Question

Simplify the expression $-\frac{7}{18}+\frac{5}{12}$.

Short answer

The simplified expression is $\frac{1}{36}$.

Step-by-step solution

Step 1. Given information.

The given expression is$-\frac{7}{18}+\frac{5}{12}$.

Step 2. Find the LCD(Least Common Denominator) of 12 and 18.

Rewrite the 12 and 18 as the product of the primes and find the LCD.

$$\begin{gathered} 12=2\times 2\times 3 \\ 18=2\times 3\times 3 \\ LCD=2\times 2\times 3\times 3=36 \end{gathered}$$

Step 3. Rewrite each fraction as an equivalent fraction with the LCD. 

Simplify the expression.

$$\begin{gathered} -\frac{7}{18}+\frac{5}{12} \\ =-\frac{7·2}{18·2}+\frac{5·3}{12·3} \\ =-\frac{14}{36}+\frac{15}{36} \\ =\frac{-14+15}{36} \\ =\frac{1}{36} \end{gathered}$$

Step 4. Conclusion. 

The simplified form of the given expression is$\frac{1}{36}$.