Solve 3-5/4/frac{1{4}-1/5}*(-frac{1/2)^-2}{3}

$$\frac { 3 - \frac { 5 } { 4 } } { \frac { 1 } { 4 } - \frac { 1 } { 5 } } \cdot \frac { ( - \frac { 1 } { 2 } ) ^ { - 2 } } { 3 }$$

Evaluate

$$\frac{140}{3}\approx 46.666666667$$

Solution Steps

Subtract \frac{5}{4} from 3 to get \frac{7}{4}.

$$\frac{\frac{7}{4}}{\frac{1}{4}-\frac{1}{5}}\times \frac{\left(-\frac{1}{2}\right)^{-2}}{3}$$

Subtract \frac{1}{5} from \frac{1}{4} to get \frac{1}{20}.

$$\frac{\frac{7}{4}}{\frac{1}{20}}\times \frac{\left(-\frac{1}{2}\right)^{-2}}{3}$$

Divide \frac{7}{4} by \frac{1}{20} by multiplying \frac{7}{4} by the reciprocal of \frac{1}{20}.

$$\frac{7}{4}\times 20\times \frac{\left(-\frac{1}{2}\right)^{-2}}{3}$$

Multiply \frac{7}{4} and 20 to get 35.

$$35\times \frac{\left(-\frac{1}{2}\right)^{-2}}{3}$$

Calculate -\frac{1}{2} to the power of -2 and get 4.

$$35\times \frac{4}{3}$$

Multiply 35 and \frac{4}{3} to get \frac{140}{3}.

$$\frac{140}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 5 \cdot 7}{3} = 46\frac{2}{3} = 46.666666666666664$$