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Section 10.3 · Number

Percentage increase and decrease

Increase and decrease a quantity by a percentage, and express a change as a percentage of the original.

6 teaching slides 52 practice questions Worked answers for every question

1 · Teaching slidesuse ← → keys

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2 · Key words

increaseMake larger; add the percentage on.
decreaseMake smaller; subtract the percentage.
percentage changeThe change as a percentage of the original.
original amountWhat you started with; the thing you divide by.
discountAn amount taken off a price.

3 · Summary of the sectionrevise from this

  • To increase by p%: find p% and add it. To decrease: find p% and subtract it.
  • In one step: increase by 20% is × 1.2; decrease by 20% is × 0.8.
  • Percentage change = change ÷ original × 100.
  • Always divide by the original amount, not the new one. This is the single most important rule in the section.
  • 40 → 50 is a 25% increase; 50 → 40 is a 20% decrease. The same change, different starting points.
  • Up 10% then down 10% does not return you to the start: 100 → 110 → 99.
  • Increasing by 100% doubles an amount; decreasing by 100% leaves nothing.
  • Always say whether the change is an increase or a decrease — the number alone is not an answer.
PDFPrintable worksheet All 52 questions, space to work PDFWorked answers Full solutions, not just the answer

Video lessons1 videos

Math Antics - What Percent Is It?

American stretchmathantics

Worth a second viewing here: percentage change is the same skill, applied to the difference rather than the whole.

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4 · Practice52 questions, easiest first

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10.2 Percentages of a quantity
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End-of-unit {UNUM} test