GCSE Maths · Percentages · Foundation · Summary

GCSE Maths Percentages (Foundation): summary and key words

Chapter summary

Skill	Method
Percentage, fraction, decimal	% to decimal: ÷ 100. Decimal to %: × 100. % to fraction: over 100 and simplify. Fraction to %: make the denominator 100, or divide then × 100
Percentage of an amount	Without a calculator: build from 10% (÷ 10) and 1% (÷ 100). With a calculator: decimal × amount
One quantity as a percentage of another	part ÷ whole × 100 (same units!)
Comparing using percentages	Write each as a percentage of its own total, then compare
Increase or decrease by p%	New amount = original × multiplier. Multiplier = 1 + p/100 (increase) or 1 − p/100 (decrease)
Percentages over 100%	100% + 150% = 250% so multiplier 2.5. An increase of 100% doubles
Percentage change, profit, loss	change ÷ original × 100
Reverse percentage	original = new amount ÷ multiplier (or find 1%, then 100%)
Simple interest	Interest = principal × rate × years ÷ 100. Same amount each year
Compound interest, growth, decay	final = start × multiplierⁿ. Interest = final − start
One change after another	Multiply the multipliers. Never add the percentages
Higher: years, rate, starting amount	Years: try powers. Rate: n-th root of (final ÷ start). Start: divide by multiplierⁿ

I can write a percentage as a fraction and a decimal, and change a fraction or decimal to a percentage.
I can find a percentage of an amount without a calculator (using 10% and 1%) and with a calculator.
I can write one number as a percentage of another, changing units first if I need to.
I can compare two results using percentages.
I can increase or decrease an amount by a percentage using a multiplier, including increases of more than 100%.
I can work out a percentage change, percentage profit and percentage loss.
I can find the original amount after a percentage increase or decrease (reverse percentages).
I can work out simple interest, with the time in years or months.
I can work out compound interest and repeated percentage growth or decay using multiplierⁿ.
I know that percentage changes one after another are multiplied, not added.
Higher: I can find the number of years or the yearly rate in a compound problem, and work backwards to a starting amount.

Percentage: A number of parts per hundred, written with the % sign. 35% means 35 out of 100.
Per cent: Out of 100.
Multiplier: The number you multiply by to get the new amount in one step. A 15% increase has multiplier 1.15; a 15% decrease has multiplier 0.85.
Percentage change: The change as a percentage of the original amount: change ÷ original × 100.
Original amount: The starting amount, which is 100% in a percentage-change problem.
Profit / loss: Selling price minus cost price: a profit if positive, a loss if negative. Percentage profit or loss is found out of the cost price.
Reverse percentage: A problem where you know the amount after a percentage change and must find the original amount.
Principal: The amount of money first invested or borrowed.
Simple interest: Interest that is the same every year because it is always a percentage of the original amount.
Compound interest: Interest worked out on the original amount plus the interest already added.
Per annum (p.a.): Each year.
Depreciation: A fall in the value of something (like a car) over time. Usually a repeated percentage decrease.
Growth and decay: A repeated percentage increase (growth) or decrease (decay).
Percentage points: The difference between two percentages. A rate that goes from 4% to 6% rises by 2 percentage points (but by 50% as a percentage change).