Lesson 3: Represent and Use the Percent Equation

Property

In percent word problems, identify three key components:

• Part: The portion or amount being compared
• Whole: The total amount (often follows the word "of")
• Percent: The rate per 100 (includes % symbol or words like "percent")

Examples

Property

To calculate a percent of a number:

1. Change the percent to a decimal fraction.
2. Multiply the number by the decimal fraction.

To change a percent to a decimal fraction, divide the percent by 100, or move the decimal point two places to the left.

Examples

• To find 8% of 300, convert 8% to a decimal by moving the decimal point two places left: $8\% = 0.08$. Then multiply: $0.08 \times 300 = 24$.
• A phone costs 850 dollars and sales tax is 7.5%. Convert 7.5% to a decimal: $0.075$. The tax is $0.075 \times 850 = 63.75$ dollars.
• Calculate 150% of 60. First, change 150% to a decimal: $1.50$. Then, multiply: $1.50 \times 60 = 90$.

Explanation

To use a percent in a calculation, you must first convert it into a form your calculator understands, like a decimal. Moving the decimal point two places left is a quick shortcut for dividing by 100.

Property

To find what percent a part is of a whole:

1. Divide the part by the whole to get a decimal fraction:
   $$\frac{\text{part}}{\text{whole}}$$
2. Multiply the decimal fraction by 100 to convert it to a percent.

Examples

• You scored 18 points out of a total of 20 on a quiz. To find your percent score, divide the part by the whole: $18 \div 20 = 0.90$. Multiply by 100 to get the percent: $0.90 \times 100 = 90\%$.
• A recipe calls for 400 grams of flour, and you have used 80 grams. The percent used is $80 \div 400 = 0.20$. This is equivalent to $20\%$.
• If you saved 30 dollars on an item that originally cost 150 dollars, you saved $\frac{30}{150} = 0.2$. As a percent, this is $0.2 \times 100 = 20\%$.

Explanation

This process reverses the calculation. By dividing the smaller part by the total whole, you find the fraction it represents. Multiplying by 100 scales that fraction up to a percentage, making it easier to understand.