Chapter 0.4, Problem 39E

To determine

To find: The simplest form of the given sum or difference.

Answer to Problem 39E

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

Explanation of Solution

Given:

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

Calculation:

Consider the given difference,

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

Consider the factors of 12 is,

  $12=3\times 2\times 2$

Consider the factors of 4 is,

  $4=2\times 2$

Consider the LCM of 4 and 12 is,

  $3\times 2\times 2=12$

Consider the fraction $\frac{3}{4}$ as,

  $\begin{array}{c}\frac{3}{4}=\frac{3\times 3}{4\times 3}\\ =\frac{9}{12}\end{array}$

Consider the fraction $\frac{1}{3}$ as,

  $\begin{array}{c}\frac{1}{3}=\frac{1\times 5}{3\times 5}\\ =\frac{5}{15}\end{array}$

Then, the difference is,

  $-\frac{1}{12}-\left(-\frac{9}{12}\right)$

The product of a negative and negative is a positive then,

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