Page 1 · Introduction
Three ways to write a part
A half can be written as a fraction (1/2), a decimal (0.5) or a percentage (50%). They’re the same amount in three outfits. Year 7 expects you to move between them confidently — and it’s easier than it looks.
The big ideaFractions, decimals and percentages are three ways of writing the same part of a whole. Learn to switch between them, and a huge range of questions becomes simple.
💡We take the conversions one step at a time, then use them. No calculator needed.
On the real testWhere this appearsFractions, decimals and percentages are core Year 7 number work and appear constantly — in maths, science and everyday money problems.
Page 2 · Fraction to decimal
Divide top by bottom
To turn a fraction into a decimal, divide the top by the bottom.
Write 3/4 as a decimal.
3 ÷ 4 = 0.75.
0.75
Write 1/5 as a decimal.
1 ÷ 5 = 0.2.
0.2
Page 3 · Decimal to percentage
Multiply by 100
To turn a decimal into a percentage, multiply by 100 (move the point two places right). To go back, divide by 100.
Write 0.35 as a percentage.
0.35 × 100 = 35%.
35%
Write 60% as a decimal.
60 ÷ 100 = 0.6.
0.6
Page 4 · Common conversions
Ones worth knowing
A few conversions are so common they’re worth memorising: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/10 = 0.1 = 10%.
What is 1/4 as a percentage?
1/4 = 0.25 = 25%.
25%
What is 0.5 as a fraction?
0.5 = 1/2.
1/2
Page 5 · Calculating
Finding a fraction or percent of an amount
To find a fraction of an amount, divide by the bottom and multiply by the top. For a percentage, 10% is a tenth — a handy building block.
Find 3/4 of 20.
20 ÷ 4 = 5, then × 3 = 15.
15
Find 20% of 50.
10% of 50 = 5, so 20% = 10.
10
Level 1 · Easy
Warm up
Simple conversions. Tap to check.
1. Write 1/2 as a decimal.
1 ÷ 2 = 0.5.
2. Write 0.25 as a percentage.
0.25 × 100 = 25%.
3. Write 10% as a decimal.
10 ÷ 100 = 0.1.
Level 2 · Medium
Building up
More conversions.
1. Write 4/5 as a decimal.
4 ÷ 5 = 0.8.
2. Write 0.7 as a percentage.
0.7 × 100 = 70%.
3. What is 3/4 as a percentage?
3/4 = 0.75 = 75%.
Level 3 · Hard
Getting tougher
Finding fractions and percents of amounts.
1. Find 1/4 of 40.
40 ÷ 4 = 10.
2. Find 20% of 60.
10% of 60 = 6, so 20% = 12.
3. Find 3/5 of 25.
25 ÷ 5 = 5, then × 3 = 15.
Level 4 · Challenge
Challenge
Multi-step conversions and calculations.
1. Which is largest: 1/2, 0.45 or 40%?
A 0.45
B 40%
C 1/2
D All equal
1/2 = 0.5, which is bigger than 0.45 and 0.40.
2. Find 75% of 80.
75% = 3/4. 80 ÷ 4 = 20, × 3 = 60.
3. A jacket is $60 with 25% off. What is the saving?
25% = 1/4. 60 ÷ 4 = $15 saved.
Page 10 · Well done
You’ve finished Fractions & Decimals
You can now convert between fractions, decimals and percentages, and calculate a fraction or percentage of an amount. This flexibility is one of the most useful skills in all of high-school maths.
RememberFraction to decimal: divide top by bottom. Decimal to percent: ×100. To find a fraction of an amount: divide by the bottom, multiply by the top.
🎉Great work getting through all four tiers. Try another module next — every one builds a different skill.
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