Finding a Percent of a Number

A percent is a ratio that compares a number to 100. The word percent literally means "per 100." In math, when we need to find a percent of a number, we are calculating a specific part of a whole.

Calculating a Percent of a Number

To find the percent of a number, you can convert the percent into a decimal (or a fraction) and multiply it by the number.

Example: What is $35\%$ of $240$?

1. Convert $35\%$ to a decimal by moving the decimal point two places to the left: $35\% = 0.35$.
2. Multiply the decimal by the number: $0.35 \times 240 = 84$

So, $35\%$ of $240$ is $84$.

Finding the Percent (Given the Part and Whole)

Sometimes you know the part and the whole, but you need to find the percentage. To do this, divide the part by the whole, then convert the resulting decimal to a percent.

Example: $15$ is what percent of $60$?

1. Set up the division: $\frac{15}{60}$.
2. Divide to get a decimal: $15 \div 60 = 0.25$.
3. Convert the decimal to a percent by moving the decimal point two places to the right: $0.25 = 25\%$.

So, $15$ is $25\%$ of $60$.

Finding the Whole (Given the Part and Percent)

If you know a part and what percent it represents, you can find the original whole number by dividing the part by the percent (as a decimal).

Example: $18$ is $60\%$ of what number?

1. Convert $60\%$ to a decimal: $0.60$.
2. Divide the part by the decimal: $18 \div 0.60 = 30$

So, $18$ is $60\%$ of $30$.

Real-World Applications: Discounts, Tax, and Tips

Percents are used every day when shopping or eating at restaurants.

Example: A shirt costs $40$ with $25\%$ off. What is the sale price?

1. Find the discount amount by calculating $25\%$ of $40$: $0.25 \times 40 = 10$
2. Subtract the discount from the original price: $40 - 10 = 30$

The sale price of the shirt is \30$.