Lesson 7: Solving Percent Problems

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.

Property

To find the percent of a number (the part), convert the percent to a fraction and multiply it by the whole number.

Examples

• What is $25\%$ of $80$?

• Find $60\%$ of $50$.

• What is $150\%$ of $40$?

Explanation

This method helps you calculate the "part" when you know the "percent" and the "whole". First, you must convert the percentage into its equivalent fraction by placing it over 100 and simplifying if possible. Then, multiply this fraction by the whole number to find the answer. This is a direct application of the concept that "of" in mathematics often means multiplication.