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• Socratic Meta

## 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?

• 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 .

• 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:

Maths with Mum

## 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 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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## Video transcript

#### IMAGES

1. how to solve percent word problems

2. Christmas Shopping Problems With Tax And Discounts Worksheet Answers

3. Solve Percent Increase Word Problems

4. solving percent change problems

5. solving percent change problems

6. Percent Change Word Problems

#### VIDEO

1. Q1 Thursday Oct 26 Homework

2. Percent Word Problems

3. Solving Percent Question 1

4. How To Calculate Percent Increase for ASVAB Math

5. Percent Increase Word Problems

6. Word Problems of Percentage

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13. Percentage Increase and Decrease Word Problems

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