Evaluate the expression. $\newline$ $\frac{3}{4} \times \frac{2}{5} + \frac{1}{2}$ $\newline$ 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}{4} \times \frac{2}{5} + \frac{1}{2}

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

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______

Multiply Fractions: First, we need to multiply the fractions $\frac{3}{4}$ and $\frac{2}{5}$ . To multiply fractions, we multiply the numerators together and the denominators together. So, $(\frac{3}{4}) \times (\frac{2}{5}) = \frac{3\times2}{4\times5} = \frac{6}{20}.$
Simplify Result: Next, we simplify the fraction $\frac{6}{20}$ if possible. $\newline$ $6$ and $20$ have a common factor of $2$ , so we can divide both the numerator and the denominator by $2$ . $\newline$ $\frac{6}{20} = \left(\frac{6\div2}{20\div2}\right) = \frac{3}{10}.$
Add Fractions: Now, we need to add the simplified fraction $\frac{3}{10}$ to $\frac{1}{2}$ . To add fractions, they must have a common denominator. The least common denominator (LCD) for $10$ and $2$ is $10$ .
Convert to Common Denominator: We convert $\frac{1}{2}$ to a fraction with a denominator of $10$ . $\frac{1}{2}$ is equivalent to $\frac{5}{10}$ because $1\times(\frac{10}{2}) = 5$ and $2\times(\frac{10}{2}) = 10$ . So, $\frac{1}{2} = \frac{5}{10}.$
Add Fractions with Common Denominator: Finally, we add the two fractions with the common denominator. $\newline$ $\frac{3}{10} + \frac{5}{10} = \frac{(3+5)}{10} = \frac{8}{10}$ .
Check for Simplification: We check if the fraction $\frac{8}{10}$ can be simplified. $\newline$ $8$ and $10$ have a common factor of $2$ , so we can divide both the numerator and the denominator by $2$ . $\newline$ $\frac{8}{10} = \frac{(8\div2)}{(10\div2)} = \frac{4}{5}.$