Fractions can also be represented as percentages and percentages can be represented as fractions.

Example: \( {\dfrac{1}{5}} = 20 \) %

This lesson teaches how to convert a fraction to a percentage and a percentage to a fraction.

Understanding the following resource center lessons is important to know 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

Video Source (07:39 mins) | Transcript

Converting from a fraction to a percentage

1. Divide the numerator by the denominator to get a decimal number.
   • Example: \(\dfrac {3}{4} = 3\: \text{divided by}\: 4 = 0.75\)
2. Multiply by 100. This moves the decimal place to the right two places.
   • Example: \(0.75 \times 100 = 75\)
3. Put a % symbol at the end.
   • Example: \(75 → 75\%\)
   • Final Answer: \(\dfrac {3}{4} = 75\%\)

Converting from a percentage to a fraction

1. Remove the % symbol from the number and divide by 100.
   • Example: \(40\% → \dfrac {40}{100}\)
2. Simplify the fraction.
   • Example: \(\displaystyle 40/100 =\frac {40}{100}=\frac {20⋅2} {20⋅5}= \frac {2}{5}\)
3. Final answer: \(40\% = \dfrac {2}{5}\)

Additional Information

• Khan Academy: Converting percents to decimals & fractions example (03:31 mins| Transcript)

Practice Problems

1. Convert \(22\%\) to a fraction. Simplify the fraction as much as possible. (
   Solution

   x

   Solution:
   \(\displaystyle \frac{22}{100}=\frac{11}{50}\)
   )
2. Convert \(5\%\) to a fraction. Simplify the fraction as much as possible. (
   Solution

   x

   Solution:
   \(\dfrac{1}{20}\)
   Details:
   \(\dfrac{5}{100}\)
   
   Simplify the fraction as much as possible.
   
   \(\displaystyle \frac{5}{100}=\frac{5\cdot1}{5\cdot20}=\frac{1}{20}\)
   )
3. Convert \(250\%\) to a fraction. Simplify as much as possible. Convert to a mixed fraction if needed. (
   Solution

   x

   Solution:
   \(\displaystyle \frac{250}{100}=\frac{5\cdot50}{2\cdot50}=\frac{5}{2}=2\frac{1}{2}\)
   )
4. Convert \(\dfrac{3}{5}\) to a percentage. (
   Solution

   x

   Solution:
   \(60\%\)
   Details:
   \(\displaystyle \frac{3}{5} = 0.6\)
   \(0.6 \times 100\) with a % symbol = \(60\%\)
   )
5. Convert \(\dfrac{5}{8}\) to a percentage. (
   Solution

   x

   Solution:
   \(62.5\%\)
   Details:
   \(\displaystyle \frac{5}{8} = 0.625\)
   \(0.625 \times 100\) with a % symbol = \(62.5\%\)
   )
6. Convert \(\dfrac{15}{8}\) to a percentage. (
   Solution

   x

   Solution:
   \(187.5\%\)
   Details:
   \(\displaystyle \frac{15}{8} = 1.875\)
   \(1.875 \times 100\) with a % symbol = \(187.5%\)
   )

Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.
3. Contact your Instructor.
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