Verified Answer :

  • Multiply the numerators \(3\) and \(2\) to obtain \(6\).
  • Multiply the denominators \(5\) and \(5\) to obtain \(25\).
  • Combine the results into the final fraction \(\frac{6}{25}\).
  • The result of the multiplication is \(\boxed{\frac{6}{25}}\).

Explanation

  1. Understanding the Operation

To calculate the product of the two fractions \(\frac{3}{5}\) and \(\frac{2}{5}\), we follow the standard rule for multiplying fractions. The rule states that when multiplying two fractions, you multiply the numerators together to get the new numerator and the denominators together to get the new denominator: \[\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}\]

  1. Performing the Multiplication

Now we apply the rule to our specific fractions:

  • The numerators are \(3\) and \(2\), so the product of the numerators is \(3 \times 2 = 6\).
  • The denominators are \(5\) and \(5\), so the product of the denominators is \(5 \times 5 = 25\).

Combining these, we get \[\frac{3}{5} \times \frac{2}{5} = \frac{3 \times 2}{5 \times 5} = \frac{6}{25}\]

  1. Final Result

The fraction \(\frac{6}{25}\) is already in its simplest form, as there are no common factors between \(6\) and \(25\) other than \(1\). Thus, the final product is \(\boxed{\frac{6}{25}}\).

Examples

Fraction multiplication is widely used in cooking and baking when you need to scale recipes. For example, if a recipe calls for \(\frac{3}{5}\) of a cup of flour, and you decide to make only \(\frac{2}{5}\) of the total batch, you would need \(\frac{3}{5} \times \frac{2}{5} = \frac{6}{25}\) of a cup of flour for your smaller batch. Mastering this operation allows you to adjust ingredients and quantities accurately in various everyday situations.

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