Solve 1/3div5/3+1/4*4/5-frac{2}{5}

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

Evaluate

$$0$$

Solution Steps

Divide \frac{1}{3} by \frac{5}{3} by multiplying \frac{1}{3} by the reciprocal of \frac{5}{3}.

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

Multiply \frac{1}{3} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Multiply \frac{1}{4} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 4 in both numerator and denominator.

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

Since \frac{1}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

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

Add 1 and 1 to get 2.

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

Subtract \frac{2}{5} from \frac{2}{5} to get 0.

$$0$$

Factor

$$0$$