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$Evaluate the expression shown below and write your answer as a fraction in simplest form. (3)/(7)+(3)/(8) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $\frac{3}{7}+\frac{3}{8}$ $\newline$ Answer:

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

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\frac{3}{7}+\frac{3}{8}

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Answer:

Identify LCD: Identify the Least Common Denominator (LCD) for the fractions $\frac{3}{7}$ and $\frac{3}{8}$ . The denominators are $7$ and $8$ . The LCD for $7$ and $8$ is $56$ because $56$ is the smallest number that both $7$ and $8$ can divide into without leaving a remainder.
Convert to Equivalent Fraction: Convert each fraction to an equivalent fraction with the LCD as the denominator. $\newline$ For $\frac{3}{7}$ , multiply both the numerator and the denominator by $8$ to get the equivalent fraction with a denominator of $56$ . $\newline$ $\left(\frac{3}{7}\right) \times \left(\frac{8}{8}\right) = \frac{24}{56}$ $\newline$ For $\frac{3}{8}$ , multiply both the numerator and the denominator by $7$ to get the equivalent fraction with a denominator of $56$ . $\newline$ $\left(\frac{3}{8}\right) \times \left(\frac{7}{7}\right) = \frac{21}{56}$
Add Equivalent Fractions: Add the equivalent fractions. $\newline$ Now that both fractions have the same denominator, we can add them directly. $\newline$ $\frac{24}{56} + \frac{21}{56} = \frac{24 + 21}{56} = \frac{45}{56}$
Simplify Fraction: Simplify the fraction, if possible. $\newline$ In this case, $45$ and $56$ have no common factors other than $1$ , so the fraction $\frac{45}{56}$ is already in its simplest form.