Evaluate the expression. $\newline$ $\frac{3}{5} + \frac{1}{5} \times \frac{1}{2}$ $\newline$ 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{3}{5} + \frac{1}{5} \times \frac{1}{2}

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

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______

Calculate Half of $\frac{1}{5}$ : First, we need to calculate half of $\frac{1}{5}$ . To find half of a fraction, we multiply the fraction by $\frac{1}{2}$ . So, we calculate $\frac{1}{5} \times \frac{1}{2}$ . $\frac{1}{5} \times \frac{1}{2} = \frac{1 \times 1}{5 \times 2} = \frac{1}{10}$
Add Fractions with Common Denominator: Now, we have the two quantities we need to add: $\frac{3}{5}$ and $\frac{1}{10}$ . To add fractions, they must have a common denominator. The common denominator for $5$ and $10$ is $10$ . We need to convert $\frac{3}{5}$ to a fraction with a denominator of $10$ . $\frac{3}{5} = \left(\frac{3 \times 2}{5 \times 2}\right) = \frac{6}{10}$
Combine Fractions: Now we can add the two fractions since they have the same denominator. $\newline$ $\frac{6}{10} + \frac{1}{10} = \frac{(6 + 1)}{10} = \frac{7}{10}$