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$Evaluate the expression shown below and write your answer as a fraction in simplest form. (2)/(9)+(11)/(18) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $\frac{2}{9}+\frac{11}{18}$ $\newline$ Answer:

Full solution

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

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\frac{2}{9}+\frac{11}{18}

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Answer:

Identify Common Denominator: Identify a common denominator for the fractions $(\frac{2}{9})$ and $(\frac{11}{18})$ . The common denominator for $9$ and $18$ is $18$ because $18$ is the least common multiple of $9$ and $18$ .
Convert to Common Denominator: Convert the fraction $(\frac{2}{9})$ to have the common denominator of $18$ . $\newline$ To convert $(\frac{2}{9})$ to a fraction with a denominator of $18$ , multiply both the numerator and the denominator by $2$ . $\newline$ $(\frac{2}{9}) \times (\frac{2}{2}) = (\frac{4}{18})$
Add Fractions: Add the converted fraction $(\frac{4}{18})$ to the fraction $(\frac{11}{18})$ . $\newline$ Now that both fractions have the same denominator, we can add them directly. $\newline$ $(\frac{4}{18}) + (\frac{11}{18}) = (\frac{4 + 11}{18})$
Perform Numerator Addition: Perform the addition of the numerators. $\newline$ Add the numerators $4$ and $11$ . $\newline$ $4 + 11 = 15$
Write Result as Fraction: Write the result as a fraction with the common denominator. $\newline$ The sum of the fractions is $(\frac{15}{18})$ .
Simplify Fraction: Simplify the fraction $(\frac{15}{18})$ to its simplest form. $\newline$ Both the numerator and the denominator are divisible by $3$ . $\newline$ $(\frac{15}{18}) \div (\frac{3}{3}) = (\frac{5}{6})$