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Convert percents to fractions

A percent represents a ratio to 100, so a whole-number percent can be expressed as the fraction p/100p/100, then written in an equivalent simplest form by dividing numerator and denominator by a common factor. This conversion preserves the quantity and supports comparison, computation, and proportional reasoning with fractions; the scope is limited to familiar percents from 0% through 100%, not repeating, fractional, or percentages greater than 100%.

Detailed Explanation: Convert percents to fractions

A percent means “out of 100.” To convert a whole-number percent to a fraction:

  1. Write the percent number as the numerator.
  2. Write (100)(100) as the denominator.
  3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor.

Example: Convert (45%)(45\%) to a fraction.

Write (45%)(45\%) as a fraction out of (100)(100):

45%=4510045\%=\frac{45}{100}

Both (45)(45) and (100)(100) can be divided by 55:

45÷5100÷5=920\frac{45\div 5}{100\div 5}=\frac{9}{20}

So,

45%=920\boxed{45\%=\frac{9}{20}}

The fraction 920\frac{9}{20} is in simplest form because 99 and (20)(20) have no common factor greater than 11.

Learn by doing: Convert percents to fractions

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    Percents to Fractions - Standard

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