Solve (1/5)div(1/5-2/1)(-3/5)^2

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

Evaluate

$$-\frac{1}{25}=-0.04$$

Solution Steps

Anything divided by one gives itself.

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

Convert 2 to fraction \frac{10}{5}.

$$\frac{\frac{1}{5}}{\frac{1}{5}-\frac{10}{5}}\left(-\frac{3}{5}\right)^{2}$$

Since \frac{1}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{5}}{\frac{1-10}{5}}\left(-\frac{3}{5}\right)^{2}$$

Subtract 10 from 1 to get -9.

$$\frac{\frac{1}{5}}{-\frac{9}{5}}\left(-\frac{3}{5}\right)^{2}$$

Divide \frac{1}{5} by -\frac{9}{5} by multiplying \frac{1}{5} by the reciprocal of -\frac{9}{5}.

$$\frac{1}{5}\left(-\frac{5}{9}\right)\left(-\frac{3}{5}\right)^{2}$$

Multiply \frac{1}{5} times -\frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-5\right)}{5\times 9}\left(-\frac{3}{5}\right)^{2}$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{5\times 9}.

$$\frac{-5}{45}\left(-\frac{3}{5}\right)^{2}$$

Reduce the fraction \frac{-5}{45} to lowest terms by extracting and canceling out 5.

$$-\frac{1}{9}\left(-\frac{3}{5}\right)^{2}$$

Calculate -\frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$-\frac{1}{9}\times \frac{9}{25}$$

Multiply -\frac{1}{9} times \frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-9}{9\times 25}$$

Cancel out 9 in both numerator and denominator.

$$\frac{-1}{25}$$

Fraction \frac{-1}{25} can be rewritten as -\frac{1}{25} by extracting the negative sign.

$$-\frac{1}{25}$$

Factor

$$-\frac{1}{25} = -0.04$$