Solve 3/4{frac{2/5-10}}

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

Evaluate

$$-\frac{36}{5}=-7.2$$

Solution Steps

Divide 3 by \frac{4}{\frac{2}{5}-10} by multiplying 3 by the reciprocal of \frac{4}{\frac{2}{5}-10}.

$$\frac{3\left(\frac{2}{5}-10\right)}{4}$$

Convert 10 to fraction \frac{50}{5}.

$$\frac{3\left(\frac{2}{5}-\frac{50}{5}\right)}{4}$$

Since \frac{2}{5} and \frac{50}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times \frac{2-50}{5}}{4}$$

Subtract 50 from 2 to get -48.

$$\frac{3\left(-\frac{48}{5}\right)}{4}$$

Express 3\left(-\frac{48}{5}\right) as a single fraction.

$$\frac{\frac{3\left(-48\right)}{5}}{4}$$

Multiply 3 and -48 to get -144.

$$\frac{\frac{-144}{5}}{4}$$

Fraction \frac{-144}{5} can be rewritten as -\frac{144}{5} by extracting the negative sign.

$$\frac{-\frac{144}{5}}{4}$$

Express \frac{-\frac{144}{5}}{4} as a single fraction.

$$\frac{-144}{5\times 4}$$

Multiply 5 and 4 to get 20.

$$\frac{-144}{20}$$

Reduce the fraction \frac{-144}{20} to lowest terms by extracting and canceling out 4.

$$-\frac{36}{5}$$

Factor

$$-\frac{36}{5} = -7\frac{1}{5} = -7.2$$