## Introduction

- Percentages have many real-life applications.
- Discounts and percent increases in price are usually expressed in percentages.
- From your laptop or phone's battery and school test scores to your home or personal loan interest, the use of percent is widespread.

## What Percent One Number is of Another

- To find what percent one number is of another, divide the number before "is" by the number after "of".

## Finding the Base

- To solve a question like 30 is 60% of what number? First, divide the number by the percent number and then convert the percent number to decimal.

## Percent Increase and Decrease

- To find the % increase or decrease, divide the change by the initial/starting value.
- Percent increase or decrease = $\frac{\mathrm{Change}}{\mathrm{Starting}/\mathrm{initial}\mathrm{value}}$
- Change = old value - new value

## Examples

**1) 30 is 60% of what number?**

= $\frac{30}{60\%}$

Remove the % sign and move the decimal two places to the left.

$=\frac{30}{0.60}$

$=\frac{300}{6}$

$=50$

**2) 25 is 40% of what number?**

**$=\frac{25}{40\%}$**

Remove the % sign and move the decimal two places to the left.

$=\frac{25}{0.4}$

$=\frac{250}{4}$

$=62.5$

**3) 40 is 120% of what number?**

$=\frac{40}{120\%}$

Remove the % sign and move the decimal two places to the left.

$=\frac{40}{1.2}$

$=\frac{400}{12}$

$=33.33$

**4) 30 is what percent of 50?**

$\frac{30}{50}=\frac{3}{5}$

$\frac{3}{5}=0.6$

$0.6=60\%$ (Move the decimal point two places to the right to convert the decimal to a percent.)

**5) 20 is what percent of 25?**

**$\frac{20}{25}=\frac{4}{5}$**

**$\frac{4}{5}=0.8$**

0.8 = 80% (Move the decimal point two places to the right to convert the decimal to a percent.)

**6) 50 is what percent of 100?**

**$\frac{50}{100}=\frac{1}{2}$**

**$\frac{1}{2}=0.5$**

$0.5=50\%$ (Move the decimal point two places to the right to convert the decimal to a percent.)

**7) An airline ticket on sale was $400. The original price of the ticket was $ 500. Find the discount.**

- Hint: This is a problem of a percent decrease.

$\mathrm{Change}=\mathrm{new}\mathrm{value}-\mathrm{old}\mathrm{value}$

$\mathrm{Change}=400-500$

$\mathrm{Change}=-100$

$\mathrm{Percent}\mathrm{change}=\frac{\mathrm{change}\mathrm{in}\mathrm{value}}{\mathrm{initial}\mathrm{value}}$

$\mathrm{Percent}\mathrm{change}=\frac{-100}{500}$

$\mathrm{Percent}\mathrm{change}=\frac{-1}{5}$

$\mathrm{Percent}\mathrm{change}=-0.2$

(move the decimal two places to the right and add the % sign)

$\mathrm{Percent}\mathrm{change}=-20\%$

**8) Movie ticket prices increased from $8 to $10 per ticket. What is the percent change?**

- Hint: This is a problem of a percent decrease.

$\mathrm{Change}\mathrm{in}\mathrm{value}=\mathrm{new}\mathrm{value}-\mathrm{old}\mathrm{value}$

$\mathrm{Change}\mathrm{in}\mathrm{value}=10-8$

$\mathrm{Change}=2$

$\mathrm{Percent}\mathrm{change}=\frac{\mathrm{change}\mathrm{in}\mathrm{value}}{\mathrm{Initial}\mathrm{value}}$

$\mathrm{Percent}\mathrm{change}=\frac{2}{8}$

$\mathrm{Percent}\mathrm{Change}=\frac{1}{4}$

$\mathrm{Percent}\mathrm{Change}=0.25$

(move the decimal two places to the right and add the % sign)

$\mathrm{Percent}\mathrm{change}=25\%$

## Cheat Sheet

- The change in percent change can be an increase or decrease.
- Percent Change = $\frac{\mathrm{Change}}{\mathrm{Starting}/\mathrm{Original}\mathrm{amount}}$

## Blunder Areas

- Pay close attention to what is being asked. Then, read the information provided twice before deciding what rules to apply.
- Students often get the percent increase or decreased answer wrong.

- Rishi Jethwa
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