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

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

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Interpret expression correctly: First, we need to interpret the expression correctly. The expression is $1 + \frac{1}{2} \times \frac{1}{5}$ . According to the order of operations (PEMDAS/BODMAS), we must perform multiplication before addition.
Perform multiplication: Now, let's perform the multiplication part of the expression: $\frac{1}{2} \times \frac{1}{5}$ . To multiply fractions, we multiply the numerators together and the denominators together. $\newline$ $(1 \times 1) / (2 \times 5) = \frac{1}{10}$
Add result to $1$ : Next, we add the result of the multiplication to $1$ . The expression now is $1 + \frac{1}{10}$ . $\newline$ To add a whole number to a fraction, we can think of the whole number as a fraction with the same denominator as the fraction we are adding to it. So, $1$ is the same as $\frac{10}{10}$ . $\newline$ $\frac{10}{10} + \frac{1}{10} = \frac{(10 + 1)}{10} = \frac{11}{10}$
Convert to mixed number: The fraction $\frac{11}{10}$ is an improper fraction, which can also be written as a mixed number. To convert it to a mixed number, we divide the numerator by the denominator. $\newline$ $11 \div 10 = 1$ with a remainder of $1$ . So, the mixed number is $1 \frac{1}{10}$ .