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Percentage increase and decrease

2026-10-04Percentage, Rate & Ratio Ms Lam

Convert between percentages and multipliers so increase and decrease problems stay consistent.

Key formulas

New = Original \times (1 \pm r/100)

\text{Percentage change} = (change/original) \times 100\%

The multiplier idea

An increase of r% multiplies the original by (1 + r/100). A decrease of r% multiplies by (1 − r/100). Working with multipliers is faster and reduces arithmetic slips compared with finding the change separately every time.

Finding the percentage change

Percentage change equals (actual change ÷ original value) × 100%. Always divide by the original, not the new value, unless the question asks for reverse percentage.

Common traps

A 20% increase followed later by a 20% decrease does not return to the original — successive changes use different bases. Also, “increased by 20% of A” is not the same wording as “increased to 20% of A”.

Exam habit

Underline original and new. Write the multiplier before substituting numbers.

Worked example

Increase with multiplier

Problem. A phone priced at $4800 rises by 7.5%. Find the new price.

Solution. Multiplier = 1.075. New price = 4800 × 1.075 = 5160. The new price is $5160.

Review quiz

1 / 4

Increase 200 by 15%. New value?

Practice questions

A price of $250 increases by 12%. Find the new price.
A quantity falls from 80 to 68. Find the percentage decrease.
A value increases by 15% to become 460. Find the original value.

Study notes

What is reverse percentage?

You are given the new value and the percentage change; divide by the multiplier to recover the original.

Can the multiplier exceed 2?

Yes — a 120% increase uses multiplier 2.2.