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$Evaluate the expression shown below and write your answer as a fraction in simplest form. (1)/(7)+(1)/(2) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $\frac{1}{7}+\frac{1}{2}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Evaluate the expression shown below and write your answer as a fraction in simplest form.

\newline

\frac{1}{7}+\frac{1}{2}

\newline

Answer:

Identify LCD: Identify the Least Common Denominator (LCD) $\newline$ To add fractions, we need a common denominator. The denominators here are $7$ and $2$ . The least common denominator (LCD) is the smallest number that both denominators can divide into without a remainder. In this case, the LCD is $14$ because it is the smallest number that both $7$ and $2$ can divide into evenly.
Convert to Same Denominator: Convert the fractions to have the same denominator $\newline$ We will convert each fraction to an equivalent fraction with the denominator of $14$ . $\newline$ For $\frac{1}{7}$ , we multiply the numerator and the denominator by $2$ to get $\frac{2}{14}$ . $\newline$ For $\frac{1}{2}$ , we multiply the numerator and the denominator by $7$ to get $\frac{7}{14}$ .
Add Fractions: Add the fractions $\newline$ Now that both fractions have the same denominator, we can add them together. $\newline$ $\frac{2}{14} + \frac{7}{14} = \frac{(2 + 7)}{14} = \frac{9}{14}$
Simplify Fraction: Simplify the fraction (if necessary) $\newline$ The fraction $\frac{9}{14}$ is already in its simplest form because $9$ and $14$ have no common factors other than $1$ .

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