Division and Percentages:
Convert between fractions and percentages
Fractions can also be represented as percentages and percentages can be represented as fractions.
Example: \(\frac{1}{5} = 20\)%
This lesson teaches how to convert a fraction to a percentage and a percentage to a fraction.
Understanding following resource center lessons is important to understanding how to convert between fractions and percentages. You may want to review these resource center lessons to help you with this lesson.
- Place value after the decimal point
- Division
- Multiplication and division by powers of 10
- Converting between decimals and percentages
- Simplifying fractions
Converting from a fraction to a percentage
- Divide the numerator by the denominator to get a decimal number
- Example: \(\frac{3}{4}\)= 3 divided by 4 = 0.75
- Multiply by 100. This moves the decimal place to the right two places.
- Example: 0.75 x 100 = 75
- Put a % symbol at the end
- Example: 75 → 75%
- Final Answer: \(\frac{3}{4}\)= 75%
Converting from a percentage to a fraction
- Remove the % symbol from the number and divide by 100.
- Example: 40% → \(\frac{40}{100}\)
- Simplify the fraction
- Example: 40/100 = \(\frac{40}{100}\) = \(\frac{20\cdot2}{20\cdot5}\) = \(\frac{2}{5}\)
- Final answer: 40% = \(\frac{2}{5}\)
Additional Information
- Khan Academy: Converting percents to decimals & fractions example (03:31 mins)
Practice Problems
- Convert 22% to a fraction. Simplify the fraction as much as possible.
- Convert 5% to a fraction. Simplify the fraction as much as possible.
- Convert 250% to a fraction. Simplify as much as possible. Convert to a mixed fraction if needed.
- Convert \(\frac{3}{5}\) to a percentage.
- Convert \(\frac{5}{8}\) to a percentage.
- Convert \(\frac{15}{8}\) to a percentage.