SM4.1 Percentages
You can move between fractions, decimals and percentages without working, and solve percentage change, profit and loss, and discount questions at examination speed.
Topics shown in module order.
A percentage is a fraction with a hundred on the bottom, and fluency means holding the common conversions in your head: an eighth is twelve and a half percent, a third is thirty-three and a third. Entrance and recruitment examinations at every stage lean on percentage change, profit and loss, discounts and simple interest, and they reward the reader who computes with fractions rather than long decimal multiplication.
Work through these
Learn the fraction-to-percentage table up to twelfths until any entry comes without working
The table is the toolbox of examination arithmetic: seeing 37.5 percent as three eighths turns a multiplication into a division by a small number. It is learned in an evening and used for years.
Solve percentage increase and decrease questions, including successive changes
Two successive changes do not add, and the ten percent up then ten percent down trap is the most asked trick in this topic. Working through why the answer dips below the start inoculates you against the whole family.
Solve profit, loss and discount questions, always writing what the base of each percentage is
Profit percent sits on cost price and discount percent on marked price, and mixing the bases is where these questions are lost. Writing the base beside every percentage is a one-word habit that removes the error.
Practise a timed set of twenty mixed percentage questions and review only the ones that were slow
Speed, not correctness, is what examinations actually test in this topic, and speed comes from reviewing the slow questions rather than the wrong ones. The review tells you which conversion or setup has not become automatic yet.
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Links last checked 7 Sept 2026.
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