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$Evaluate the expression shown below and write your answer as a fraction in simplest form. -(5)/(12)+(10)/(9) Answer:$

Evaluate the expression shown below and write your answer as a fraction in simplest form. $\newline$ $-\frac{5}{12}+\frac{10}{9}$ $\newline$ Answer:

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Roots of rational numbers

Full solution

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

\newline

-\frac{5}{12}+\frac{10}{9}

\newline

Answer:

Identify LCD: Identify the least common denominator (LCD) for the fractions $-\frac{5}{12}$ and $\frac{10}{9}$ . The denominators are $12$ and $9$ . The LCD for $12$ and $9$ is $36$ because it is the smallest number that both $12$ and $9$ can divide into without leaving a remainder.
Convert to LCD: Convert each fraction to an equivalent fraction with the LCD as the denominator. $\newline$ For $-\frac{5}{12}$ , we multiply both the numerator and the denominator by $3$ to get $-\frac{15}{36}$ . $\newline$ For $\frac{10}{9}$ , we multiply both the numerator and the denominator by $4$ to get $\frac{40}{36}$ .
Add fractions: Add the two fractions with the common denominator. $\newline$ $-\frac{15}{36} + \frac{40}{36} = \frac{40 - 15}{36} = \frac{25}{36}$
Check for simplification: Check if the resulting fraction can be simplified further. The fraction $\frac{25}{36}$ cannot be simplified further because $25$ and $36$ have no common factors other than $1$ .

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