Solve 1/3div(1/3-5/5)*5/5

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

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Divide 5 by 5 to get 1.

$$\frac{\frac{1}{3}}{\frac{1}{3}-1}\times \frac{5}{5}$$

Divide 5 by 5 to get 1.

$$\frac{\frac{1}{3}}{\frac{1}{3}-1}\times 1$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{1}{3}}{\frac{1}{3}-\frac{3}{3}}\times 1$$

Since \frac{1}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{3}}{\frac{1-3}{3}}\times 1$$

Subtract 3 from 1 to get -2.

$$\frac{\frac{1}{3}}{-\frac{2}{3}}\times 1$$

Divide \frac{1}{3} by -\frac{2}{3} by multiplying \frac{1}{3} by the reciprocal of -\frac{2}{3}.

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

Multiply \frac{1}{3} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-3\right)}{3\times 2}.

$$\frac{-3}{6}\times 1$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

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

Factor

$$-\frac{1}{2} = -0.5$$