Percent

Percents, Decimals, and Fractions

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

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%) = 45 = 36% = ? 10.5% = ?

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% = ? 23.5% = ? 100% = 100(0.01) = 1.00 or 1 100% = 1 Remember this fact! 150% = ? 200% = ?

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 = ? % 1.2 = ? % 0.072 = ? % 1.025 = ? %

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

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.

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).

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

Solving Basic Percent Problems with Equations

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

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

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

Solving Basic Percent Problems with Equations. Example 1. What number is 36% of 120? Answer: 43.2 Example 2. 14 is what percent of 25? Answer: 56% Example 3. 20% of what number is 40? Answer: 225

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.

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)

Solving Basic Percent Problems with Proportions

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

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

Percent Proportion always 100% or amount percent base

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.

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

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

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

Solving Proportions for the Percent What percent of 40 is 8? percent base amount amount percent base

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