430 decreased by 35%: the new value = □

279.5. 430 × 35% = 150.5, and 430 − 150.5 = 279.5; or in one step: down 35% leaves 0.65 of it, 430 × 0.65 = 279.5.

Cost $60, 50% profit: selling price = $□

90. Profit = 60 × 50% = 30, so the price = 60 + 30 = 90; or in one step, 60 × 1.5 = 90.

8,880. Tax = taxable amount × rate = 296000 × 3% = 8880.

Percentages and ratio · Ages 12–13

From “Percentage increase and decrease” to “Tax, pay and commission”, step by step, each skill with its methods, worked examples and answers.

Percentage increase and decreaseA percentage change is always of the original
Method120 up 20%: 120 × 20% = 24, 120 + 24 = 144
Another way: One multiplication120 × (1 + 20%) = 120 × 1.2 = 144
Back to the original valueNew ÷ (1 ± rate), not the rate taken back off
Methodx × 1.2 = 144, x = 144 ÷ 1.2 = 120
Another way: Match the percentages120% is 144, 1% is 1.2, 100% is 120
One change after anotherMultiply the factors; never add the rates
Method+20% then −20%: 1.2 × 0.8 = 0.96, 4% down
Another way: Start from 100100 → 120 → 96
Profit and lossProfit and loss percentages are of the cost
MethodCost 80, sold at 100: 20 ÷ 80 × 100% = 25%
Another way: One multiplicationSelling price = 80 × 1.25 = 100
Marked prices and discountsA discount is of the marked price; discounts in a row multiply
MethodMarked 250, 20% off: 250 × 0.8 = 200
Another way: The discount first250 × 20% = 50, 250 − 50 = 200
Simple and compound interestSimple: principal × rate × years; compound: multiply year by year
Method5000 × 3% × 4 = 600, amount 5600
Another way: A year's interest first5000 × 3% = 150, 150 × 4 = 600
Tax, pay and commissionName the base first: a percentage of what?
Method380 × 10% = 38, 380 + 38 = 418
Another way: One multiplication380 × 1.1 = 418

From different skills in this topic. Have a go first, then open each one for the answer and the working.

Example 1Percentage increase and decrease →
430 decreased by 35%: the new value =
Show the answer and working
Answer: 279.5
430 × 35% = 150.5, and 430 − 150.5 = 279.5; or in one step: down 35% leaves 0.65 of it, 430 × 0.65 = 279.5.
Example 2Profit and loss →
Cost $60, 50% profit: selling price = $
Show the answer and working
Answer: 90
Profit = 60 × 50% = 30, so the price = 60 + 30 = 90; or in one step, 60 × 1.5 = 90.
Example 3Tax, pay and commission →
Taxable amount $296,000, tax rate 3%: tax = $
Show the answer and working
Answer: 8,880
Tax = taxable amount × rate = 296000 × 3% = 8880.

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working