Solve 2+1/3/2-frac{1{3}}:1/5+(1/3)^-1

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

Evaluate

$$10$$

Solution Steps

Divide \frac{2+\frac{1}{3}}{2-\frac{1}{3}} by \frac{1}{5} by multiplying \frac{2+\frac{1}{3}}{2-\frac{1}{3}} by the reciprocal of \frac{1}{5}.

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

Add 2 and \frac{1}{3} to get \frac{7}{3}.

$$\frac{\frac{7}{3}\times 5}{2-\frac{1}{3}}+\left(\frac{1}{3}\right)^{-1}$$

Multiply \frac{7}{3} and 5 to get \frac{35}{3}.

$$\frac{\frac{35}{3}}{2-\frac{1}{3}}+\left(\frac{1}{3}\right)^{-1}$$

Subtract \frac{1}{3} from 2 to get \frac{5}{3}.

$$\frac{\frac{35}{3}}{\frac{5}{3}}+\left(\frac{1}{3}\right)^{-1}$$

Divide \frac{35}{3} by \frac{5}{3} by multiplying \frac{35}{3} by the reciprocal of \frac{5}{3}.

$$\frac{35}{3}\times \frac{3}{5}+\left(\frac{1}{3}\right)^{-1}$$

Multiply \frac{35}{3} and \frac{3}{5} to get 7.

$$7+\left(\frac{1}{3}\right)^{-1}$$

Calculate \frac{1}{3} to the power of -1 and get 3.

$$7+3$$

Add 7 and 3 to get 10.

$$10$$

Factor

$$2\times 5$$