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## How do you solve percent change in word problems?

## Percentage Change

Subtract the old from the new, then divide by the old value. Show that as a Percentage.

## Comparing Old to New

Percentage Change is all about comparing old to new values. See percentage change, difference and error for other options.

## How to Calculate

Here are two ways to calculate a percentage change, use the one you prefer:

## Example: A pair of socks went from $5 to $6, what is the percentage change?

Answer (Method 1):

- Step 1: $5 to $6 is a $1 increase
- Step 2: Divide by the old value: $1/$5 = 0.2
- Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise .

Answer (Method 2):

- Step 1: Divide new value by old value: $6/$5 = 1.2
- Step 2: Convert to percentage: 1.2×100 = 120% (i.e. $6 is 120% of $5)
- Step 3: Subtract 100%: 120% − 100% = 20%, and that means a 20% rise .

## Another Example: There were 160 smarties in the box yesterday, but now there are 116, what is the percentage change?

Answer (Method 1): 160 to 116 is a decrease of 44. Compared to yesterday's value: 44/160 = 0.275 = 27.5% decrease .

Answer (Method 2): Compare today's value with yesterday's value: 116/160 = 0.725 = 72.5%, so the new value is 72.5% of the old value. Subtract 100% and you get −27.5%, or a 27.5% decrease .

## Why Compare to Old Value?

Because you are saying how much a value has changed.

## Example: Milk was $2, now it is $3, did it rise $1 compared to $2 or $3 ?

We compare to the original $2 value , so we say the change is $1/$2 = 0.5 which is a 50% increase .

## The Formula

You can also put the values into this formula:

New Value − Old Value |Old Value| × 100%

(The "|" symbols mean absolute value , so negatives become positive)

## Example: There were 200 customers yesterday, and 240 today:

240 − 200 |200| × 100% = 40 200 × 100% = 20%

A 20% increase.

## Example: But if there were 240 customers yesterday, and 200 today we would get:

200 − 240 |240| × 100% = −40 240 × 100% = −16.6...%

A 16.6...% decrease.

## How to Reverse a Rise or Fall

Some people think that a percentage increase can be "reversed" by the same percentage decrease. But no!

## Example: 10% of 100

A 10% increase from 100 is an increase of 10 , which equals 110 ...

... but a 10% reduction from 110 is a reduction of 11 (10% of 110 is 11)

So we ended up at 99 (not the 100 we started with)

What happened?

- 10% took us up 10
- Then 10% took us down 11

Because the percentage rise or fall is in relation to the old value :

- The 10% increase was applied to 100
- But the 10% decrease was applied to 110

## How to do it properly

To "reverse" a percentage rise or fall, use the right formula here:

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## Percentage Increase and Decrease Word Problems

- To find 10%, divide a number by 10.
- The original mass of chocolate is 200 grams.
- 200 ÷ 10 = 10 and so 10% of 200 grams in 20 grams.
- To increase an amount by 10%, add 10% to the original amount.
- 200 + 20 = 220. Therefore the new mass is 220 grams

- To find 40%, first find 10% and then multiply it by 4.
- 10% is found by dividing the number by 10. £50 ÷ 10 = £5 and so, 10% is £5.
- We multiply 10% by 4 to get 40%. £5 × 4 = £20 and so, 40% is £20.
- In a sale, the price is decreased.
- To decrease by a percentage, subtract the percentage from the original number.
- £50 – £20 = £30 and so, the new price is £30.

- Percentages of Amounts

## Percentage Change Word Problems

How to work out percentage change.

- Work out the percentage by dividing the original number by 100 and multiplying by the percentage.
- For a percentage increase, add this percentage to the original number.
- For a percentage decrease, subtract this percentage from the original number.

- To find 1%, divide by 100.
- To find 5%, divide by 20.
- To find 10%, divide by 10.
- To find 20%, divide by 5.
- To find 25%, divide by 4.
- To find 50%, divide by 2.

## Percentage Increase Word Problems

## Percentage Decrease Word Problems

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## Course: 7th grade > Unit 2

Solving percent problems.

- Equivalent expressions with percent problems
- Percent word problem: magic club
- Percent problems
- Percent word problems: tax and discount
- Tax and tip word problems
- Percent word problem: guavas
- Discount, markup, and commission word problems
- Multi-step ratio and percent problems

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