One-page revision sheet

• Per cent means out of a hundred. 45% is 45 out of every 100.
• Percentage → decimal: divide by 100. 35% = 0.35.
• Decimal → percentage: multiply by 100. 0.35 = 35%.
• Percentage → fraction: put it over 100 and simplify. 45% = 45/100 = 9/20.
• Fraction → percentage: divide, then multiply by 100. 3/8 = 0.375 = 37.5%.
• Learn the common ones by heart: 1/2, 1/4, 3/4, 1/5, 1/10, 1/8.
• To compare, convert everything to one form — percentages are usually easiest.
• A percentage can be more than 100. 150% of 20 is 30.

Key words: per cent  ·  percentage  ·  equivalent  ·  convert  ·  simplest form

• 10% is one tenth — divide by 10. This is the building block for everything else.
• 1% is one hundredth — divide by 100. From 1% you can build any percentage at all.
• 50% is halving, 25% is dividing by 4, 75% is three quarters.
• Build the awkward ones: 35% = 10% + 10% + 10% + 5%.
• 5% is always half of 10%, and 2.5% is half of that.
• p% of n and n% of p are equal — both are p × n ÷ 100. Use whichever is easier.
• Over 100% gives more than you started with: 150% of 200 is 300.
• To go backwards, find 1% first: if 30% is 24, then 1% is 0.8 and 100% is 80.

Key words: of  ·  mental method  ·  quantity

• To increase by p%: find p% and add it. To decrease: find p% and subtract it.
• In one step: increase by 20% is × 1.2; decrease by 20% is × 0.8.
• Percentage change = change ÷ original × 100.
• Always divide by the original amount, not the new one. This is the single most important rule in the section.
• 40 → 50 is a 25% increase; 50 → 40 is a 20% decrease. The same change, different starting points.
• Up 10% then down 10% does not return you to the start: 100 → 110 → 99.
• Increasing by 100% doubles an amount; decreasing by 100% leaves nothing.
• Always say whether the change is an increase or a decrease — the number alone is not an answer.

Key words: increase  ·  decrease  ·  percentage change  ·  original amount  ·  discount