A percent is a ratio that compares a quantity to 100, so \(35\%\) means 35 out of every 100. Percents convert to fractions and decimals: \(35\% = \frac{35}{100} = 0.35\). To find a percent of a quantity, multiply by the decimal; to find the whole, divide the part by the percent as a decimal.
Key facts:
- A percent is a rate per 100: \(35\% = \frac{35}{100} = 0.35\).
- To find a percent of a number, multiply the number by the percent written as a decimal.
- To find the whole, divide the part by the percent written as a decimal.
- To find what percent a part is, divide the part by the whole and multiply by 100.
- A percent bar model shows \(100\%\) split into equal parts.
What is a percent?
A percent is a ratio that compares a quantity to 100. The word comes from “per hundred.” If 35 out of every 100 students at a school ride the bus, then \(35\%\) of the students ride the bus.
\(35\% = \frac{35}{100} = 0.35\). To change a percent to a decimal, divide by 100 (move the decimal point two places left). To change a decimal to a percent, multiply by 100.
How do you convert between percents, fractions, and decimals?
| Percent | Fraction | Decimal |
|---|---|---|
| \(25\%\) | \(\frac{1}{4}\) | 0.25 |
| \(60\%\) | \(\frac{3}{5}\) | 0.6 |
| \(75\%\) | \(\frac{3}{4}\) | 0.75 |
| \(8\%\) | \(\frac{2}{25}\) | 0.08 |
To turn a fraction into a percent, write an equivalent fraction with denominator 100, or divide the numerator by the denominator and multiply by 100. For \(\frac{3}{8}\): \(3 : 8 = 0.375 = 37.5\%\).
How do you find a percent of a quantity?
Use the rate “per 100.” Since \(25\%\) means 25 for every 100, the percent of a number is the same as that fraction of the number.
- Write the percent as a decimal or fraction.
- Multiply it by the whole.
- Label the answer with the correct units.
Example. Find \(25\%\) of 80. Compute \(0.25 \times 80 = 20\). A quick check: \(25\%\) is one fourth, and \(80 : 4 = 20\).
How do you find the whole when you know a part and the percent?
Divide the part by the percent written as a decimal. Suppose \(30\%\) of a number is 21. Then \(21 : 0.30 = 70\). Check: \(0.30 \times 70 = 21\). On a bar model, \(30\%\) is 3 of the 10 equal parts, so one part (\(10\%\)) is \(21 : 3 = 7\), and the whole (10 parts) is \(7 \times 10 = 70\).
To find what percent one number is of another, divide the part by the whole: 18 out of 24 is \(18 : 24 = 0.75 = 75\%\).
Percents: frequently asked questions
What does percent mean?
Percent means per 100. A score of \(80\%\) means 80 out of every 100, which is the same as the fraction \(\frac{80}{100}\) or the decimal 0.80.
How do you change a percent to a decimal?
Divide the percent by 100, which moves the decimal point two places to the left. For example, \(6\%\) becomes 0.06 and \(125\%\) becomes 1.25.
How do you find a percent of a number?
Convert the percent to a decimal and multiply. To find \(15\%\) of 60, compute 0.15 times 60, which equals 9.
How do you find the whole if you know a part and the percent?
Divide the part by the percent written as a decimal. If \(40\%\) of a class is 18 students, the class has 18 divided by 0.40, or 45 students.
Can a percent be greater than \(100\%\)?
Yes. A percent greater than \(100\%\) means more than the whole. For example, \(150\%\) of 40 is 60, because 1.5 times 40 equals 60.
See every chapter on the Grade 6 math page.