Topic notes and worked questions
Fractions, Ratios & Percentages
These topics often look different on the page but share one idea: compare quantities carefully, keep track of what the whole is, and make units consistent before calculating.
Percentage increase and decrease
Find the change, divide by the original, and know when a multiplier is faster.
Reverse percentages without guessing
Work backwards from a discounted or increased value using multipliers.
Simplify ratios when units are different
Convert units first, then simplify with the greatest common factor.
Before you calculate
Underline what the question gives you and what it actually asks for. Many errors happen before the arithmetic starts.
After you calculate
Look at the size and sign of the answer. A ten-second sense check can catch a wrong setup.
When units appear
Keep them beside the numbers. Converting early is often safer than trying to repair units at the end.