Q40. - Algebra 1

Question

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

Step-by-Step Solution

Answer

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

Step 1.

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

Step 2. Concept.

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).

Step 3. Calculation.

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,

$-\frac{7}{8}-\left(-\frac{3}{16}\right)=-\frac{7}{8}+\frac{3}{16}$

$-\frac{7}{8}-\left(-\frac{3}{16}\right)=-\frac{7\times 2}{8\times 2}+\frac{3}{16}$

$-\frac{7}{8}-\left(-\frac{3}{16}\right)=-\frac{14}{16}+\frac{3}{16}$

$-\frac{7}{8}-\left(-\frac{3}{16}\right)=-\frac{11}{16}$

Step 4. Recheck.

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

 

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