lesson
The final amount may not be one hundred per cent
1 · Learn
After a 20% reduction, the final price is 80% of the original. To recover the original, divide the final amount by 0.8. Adding 20% of the final amount uses the wrong base.
Draw a bar showing the known percentage and the unknown whole. Check by applying the original change to your recovered amount.
2 · Worked example
A sale price of £64 after 20% off came from £64 ÷ 0.8 = £80. Checking 80 × 0.8 returns 64.
3 · Your turn
A price after a 10% increase is £99. Find the original price.
Check your answer
£90, because 99 ÷ 1.1 = 90.
4 · Apply your learning
Compare reversing an increase with reversing a decrease and explain why adding or subtracting the same percentage is not enough.
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment programme.
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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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