Solve 9/4-8/frac{-1{2}-2}

$$\frac { \frac { 9 } { 4 } - 8 } { \frac { - 1 } { 2 } - 2 }$$

Evaluate

$$\frac{23}{10}=2.3$$

Solution Steps

Convert 8 to fraction \frac{32}{4}.

$$\frac{\frac{9}{4}-\frac{32}{4}}{\frac{-1}{2}-2}$$

Since \frac{9}{4} and \frac{32}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-32}{4}}{\frac{-1}{2}-2}$$

Subtract 32 from 9 to get -23.

$$\frac{-\frac{23}{4}}{\frac{-1}{2}-2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$\frac{-\frac{23}{4}}{-\frac{1}{2}-2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{-\frac{23}{4}}{-\frac{1}{2}-\frac{4}{2}}$$

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{23}{4}}{\frac{-1-4}{2}}$$

Subtract 4 from -1 to get -5.

$$\frac{-\frac{23}{4}}{-\frac{5}{2}}$$

Divide -\frac{23}{4} by -\frac{5}{2} by multiplying -\frac{23}{4} by the reciprocal of -\frac{5}{2}.

$$-\frac{23}{4}\left(-\frac{2}{5}\right)$$

Multiply -\frac{23}{4} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-23\left(-2\right)}{4\times 5}$$

Do the multiplications in the fraction \frac{-23\left(-2\right)}{4\times 5}.

$$\frac{46}{20}$$

Reduce the fraction \frac{46}{20} to lowest terms by extracting and canceling out 2.

$$\frac{23}{10}$$

Factor

$$\frac{23}{2 \cdot 5} = 2\frac{3}{10} = 2.3$$