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Percentage change: increase and decrease

We divide the change by the old value. From 200 kr to 260 kr the change is 260 − 200 = 60 kr, and 60 ÷ 200 = 0.30. So the price has increased by 30%.

Years 7–9 · Updated

Watch Fox work it out on the board

Fox works one step at a time. Press play.

How we work it out

We want to know how big the change is compared with the old value.

  • Work out the change: new value − old value.
  • Divide the change by the old value.
  • Multiply by 100 to get the percentage.
  • Say whether it is an increase or a decrease, and check.

percentage change = (new − old) ÷ old

We divide by the old value because it is the starting point, the whole, 100%. If the difference is negative, it is a decrease.

Example

Example 1: The bus pass went up in price

A bus pass went from 550 kr to 605 kr. We want to know the increase as a percentage.

  1. The change is the new price minus the old price.

    605 − 550 = 55

  2. We compare the increase with the old price.

    55 ÷ 550 = 0.1

  3. 0.1 is 10 hundredths. The price has increased by 10%.

    0.1 = 10%

10% of 550 is 55, and 550 + 55 = 605. That is correct.

Example 2: The phone in the sale

A phone went from 4 500 kr to 3 600 kr. We want to know the reduction as a percentage.

  1. New minus old is negative. That shows a decrease.

    3 600 − 4 500 = −900

  2. We divide the decrease by the old price.

    900 ÷ 4 500 = 0.2

  3. 0.2 is 20 hundredths. The price has been reduced by 20%.

    0.2 = 20%

After a 20% reduction we pay 80%: 0.8 · 4 500 = 3 600. That is correct.

Example 3: Up and then back down to the same price

A price goes from 160 kr to 200 kr and then back again. We want to know both changes as percentages.

  1. The increase is 200 − 160 = 40 kr. We compare it with 160 kr.

    40 ÷ 160 = 0.25 = 25%

  2. The decrease is also 40 kr, but this time we started at 200 kr.

    40 ÷ 200 = 0.2 = 20%

  3. The same 40 kr is a different percentage, because the starting point is different.

160 · 1.25 = 200 and 200 · 0.8 = 160. Both are correct.

Pitfalls

  • Dividing by the new value, so that 160 kr to 200 kr becomes 40 ÷ 200 = 20%.

    Divide by the value before the change: 40 ÷ 160 = 0.25, so 25%.

  • Answering with the kronor, so that 80 kr to 100 kr becomes "20%".

    20 kr is the change in kronor. As a percentage: 20 ÷ 80 = 0.25, so 25%.

  • Writing 0.25 as "0.25%".

    Multiply by 100 first: 0.25 = 25%. 0.25% is a quarter of one percent.

Practise on your own

0 of 4 correct

  1. A cinema ticket cost 200 kr and now costs 250 kr. By what percentage has the price increased?

  2. A pair of headphones cost 500 kr and now costs 400 kr. By what percentage has the price been reduced?

  3. A chess club had 40 members and now has 46. By what percentage has the number of members increased?

  4. A jumper cost 349 kr and now costs 399 kr. By what percentage has the price increased? Round to the nearest whole percent.

More walkthroughs with Fox

Common questions

How do you work out a percentage decrease?

In the same way as an increase: divide the decrease by the old value. From 4 500 kr to 3 600 kr: 900 ÷ 4 500 = 0.2, so 20%.

Why do you divide by the old value and not the new one?

We compare with how things were at the start. The old value is the starting point and counts as 100%.

Can an increase be more than 100%?

Yes. From 50 kr to 150 kr the increase is 100 kr, and 100 ÷ 50 = 2, so 200%. The price has tripled.

How do you work out the new price when you know the percentage?

Multiply by the change factor. 400 kr increased by 15%: 400 · 1.15 = 460 kr. Reduced by 15%: 400 · 0.85 = 340 kr.

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