Chapter 0.4, Problem 39E

To determine

To calculate: The simplified form of $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ .

Answer to Problem 39E

The simplified form of $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ is $\frac{2}{3}$ .

Explanation of Solution

Given information:

The statement “ $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ .”

Formula used:

When two fractions with different denominators are subtracted then the two unlike fractions are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple(LCM).

Consider the provided statement “ $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ .”

Recall that when two fractions with different denominators are subtracted then the two unlike fractions are converted into like fractions by multiplying the denominators with a common factor of their lowest common multiple(LCM).

LCM of $12$ and $4$ is $12$ .

So, multiply $\frac{3}{4}$ by 3 in both numerator and denominator,

Thus, the given expression can be simplified as,

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

Now,

8 can be written as the product of 4 and 2.

12 can be written as product of 4 and 3.

So, $\frac{8}{12}$ can be simplified as,

  $\frac{8}{12}=\frac{4\times 2}{4\times 3}$

Striking off the common terms, we get,

  $\frac{8}{12}=\frac{2}{3}$

Hence, the simplified form of $-\frac{1}{12}-\left(-\frac{3}{4}\right)$ is $\frac{2}{3}$ .