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Chapter 6  Percents

6-3 Solving Percent Problems

There are three basic types of percent problems. Two of them are used quite often in the "real" world. The third is sort of weird, and is mainl used on math tests. Here are examples of the two main types of percent problems:

  1. How much is 12% of 25?
  2. 55 is what percent of 70?

And the "weird" one looks like this:

  1. 16 is 20% of what number?

This lesson helps you understand how to work all three types of percent problems.

6-3.1    Finding the Part

Finding the part is the most common type of percent problem. You are given the total amount of something, and asked to determine some percentage of that total. For example:

What is 35% of 20?

Procedure

To find the part of a percentage problem, multiply the rate times the base amount.

Part = Percent x Whole

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Example

What is 30% of 50?

Problem   30% of 50 =   ? 

Express the percent as a decimal value and multiply it by the base amount.

 0.30 x 50 = 15  
Solution   30% of 50 = 15

 

Exercises

Click the  ?  symbol to see the correct answer.

1.    10% of 150 =  ?  2.  22% of 100 =  ? 
3.    98% of 160 =  ?  4.  75% of 2200 =  ? 
5.    12 1/2% of 60 =  ?   

6-3.2    Finding the Rate

Finding the percent is the secon-most common type of percent problem. You are given the total amount and the partial amount, and asked to determine the percentage. For example:

What percent is 7 out of 20?

Procedure

To find the percent:

  1. Divide the part by the whole
  2. Multiply by 100.
  3. Add the % sign.

Percent =

Part x 100
Whole

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Example

Determine the percent of 81 out of 180

Problem   81 out of 180  =   ?  %

Divide the part by the whole.

 81/180 = 0.45  

Multiply by 100 and add the % sign.

 0.45 x 100 = 45%  
Solution   81 out of 180  = 45%

 

Exercises

Click the  ?  symbol to see the correct answer.

1.   22 is  ? % of 50 2.   50 is  ? % of 100
3.   50 is  ? % of 50 4.   12 is  ? % of 120
5.   1.25 is  ? % of 250  

6-3.3    Finding the Whole Amount

Procedure

To find the whole amount of a percent problem:

  1. Convert the percent to a decimal.
  2. Divide the part by the decimal percent.

Whole =

Part
Decimal Percent

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Example

45 is 5% of _____.

Problem   45 is 5% of    ? 

Convert the percent to a decimal.

 5% = 0.05  

Divide the part by the decimal percent.

 45 ÷ 0.05 = 900  
Solution   45 is 5% of 900

Exercises

Click the  ?  symbol to see the correct answer.

1.    49 is 50% of   ?  2.  15 is 30% of    ? 
3.   240 is 32% of   ?  4.    23.6 is 40% of    ? 
5.    276 is 69& of  ?   

Author: David L. Heiserman
Publisher: SweetHaven Publishing Services

Copyright © 2006, David L. Heiserman
All Rights Reserved