Verified Answer :

  • The percentage 60% is converted to the fraction \(\frac{60}{100}\).
  • Simplifying \(\frac{60}{100}\) by dividing by 20 yields \(\frac{3}{5}\).
  • The problem is rewritten as: Find \(\boxed{\frac{3}{5}}\) of 40.
  • Calculating \(\frac{3}{5} \times 40\) results in \(\boxed{24}\).

Explanation

  1. Converting Percent to Simplified Fraction

The problem asks us to rewrite "Find 60% of 40" as a fraction problem in simplest terms and then calculate the result. The percent symbol (%) represents a fraction with a denominator of 100. Thus, 60% can be written as \(\frac{60}{100}\). To simplify this fraction, we identify the greatest common divisor (GCD) of 60 and 100, which is 20. Dividing both the numerator and the denominator by 20 gives us \(\frac{60 \div 20}{100 \div 20} = \frac{3}{5}\). Thus, finding 60% of 40 is equivalent to finding \(\frac{3}{5}\) of 40.

  1. Calculating the Result

Now that we have the fraction in its simplest form, \(\frac{3}{5}\), we calculate \(\frac{3}{5}\) of 40. This is done by multiplying 40 by the fraction: \(\frac{3}{5} \times 40 = \frac{3 \times 40}{5} = \frac{120}{5} = 24\). Therefore, 60% of 40 is equal to 24.

Examples

Understanding how to convert percentages to fractions is essential in everyday life, such as calculating discounts during sales. For example, if an item costs \$40 and it is 60% off, you are essentially saving \(\frac{3}{5}\) of the original price, which is \(\$24\). Mastering this conversion helps you quickly determine the final price of items without relying on calculators.

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