Question

Evaluate the expression: $\frac{7}{8}-\frac{7}{4}+\frac{1}{2}$

The decimal form of the number is

Answer 1

According to PEMDAS, addition and subtraction have same priority. Therefore we must evaluate the expression from left to right.

$\frac{7}{8}-\frac{7}{4}+\frac{1}{2}=\frac{7}{8}-\frac{7\times 2}{4\times 2}+\frac{1}{2}$
(converting the denominator into same base for subtraction)
$=\frac{7}{8}-\frac{14}{8}+\frac{1}{2}=\frac{7-14}{8}+\frac{1}{2}=\frac{-7}{8}+\frac{1}{2}=-\frac{7}{8}+\frac{1\times 4}{2\times 4}=-\frac{7}{8}+\frac{4}{8}=\frac{-7+4}{8}=-\frac{3}{8}$

We know that $8\times 125=1000$
$\therefore$ Multiply the numerator and denominator by $125$ to make the denominator as a power of $10.$

$\Rightarrow -\frac{3\times 125}{8\times 125}=-\frac{375}{1000}=-0.375$