths to make the link to fractions.

Keywords

Equivalent - Numbers are equivalent if they have exactly the same value.
Tenth - When one whole is divided into 10 equal parts, each part is one tenth. This can be expressed as a fraction or as a decimal.
Hundredth - When one whole is divided into 100 equal parts, each part is one hundredth. This can be expressed as a fraction or as a decimal.