Evaluate the expression. $\newline$ $\frac{1}{2} \div \frac{4}{5} - \frac{1}{4}$ $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ ______

Full solution

Q. Evaluate the expression.

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\frac{1}{2} \div \frac{4}{5} - \frac{1}{4}

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Write your answer as a fraction or as a whole or mixed number.

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______

Divide fractions: First, we need to divide $\frac{1}{2}$ by $\frac{4}{5}$ . To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. $\newline$ $\frac{1}{2} \div \frac{4}{5} = \frac{1}{2} \times \frac{5}{4}$
Perform multiplication: Now, we perform the multiplication. $\newline$ $(\frac{1}{2}) \times (\frac{5}{4}) = (\frac{1\times5}{2\times4}) = \frac{5}{8}$
Subtract fractions: Next, we need to subtract $\frac{1}{4}$ from the result of the division. $\newline$ $\frac{5}{8} - \frac{1}{4}$
Find common denominator: To subtract fractions, they must have a common denominator. The least common denominator (LCD) for $8$ and $4$ is $8$ . $\newline$ $\frac{1}{4}$ can be converted to $\frac{2}{8}$ to have the same denominator as $\frac{5}{8}$ .
Perform subtraction: Now, subtract the fractions with the common denominator. $\frac{5}{8} - \frac{2}{8} = \left(\frac{5 - 2}{8}\right) = \frac{3}{8}$