Percent increase and decrease

To increase an amount by a percent, add that percent of it. To decrease, take it away. A multiplier does both in one step.

The two-step method

  1. Find the percent of the amount.
  2. Add it for an increase, or subtract it for a decrease.

For example, increase 80 by 15%. 15% of 80 is 12, so the new amount is 80 + 12 = 92. To decrease 80 by 15%, subtract instead: 80 − 12 = 68.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

Before: 80After: 92
An increase of 15%: the new bar is the old bar plus 12.
Before: 80After: 68
A decrease of 15%: 12 is taken away, leaving 68.
percentamount0%085%68100%80115%92
On a double number line, 85% of 80 is 68 and 115% of 80 is 92.

The multiplier method

A quicker way uses one multiplication. An increase of 15% leaves you with 100% + 15% = 115% of the amount. As a decimal that is 1.15, so multiply by 1.15. For example, 80 × 1.15 = 92.

A decrease of 15% leaves 100% − 15% = 85%. Multiply by 0.85: 80 × 0.85 = 68. The multiplier is the key idea for grade 7 and beyond.

Common multipliers

ChangeNew amount isMultiplier
Increase by 10%110%× 1.1
Increase by 25%125%× 1.25
Increase by 50%150%× 1.5
Increase by 100%200%× 2
Decrease by 10%90%× 0.9
Decrease by 25%75%× 0.75
Decrease by 50%50%× 0.5

Percent change calculator

Type a starting amount and a new amount to see the percent increase or decrease, step by step.

Why up 10% then down 10% is not the same

Increase 100 by 10% to get 110. Now decrease 110 by 10%: 10% of 110 is 11, so you get 99, not 100. The second change is a percent of a bigger number.

With multipliers it is clear: 100 × 1.1 × 0.9 = 99. This surprises many adults, and it is a great talking point with older children.

Going the other way: finding the percent change

Sometimes you know the old and new amounts and need the percent. Find the change, then divide by the starting amount. From 80 to 92 is a change of 12, and 12 ÷ 80 = 0.15 = 15%.

The percent change page covers this in full. Remember to always divide by the starting amount, never the new one.

Percent increase and decrease in real life

Prices, pay and populations all change by percents. A $2.00 bus fare that rises by 5% becomes $2.10. A town of 8,000 people that grows by 3% gains 240 people.

Decreases are everywhere too. A phone that loses 20% of its value each year is worth 80% of last year’s price. After two years, a $500 phone is worth $500 × 0.8 × 0.8 = $320.

Ask your child to spot these in the news or at the shops. Each one is a chance to choose between the two-step method and the multiplier.

Quiz: increase and decrease

Find the new amount, or the percent change. Type numbers only.

Where this fits: percentages step by step

  1. What is a percent
  2. Percent to fraction
  3. Fraction to percent
  4. Percent to decimal
  5. Decimal to percent
  6. Comparing fractions, decimals and percents
  7. Benchmark percents
  8. Percent mental math
  9. Over 100% and under 1%
  10. Percent of a number
  11. Finding the percent
  12. Finding the whole
  13. Percent change
  14. Percent increase and decrease (this page)
  15. Discounts and sale price
  16. Sales tax
  17. Tips
  18. Simple interest
  19. Markup, commission and percent error
  20. Percent word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “A $40 game goes up by 10%. What is 10% of 40?” ($4.)
  2. “So the new price is …” ($44.)
  3. “What percent of the old price is that?” (110%.)
  4. “So we could just multiply by …” (1.1.)
  5. “What would we multiply by for a 10% decrease?” (0.9.)

More worked examples

Example 1: increase 60 by 20%

20% of 60 is 12. 60 + 12 = 72. Or 60 × 1.2 = 72.

Example 2: decrease 250 by 30%

30% of 250 is 75. 250 − 75 = 175. Or 250 × 0.7 = 175.

Example 3: a population

A town of 5,000 grows by 4%. 5,000 × 1.04 = 5,200.

Example 4: a price drop

A $90 bike drops 1/3 in price, about 33%. 90 × 2/3 = $60.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. Increase 50 by 10%
  2. Increase 200 by 25%
  3. Decrease 80 by 25%
  4. Decrease 40 by 5%
  5. Multiplier for a 30% increase
  6. Multiplier for a 20% decrease
  7. 120 × 1.5
  8. From 50 to 60: percent increase?
  9. From 80 to 60: percent decrease?
  10. Stretch: 100 up 20% then down 20%
Show the answers
  1. 55
  2. 250
  3. 60
  4. 38
  5. 1.3
  6. 0.8
  7. 180
  8. 20%
  9. 25%
  10. 96

Common mistakes

Forgetting to add or subtractGives 15% of 80 = 12 as the answer.Fix: 12 is the change. Add it to 80: 92.
Using 0.15 as the multiplierWrites 80 × 0.15.Fix: the new amount is 115%, so multiply by 1.15.
Dividing by the new amountFrom 80 to 92: 12 ÷ 92.Fix: always divide by the starting amount: 12 ÷ 80.

How to teach it at home

Price watch

Track a price over a few weeks and work out each percent change.

Growth chart

Find your child’s height increase as a percent.

Multiplier match

Match cards: “up 25%” and “× 1.25”.

By grade

More for each grade: Grade 7 math and the CBSE class 7 maths guide.

Worksheets and practice

Percent increase and decrease worksheet, page 1

Percent increase and decrease worksheet: printable PDF with an answer key. · Make a fresh test

Percent practice · percent calculator · fraction, decimal and percent converter · percentage quiz · percent levels · percent games · percentages for kids

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Questions parents ask

How do you increase a number by a percent?

Find the percent of the number and add it on. Or multiply by 1 plus the percent as a decimal: × 1.15 for 15%.

How do you decrease a number by a percent?

Find the percent and subtract it. Or multiply by 1 minus the percent: × 0.85 for 15%.

What is a multiplier?

The single number you multiply by to make a percent change, like 1.2 for +20% or 0.75 for −25%.

Why doesn’t up 10% then down 10% get back to the start?

The second 10% is taken from a bigger amount. 100 × 1.1 × 0.9 = 99.

What grade learns percent increase and decrease?

Grade 7 under Common Core 7.RP.A.3. In India, class 8.