Question

Find each sum or difference. Write in the simplest form.

$-\frac{1}{12}-\left(-\frac{3}{4}\right)$

Short answer

The simplest form is$\frac{2}{3}$.

Step-by-step solution

Step 1. Concept of like and unlike signs.

If there is sign like$+\left(+\right)$ or$-\left(-\right)$ then the resulting sign will be positive and if there is an unlike$+\left(-\right)$ sign$-\left(+\right)$ or then the resulting will be negative

Thus the simple form of given expression by nature of sign is

$-\frac{1}{12}+\frac{3}{4}$

Step 2. Take L.C.M of the denominators of each fraction.

Since, 12 is completely divided by 4.

Thus

$\text{L.C.Mof12and4is}=12$

Step 3. Evaluate the sum.

First, make the denominators of all fractions equal to LCM by multiplying the numerator and denominator with an integer. Then add/subtract the numerators directly over the common denominator.

$$\begin{gathered} \frac{-1}{12}+\frac{3}{4}=\frac{-1}{12}+\frac{3\cdot 3}{4\cdot 3} \\ =\frac{-1}{12}+\frac{9}{12} \\ =\frac{-1+9}{12} \\ =\frac{8}{12} \end{gathered}$$

Step 4. Simplify the result.

Write the fraction with factor form and then simplify it.

$\begin{array}{l}=\frac{2\times 2\times 2}{2\times 2\times 3}\\ =\frac{2}{3}\end{array}$

Therefore, the simplest form is $\frac{2}{3}$.