Solve [5:(1/2-1)+3:1/4]:(-2/5)

$$[ 5 : ( \frac { 1 } { 2 } - 1 ) + 3 : \frac { 1 } { 4 } ] : ( - \frac { 2 } { 5 } )$$

Evaluate

$$-5$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{5}{\frac{1}{2}-\frac{2}{2}}+\frac{3}{\frac{1}{4}}}{-\frac{2}{5}}$$

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

$$\frac{\frac{5}{\frac{1-2}{2}}+\frac{3}{\frac{1}{4}}}{-\frac{2}{5}}$$

Subtract 2 from 1 to get -1.

$$\frac{\frac{5}{-\frac{1}{2}}+\frac{3}{\frac{1}{4}}}{-\frac{2}{5}}$$

Divide 5 by -\frac{1}{2} by multiplying 5 by the reciprocal of -\frac{1}{2}.

$$\frac{5\left(-2\right)+\frac{3}{\frac{1}{4}}}{-\frac{2}{5}}$$

Multiply 5 and -2 to get -10.

$$\frac{-10+\frac{3}{\frac{1}{4}}}{-\frac{2}{5}}$$

Divide 3 by \frac{1}{4} by multiplying 3 by the reciprocal of \frac{1}{4}.

$$\frac{-10+3\times 4}{-\frac{2}{5}}$$

Multiply 3 and 4 to get 12.

$$\frac{-10+12}{-\frac{2}{5}}$$

Add -10 and 12 to get 2.

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

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

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

Cancel out 2 and 2.

$$-5$$

Factor

$$-5$$