Chapter 0.4, Problem 40E

To determine

To calculate: The simplified form of $-\frac{7}{8}-\left(-\frac{3}{16}\right)$ .

Answer to Problem 40E

The simplified form of $-\frac{7}{8}-\left(-\frac{3}{16}\right)$ is $-\frac{11}{16}$ .

Explanation of Solution

Given information:

The statement “ $-\frac{7}{8}-\left(-\frac{3}{16}\right)$ .”

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 “ $-\frac{7}{8}-\left(-\frac{3}{16}\right)$ .”

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 $8$ and $16$ is $16$ .

So, multiply $\frac{7}{8}$ by 2 in both numerator and denominator,

Thus, the given expression can be simplified as,

  $\begin{array}{c}-\frac{7}{8}-\left(-\frac{3}{16}\right)=-\frac{7}{8}+\frac{3}{16}\\ -\frac{7}{8}-\left(-\frac{3}{16}\right)=-\frac{7\times 2}{8\times 2}+\frac{3}{16}\\ -\frac{7}{8}-\left(-\frac{3}{16}\right)=-\frac{14}{16}+\frac{3}{16}\\ -\frac{7}{8}-\left(-\frac{3}{16}\right)=-\frac{11}{16}\end{array}$

Since, $-\frac{11}{16}$ cannot be simplified further,

Hence, the simplified form of $-\frac{7}{8}-\left(-\frac{3}{16}\right)$ is $-\frac{11}{16}$ .