Understanding the Percent Proportion
Pre-algebra students in OpenStax Prealgebra 2E learn to solve any percent problem using the percent proportion: amount/base = percent/100. To find 45% of 80, set up n/80 = 45/100, cross-multiply to get 100n = 3,600, and solve for n = 36. To find the base when 6.5% of it equals $1.56, set up 1.56/n = 6.5/100, cross-multiply to get 156 = 6.5n, so n = 24. This single formula handles all three types of percent problems: finding the amount, the base, or the percent.
Key Concepts
Property A percent proportion is an equation where a percent is equal to an equivalent ratio. The amount is to the base as the percent is to 100. $\frac{\text{amount}}{\text{base}} = \frac{\text{percent}}{100}$ We can restate this as: The amount out of the base is the same as the percent out of one hundred.
Examples To solve "What number is 45% of 80?", set up the proportion $\frac{n}{80} = \frac{45}{100}$. Cross multiply to get $100n = 3600$, so $n=36$. To solve "6.5% of what number is 1.56 dollars?", set up $\frac{1.56}{n} = \frac{6.5}{100}$. Cross multiply to get $156 = 6.5n$, so $n=24$. To solve "What percent of 72 is 9?", set up $\frac{9}{72} = \frac{p}{100}$. Cross multiply to get $900 = 72p$, so $p=12.5$. The answer is 12.5%.
Explanation This special proportion is a powerful tool for any percent problem. It turns sentences like "What is 25% of 80?" into an equation you can easily solve by finding the missing piece. Just fill in what you know!
Common Questions
What is the percent proportion formula?
amount/base = percent/100. The amount is the part, the base is the whole, and the percent is out of 100.
How do you find 45% of 80?
Set up n/80 = 45/100. Cross-multiply: 100n = 3,600, so n = 36.
How do you find a base when you know the percent and amount?
Place the amount over n: amount/n = percent/100. Cross-multiply and solve for n.
How do you find the percent when you know the amount and base?
Set up amount/base = n/100. Cross-multiply: n = (amount/base) × 100.
What does cross-multiplying mean in a proportion?
Cross-multiplying means multiplying the numerator of one fraction by the denominator of the other and setting the two products equal.