Evaluate the expression. $\newline$ $1 + \frac{1}{2} \times \frac{3}{4}$ $\newline$ Write your answer as a fraction or as a whole or mixed number. $\newline$ ______

Full solution

Q. Evaluate the expression.

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1 + \frac{1}{2} \times \frac{3}{4}

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

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Identify Order of Operations: Identify the order of operations for the given expression. $\newline$ According to the order of operations (PEMDAS/BODMAS), we should perform multiplication before addition. $\newline$ Expression: $1 + \left(\frac{1}{2} * \frac{3}{4}\right)$
Perform Multiplication: Perform the multiplication part of the expression. $\newline$ Calculate $\frac{1}{2} \times \frac{3}{4}$ . $\newline$ $(\frac{1}{2}) \times (\frac{3}{4}) = (\frac{1\times3}{2\times4}) = \frac{3}{8}$
Add Result to Whole Number: Add the result from Step $2$ to the whole number in the expression. $\newline$ Add $1$ to the fraction $\frac{3}{8}$ . $\newline$ $1 + \frac{3}{8} = \frac{8}{8} + \frac{3}{8} = \frac{(8+3)}{8} = \frac{11}{8}$
Convert to Mixed Number: Convert the improper fraction to a mixed number if necessary. $\newline$ Since $\frac{11}{8}$ is an improper fraction, we can convert it to a mixed number. $\newline$ $\frac{11}{8} = 1 \frac{3}{8}$ (since $8$ goes into $11$ once with a remainder of $3$ )