Verified Answer :

  • Identify the rule for multiplying fractions: multiply the numerators to get the new numerator and the denominators to get the new denominator.
  • Calculate the numerator: \(4 \times 1 = 4\).
  • Calculate the denominator: \(5 \times 3 = 15\).
  • Conclude that the result is \(\frac{4}{15}\), which matches the second option provided. The final answer is \(\boxed{\frac{4}{15}}\).

Explanation

  1. Understanding the Rule of Multiplication for Fractions

To compute the product \(\frac{4}{5} \times \frac{1}{3}\), we need to follow the fundamental rule for multiplying fractions. When multiplying two fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), the product is obtained by multiplying the numerators together and the denominators together, resulting in \(\frac{a \times c}{b \times d}\). In this problem, we have \(a=4, b=5, c=1,\) and \(d=3\).

  1. Performing the Calculation

Using the rule stated above, we multiply the numerators and denominators separately:

  • Numerator: \(4 \times 1 = 4\)
  • Denominator: \(5 \times 3 = 15\)

Thus, the product is \(\frac{4}{15}\).

  1. Identifying the Correct Option

Comparing our result \(\frac{4}{15}\) with the given options:

  • \(\frac{1}{4}\)
  • \(\frac{4}{15}\)
  • \(\frac{5}{12}\)
  • \(\frac{6}{8}\)

Our calculated result is \(\frac{4}{15}\), which matches the second option. Therefore, the final result is \(\boxed{\frac{4}{15}}\).

Examples

Imagine you are baking cookies and the recipe requires \(\frac{4}{5}\) of a bag of sugar for a full batch. If you decide to make only \(\frac{1}{3}\) of the batch, you will need to calculate \(\frac{1}{3}\) of the \(\frac{4}{5}\) of a bag of sugar. This is a perfect example of using fraction multiplication: \(\frac{4}{5} \times \frac{1}{3} = \frac{4}{15}\) of a bag of sugar. Understanding how to multiply fractions allows you to easily scale recipes and adjust quantities in your daily life.

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