1. Percent

2. Percents, Decimals, and Fractions

3. Understanding Percent
The word percent comes from the Latin phrase per centum, which means “per 100.”
Percent means per one hundred.
The “%” symbol is used to denote percent.
1% = = 0.01
Remember this fact!
53% = = 0.53

4. Writing a Percent as a Fraction
1% = = 0.01
Replace the percent symbol with its fraction equivalent, ; then multiply.
Simplify the fraction, if possible.
45% = 45(1%) = =
36% = ? % = ?

5. Chapter 1 / Whole Numbers and Introduction to Algebra
Writing a Percent as a Decimal
1% = = 0.01
Replace the percent symbol with its decimal equivalent, 0.01; then multiply.
45% = 45(1%) = 45(0.01) = 0.45
25% = ? 5% = ? % = ?
100% = 100(0.01) = 1.00 or 1
100% = 1
Remember this fact!
150% = ? % = ?

6. Writing a Decimal As a Percent
1 =100%
Multiply by 1 in the form of 100%.
0.65 = 0.65(1) = 0.65(100%) = 65.% or 65%
0.4 = ? % = ? %
0.072 = ? % = ? %

7. Writing a Fraction as a Percent
1 =100%
Multiply by 1 in the form of 100%.

8. Helpful Hint
100% = 1
Recall that when we multiply a number by 1, we are not changing the value of that number.
Therefore, when we multiply a number by 100%, we are not changing its value but rather writing the number as an equivalent percent.

9. Summary of Converting Percents, Decimals, and Fractions
To write a percent as a decimal, replace the % symbol with its decimal equivalent, 0.01; then multiply (Drop the symbol and move the decimal dot 2 places to the left.)
To write a percent as a fraction, replace the % symbol with its fraction equivalent, ; then multiply.
To write a decimal or fraction as a percent, multiply by 100% (which is 1).

10. Writing a Fraction as a Decimal and Percent.
Write the equivalent decimal and percent forms for Round to thousandths.

11. Solving Basic Percent Problems with Equations

12. Key Words of means multiplication () is means equals (=)
what (or some equivalent) means the unknown number
Let x stand for the unknown number.

13. Helpful Hint
Remember that an equation is simply a mathematical statement that contains an equal sign (=).
6 = 18x
equal sign

14. Solving Basic Percent Problems with Equations
20% of is 10
20% • 50 = 10
percent
base
amount
Percent Equation
percent • base = amount

15. Solving Basic Percent Problems with Equations.
Example What number is 36% of 120?
Answer: 43.2
Example is what percent of 25?
Answer: 56%
Example % of what number is 40?
Answer: 225

16. Helpful Hint
When solving a percent equation, write the percent as a decimal or fraction.
If your unknown in the percent equation is percent, don’t forget to convert your answer to a percent.

17. a percent greater than 100%
Helpful Hint
Use the following to see if your answers are reasonable.
100% of a number = the number
a percent greater than 100% =
a number larger than the original number (base)
a percent less than 100% =
a number less than the original number (base)

18. Solving Basic Percent Problems with Proportions

19. Writing Basic Percent Problems as Proportions
To understand the proportion method, recall that 30% means the
ratio of 30 to 100, or
30% = =

20. Writing Basic Percent Problems as Proportions
Since the ratio is equal to the
ratio , we have the proportion ,
called the percent proportion.

21. Percent Proportion
always 100% or
amount
percent
base

22. Helpful Hints
When we translate percent problems to proportions,
the percent can be identified by looking for the symbol % or the word percent.
The base usually follows the word of.
The amount is the part compared to the whole.

23. Helpful Hint Part of Proportion How It’s Identified Percent
% or percent
Base
Appears after of
Amount
Part compared to whole

24. Solving Percent Proportions for the Amount
What number is 20% of 8?
amount
percent
base
amount
percent
base

25. Solving Percent Proportions for the Base
20 is 40% of what number?
amount
percent
base
amount
percent
base

26. Solving Proportions for the Percent
What percent of is 8?
percent
base
amount
amount
percent
base

27. Solving Basic Percent Proportions for the Amount
What number is 20% of 8?
amount
percent
base
amount
percent
base