This document defines percents and discusses how to convert between fractions, decimals, and percents. It provides examples for expressing decimals as percents by moving the decimal point two places right, converting fractions to percents by first expressing them as decimals, and converting percents to fractions by moving the decimal point two places left. It also introduces the proportion formula used to solve percent problems where B=base, P=percentage, and R=rate.

1. Percents

2. PERCENTS
• Indicates number of hundredths in a
whole
• A decimal fraction can be expressed
as a percent by moving the decimal
point two places to the right and
inserting the percent symbol

3. ESTIMATING
• Example: Express 0.0152 as a
percent:
• Move decimal point two places to right
0.0152 = 1.52
• Insert percent symbol
0.0152 = 1.52%

4. FRACTIONS TO PERCENTS
• To express a common fraction as a
percent:
• First, express the fraction as a decimal
by dividing the numerator by the
denominator
• Convert the answer to a percent by
moving the decimal point two places to
the right

5. FRACTIONS TO PERCENTS
• Example: Express as a percent:
• First convert the fraction to a
decimal by dividing
• Then change the decimal to a
percent
0.875 = 87.5%
7
8
0.875
8 7.000
64
60
56
40
40

6. PERCENTS TO FRACTIONS
• To express percent as decimal
fraction:
• Drop the percent symbol
• Move decimal point two places to
the left

7. PERCENTS TO FRACTIONS
• Example: Express as a
decimal and round the answer to 4
decimal places
• Convert the fraction to 0.76
• Drop the percent symbol and move the
decimal point 2 places to the left:
38.76% = 0.3876

8. PERCENTS TO FRACTIONS
• To express a percent as a common
fraction:
• First convert percent to a decimal
fraction
• Then express the decimal fraction as a
common fraction

9. PERCENTS TO FRACTIONS
• Example: Express 37.5% as a
common fraction
• Express 37.5% as a decimal
• Express 0.375 as a common fraction
37.5% 0.375


10. PERCENT TERMS DEFINED
• All simple percent problems have three
parts:
• Rate is the percent (%)
• Base represents whole or quantity equal to 100%
• Word “of” generally relates to the base
• Percentage is part or quantity of percent of the base
• Word “is” generally relates to the percentage

11. PERCENT TERMS DEFINED
• Example: Identify base, rate, and percentage
What percent of 48 is 12?
• Problem is asking for rate (percent)
• The number 48 represents whole and is
identified by word “of,” so it is the base
• The number 12 represents part and is identified
by word “is,” so it is the percentage

12. FINDING THE PERCENTAGE
• Proportion formula for all three types of
percentage problems:
• Where:
• B is the base
• P is the percentage or part of the base
• R is the rate or percent

100
P R
B

13. FINDING THE PERCENTAGE
• Example: What is 15% of 60?
• The base, B, is 60: the number of
which the rate is taken—the whole or a
quantity equal to 100%
• The problem is asking for the
percentage (part): the quantity of the
percent of the base

14. FINDING THE PERCENTAGE
• The proportion is:
• Use cross-products and division:
15
60 100
P

100 15 60
100 900
900
100
P
P
P
 



15. FINDING THE RATE
• Example: What percent of 12.87 is 9.62
rounded to 1 decimal place?
• The base, B, or whole quantity equal to
100% is 12.87
• The percentage, P, or quantity of the
percent of the base is 9.620
• The rate, R, is to be found

16. FINDING THE RATE
• The proportion is:
• Cross multiply:
• Divide:
9.620
12.87 100
R

9.620 100 12.87
962 12.87
R
R
 


17. FINDING THE BASE
• Example: 816 is 68% of what number?
• The rate, R, is 68%
• The percentage, P, is 816
• The base, B, is to be found
• The proportion is:
• Solve for B:
816 68
100
B


18. PRACTICAL PROBLEMS
• A 22-liter capacity radiator requires 6.5
liters of antifreeze to give protection to -
17ºC.
• What percent of the coolant is
antifreeze? Round the answer to the
nearest whole percent.

19. PRACTICAL PROBLEMS
• In this problem:
• The percentage (P) or the part is 6.5 liters
• The base (B) is 22 liters
• The rate (R) or percent is unknown
• Set up the formula and solve

20. PRACTICAL PROBLEMS
• Solve:
• The antifreeze is 30% of the coolant