lesson
A multiplier includes the original amount
1 · Learn
An increase of 15% gives 115% of the original, so multiply by 1.15. A decrease of 15% leaves 85%, so multiply by 0.85. The percentage refers to a specific original quantity.
An increase followed by the same percentage decrease generally does not return to the start because the second percentage is calculated from a different amount.
2 · Worked example
£80 increased by 10% becomes £88. Decreasing £88 by 10% removes £8.80, leaving £79.20, not £80.
3 · Your turn
Increase £60 by 20%, then decrease the result by 20%.
Check your answer
£72, then £57.60. The second percentage uses £72 as its base.
4 · Apply your learning
Explain the two bases with a bar model and test another starting amount.
Adult guidance and safety
Require a reasoned method and an independent check. Use accurate number lines, geometric drawings and data displays where the task needs them. These text models require varied practice and diagnostic assessment before curriculum approval.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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