Chapter 0, Problem 19POT

To determine

To calculate: The value of expression $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ in the simplest form.

Answer to Problem 19POT

The value of expression $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ in the simplest form is $\frac{2}{3}$ .

Explanation of Solution

Given information:

The given expression is $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ .

Formula used:

The outcome sign for $-(-)$ is $+$ .

The addition of two or more terms is denoted by $+$ sign that is if two terms are separated by $+$ then they are added up together.

The difference of two or more terms is denoted by $-$ sign that is if two terms are separated by $-$ then they are subtracted from one term to the other.

Calculation:

Consider the provided expression,

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

Observe that the denominator is not same in both the rational numbers, so take the lowest common multiple of denominators 12 and 4 as 12.

  $\begin{array}{c}-\frac{1}{12}+\frac{3}{4}=\frac{\left(-1\times 1\right)+\left(3\times 3\right)}{12}\\ =\frac{-1+9}{12}\\ =\frac{8}{12}\\ =\frac{2}{3}\end{array}$

The above expression cannot be simplified further.

Therefore, the value of expression $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ in the simplest form is $\frac{2}{3}$ .