Fraction Reaction
Move fluently between fractions, decimals and percentages, then master the multiplier method — percentage change, reverse percentages, and the recurring-decimal proof that grade 9s never miss.
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Fraction Reaction 🔀
Fractions, decimals and percentages are three ways of writing the **same** thing: ¾ = 0.75 = 75%. Being able to flip between them at will is the key to the whole topic. Then one powerful tool — the **multiplier** — turns percentage change, reverse percentages and compound problems into quick one-step calculations.
Flip between the three ↔️
The conversions you need on demand: • **Fraction → decimal:** divide top by bottom. 3 ÷ 4 = 0.75. • **Decimal → percentage:** multiply by 100. 0.75 → 75%. • **Percentage → fraction:** put over 100 and simplify. 40% = 40/100 = 2/5. Learn the common ones by heart (½, ¼, ⅕, ⅒) so you can recognise them instantly.
Match each fraction to its percentage
- 1/2
- 1/4
- 3/4
- 1/5
- 50%
- 25%
- 75%
- 20%
Fraction to decimal
An interactive activity.
Percentages as operators 💯
A percentage can act **on** an amount. To find a percentage of something, turn the percentage into a decimal and multiply: **15% of 240** = 0.15 × 240 = **36**. This "×decimal" idea is the seed of the multiplier method you will use for every percentage-change question.
Percentage of an amount
An interactive activity.
The multiplier method 📈
To CHANGE an amount by a percentage, multiply by a single **multiplier**: • Increase by 15% → × **1.15** (that is 100% + 15%). • Decrease by 20% → × **0.8** (that is 100% − 20%). • Increase by 150% → × **2.5** (percentages over 100% are fine). One multiplication does it — faster and safer than working out the part and adding it on.
Increase by a percentage
An interactive activity.
Reverse percentage
After a 20% increase, a coat costs £60. What was the ORIGINAL price?
- £50
- £72
- £48
- £40
Recurring decimals ↩️
A recurring decimal such as 0.4545... is exactly equal to a fraction, and you prove it with algebra (a Higher "show that"): Let **x = 0.4545...** Two digits repeat, so multiply by 100: **100x = 45.4545...** Subtracting removes the recurring tail: **100x − x = 45**, so **99x = 45** and **x = 45/99 = 5/11**. Every algebraic line must be written down to score full marks.
Order the proof
An interactive activity.
Percentage rules
To increase an amount by 15%, multiply by _____. To reverse a percentage change and find the original amount, you _____ by the multiplier. To write a percentage as a fraction, put it over _____.