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Change factor (percentage multiplier)

The change factor, also called the multiplier, is the number we multiply the old value by to get the new one. An increase of 15% gives 1.15, because 100% + 15% = 115%. A decrease of 20% gives 0.80. With several changes, we multiply the factors.

Years 8–9 and upper secondary · Updated

Watch Fox work it out on the board

Fox works one step at a time. Press play.

What is a change factor?

Before a change we have the whole of the old value, 100% = 1. The change factor is the share afterwards, written as a decimal.

100% + 15% = 115% = 1.15

100% − 20% = 80% = 0.80

We want the new value in one step: new = old · change factor.

ChangeShare afterwardsChange factor
5% increase105%1.05
30% increase130%1.30
100% increase200%2
3% decrease97%0.97
10% decrease90%0.90
25% decrease75%0.75

Above 1 is an increase, below 1 a decrease. If we know both values, the change factor is new ÷ old.

Several changes in a row

Each change is worked out on the value at that moment. That is why we multiply the factors instead of adding the percentages.

500 · 1.2 · 0.8 = 500 · 0.96 = 480

If the same change is repeated, we get a power: a 10% increase per year for n years gives the factor 1.1ⁿ.

Working backwards to the old value

Because old · change factor = new, we divide the new value by the change factor. Division undoes the multiplication.

old = new ÷ change factor

A jacket costs 480 kr after a 20% discount: 480 ÷ 0.8 = 600 kr. Check: 600 · 0.8 = 480.

Example

Example 1: The rent goes up by 4%

A rent of 6 400 kr a month goes up by 4%. We want to know the new rent.

  1. After the increase the rent is 100% + 4% = 104%.

    104% = 1.04

  2. We multiply the old rent by the change factor.

    6 400 · 1.04 = 6 656

  3. The new rent is 6 656 kr a month.

The increase on its own: 0.04 · 6 400 = 256 kr, and 6 400 + 256 = 6 656. That is correct.

Example 2: A car loses 15% of its value

A car worth 180 000 kr loses 15% of its value in one year. We want to know the new value.

  1. What is left after the decrease is 100% − 15% = 85%.

    85% = 0.85

  2. The factor is below 1, because the value goes down.

    180 000 · 0.85 = 153 000

  3. The car is worth 153 000 kr after one year.

The decrease is 0.15 · 180 000 = 27 000 kr, and 180 000 − 27 000 = 153 000. That is correct.

Example 3: Up 20% and then down 20%

Shoes costing 500 kr go up by 20% and are then reduced by 20%. We want to know the final price.

  1. The increase has the change factor 1.2.

    500 · 1.2 = 600

  2. The reduction has the factor 0.8 and is worked out on 600 kr.

    600 · 0.8 = 480

  3. We get the overall factor by multiplying.

    1.2 · 0.8 = 0.96

  4. 0.96 is 96%. The final price of 480 kr is 4% lower than at the start.

500 · 0.96 = 480, the same final price. The increase was 100 kr and the reduction 120 kr, so 20 kr below 500 kr is correct.

Pitfalls

  • Writing the factor for an increase of 15% as 0.15 or 1.5.

    We keep the whole of the old value: 1 + 0.15 = 1.15. The factor 1.5 means an increase of 50%.

  • Writing the factor for a decrease of 20% as 0.2 or 1.2.

    Ask how much is left: 100% − 20% = 80%, so 0.8.

  • Thinking that +20% and then −20% cancel each other out.

    Multiply the factors: 1.2 · 0.8 = 0.96, so a decrease of 4%.

Practise on your own

0 of 4 correct

  1. Which change factor goes with an increase of 12%?

  2. A gym membership costs 850 kr and goes up by 6%. What is the new price?

  3. A phone costs 5 000 kr new and loses 30% of its value in the first year. What is it worth after one year?

  4. A lamp costs 400 kr. The price goes up by 25% and is then reduced by 20%. What is the final price?

More walkthroughs with Fox

Common questions

How do you work out the change factor from two values?

Divide the new value by the old one: 6 656 ÷ 6 400 = 1.04, so an increase of 4%.

What does a change factor below 1 mean?

That the value has gone down. 0.85 means that 85% is left, so a decrease of 15%.

How do you find the original price with a change factor?

Divide the new price by the change factor. 480 kr after a 20% discount: 480 ÷ 0.8 = 600 kr.

Why do you not get back to the start after +20% and then −20%?

The reduction is worked out on the higher price and takes away more kronor. Overall the factor is 1.2 · 0.8 = 0.96, a decrease of 4%.

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