Percentage Increase and Decrease

What increasing and decreasing by a percentage means

A percentage increase adds a percentage of the original amount on top. A percentage decrease takes a percentage of the original away. Prices rising with tax, wages going up, sales discounts and population changes are all percentage changes.

You could do these in two steps — find the percentage, then add or subtract — but there is a faster, cleaner method using a multiplier.

Building the multiplier

Every amount starts as 100% of itself.

• An increase of p% gives you (100 + p)%.
• A decrease of p% leaves you (100 − p)%.

Convert that percentage to a decimal (divide by 100) and you have the multiplier.

Change	Percentage left	Multiplier
increase by 10%	110%	1.10
increase by 25%	125%	1.25
increase by 5%	105%	1.05
decrease by 10%	90%	0.90
decrease by 30%	70%	0.70
decrease by 15%	85%	0.85

Applying an increase in one step

Worked example 1: increase $80 by 25%

1. Multiplier for a 25% increase = 1.25.
2. 80 × 1.25 = $100.

Compare with the two-step way: 25% of 80 = 20, then 80 + 20 = 100. Same answer, but the multiplier did it in one move.

Worked example 2: a $1,200 salary rises by 4%

1. Multiplier = 1.04.
2. 1200 × 1.04 = $1,248.

Applying a decrease in one step

Worked example 3: a $50 coat is reduced by 30%

1. Multiplier for a 30% decrease = 0.70.
2. 50 × 0.70 = $35 sale price.

Worked example 4: a population of 8,000 falls by 12%

1. Multiplier = 0.88.
2. 8000 × 0.88 = 7,040.

Finding the percentage change

Sometimes you know the old and new values and need the percentage change:

percentage change = (change ÷ original) × 100

The "original" is always the starting amount.

Worked example 5: a price rises from 40 to 50

1. Change = 50 − 40 = 10.
2. (10 ÷ 40) × 100 = 25% increase.

Worked example 6: a value drops from 200 to 150

1. Change = 200 − 150 = 50.
2. (50 ÷ 200) × 100 = 25% decrease.

Notice the change is always divided by the original, not the new value — a common mistake.

Why the multiplier works

When you increase $80 by 25%, you keep the whole original (100%) and add a quarter more (25%), so you end with 125% of $80. Writing 125% as the decimal 1.25 and multiplying does both jobs at once:

80 × 1.25 = 80 × (1 + 0.25) = 80 + 20 = 100 ✅

For a decrease you keep what is left over: a 30% cut leaves 70%, so you multiply by 0.70.

Try it yourself: the price board

Make a small shop price list and apply changes with multipliers:

• A $25 game with 8% tax → 25 × 1.08
• A $60 jacket with 40% off → 60 × 0.60
• A $4.50 drink with a 15% loyalty discount → 4.50 × 0.85

Then pick two before-and-after prices and work out the percentage change.

Why this matters

Percentage increase and decrease run through tax, tips, sales, interest and statistics. The multiplier method is the foundation for reverse percentages and the everyday examples in percentages in real life.