7th Grade - Application of Percentage

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.