How can I convert a percentage into a fraction?

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Converting a percentage into a fraction is a straightforward process. Here’s how to do it step by step:

  1. Understand the Definition: A percentage represents a part of a whole out of 100. For example, 25% means 25 out of 100.
  2. Write the Percentage as a Fraction: To convert the percentage to a fraction, you can start by writing it over 100. For example, to convert 40%, write it as:
    3. 40% = 40/100
  3. Simplify the Fraction: If the fraction can be simplified, you simplify it by finding the greatest common divisor (GCD) of the numerator and denominator. In the case of 40/100:
    4. GCD of 40 and 100 is 20.
    Dividing both by 20 gives:
    40 ÷ 20 = 2
    100 ÷ 20 = 5
    So, 40/100 simplifies to 2/5.
  4. Final Fraction: Therefore, 40% as a fraction is 2/5.

Example: Let’s take another example, say 75%. To convert 75% to a fraction:

  1. Write it as 75/100.
  2. The GCD of 75 and 100 is 25.
  3. Dividing by 25, you get:
    4. 75 ÷ 25 = 3
    100 ÷ 25 = 4
    Hence, 75/100 simplifies to 3/4.

In summary, to convert a percentage to a fraction, write it over 100 and simplify if possible. This not only makes the fraction easier to understand but also allows for easier calculations in mathematical operations.

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