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Maths Lab · Free lesson · 22 minutes

Two percentage changes do not simply cancel

Model successive percentage changes with multipliers, distinguish simple and repeated growth and verify the base at every step.

SS3 · financial mathematics

01 · Think first

Start with a question.

A price rises 20%, then falls 20%. The second percentage is calculated on a different price. Is the final price equal to the original? Use numbers before trusting an intuition.

What you already know
  • Percent of a quantity
  • Multiply decimal factors
  • Interpret a positive integer exponent
₦100 rises by 20% and then falls by 20%. What is the final value?

02 · See it

Track each new base

This is a mathematical scenario, not a current price or investment promise. A multiplier includes the unchanged original portion.

Start
₦100
Rise 20%: ×1.20
₦120
Fall 20%: ×0.80
₦96
Combined multiplier
0.96 = 4% net decrease

Use the justified worked steps below to explore this idea.

03 · Show steps · explain why

One justified step at a time.

  1. 1

    Increase by r% → multiply by 1 + r/100

    The multiplier retains all of the original amount and adds the stated proportion.

04 · Mistake clinic

Find the first wrong idea.

Tempting wrong line

Increase 20%, decrease 20% → net change is zero.

Compare the correction and its reason

The combined multiplier is 1.20 × 0.80 = 0.96.

Adding signed rates ignores their different bases. To undo a 20% rise, divide by 1.20; this is a 16⅔% decrease from the new amount.

Check: Try a starting value of 100. Track the amounts and distinguish a percentage-point change from a percentage of a quantity.

A mistake is evidence about the next idea to repair. It is not a label for the learner.

05 · Your turn

Try first. Then use a hint.

1. Increase 500 by 12%. Enter the final value.guided practice
2. A value of 200 rises 25% then falls 20%. Enter the final value.independent practice
3. After a 20% discount, an item costs ₦720. Find its original price in naira.far practice

06 · Check & reflect → next step

Understanding includes explaining.

For each change, name the base and multiplier. Explain how to reverse a decrease.

Choose your next learning need

If you missed the reverse problem, revisit equations and percentage bases before timed exam practice.

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Source and review status

JEM-S3-M03-001 · Phase 4C SS3 General Mathematics Exam Overlays · Lab 02 · printed pp. 13–14

This published free lesson contains selected explanations and authored practice. Complete canonical volumes and tutor solutions remain in the protected Content Vault.