Verified Answer :

  • Identify that dividing by a fraction is equivalent to multiplying by its reciprocal.
  • Reciprocate \(\frac{1}{2}\) to get 2.
  • Multiply \(\frac{4}{5}\) by 2 to get \(\frac{8}{5}\).
  • Final result: \(\boxed{\frac{8}{5}}\).

Explanation

  1. Understanding the Problem and Identifying the Method

We are given the expression \(\frac{4}{5} \div \frac{1}{2}\). The goal is to compute the value of this division. To divide by a fraction, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). In our case, the second fraction is \(\frac{1}{2}\), so its reciprocal is \(\frac{2}{1}\), which simplifies to 2.

  1. Performing the Calculation

We convert the division problem into a multiplication problem:
\[\frac{4}{5} \div \frac{1}{2} = \frac{4}{5} \times \frac{2}{1}.\]
Now, we perform the multiplication:
\[\frac{4}{5} \times \frac{2}{1} = \frac{4 \times 2}{5 \times 1} = \frac{8}{5}.\]
The result of the multiplication is \(\frac{8}{5}\), which can also be written as a decimal by dividing 8 by 5, giving 1.6. We will express the final answer as the fraction \(\frac{8}{5}\).

Examples

Imagine you have \(\frac{4}{5}\) of a pizza, and you want to share it among friends such that each person receives a \(\frac{1}{2}\) size portion. By dividing the total amount of pizza by the size of each portion, \(\frac{4}{5} \div \frac{1}{2} = \frac{8}{5}\), you discover that you would need 1.6 portions, meaning you have enough pizza for one full portion and more. This method of dividing by a fraction is essential for understanding how to distribute resources when the units are fractional parts of a whole.

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