Solve (6.7)2+1/3/2-frac{1{5}}:1/5+(1/3)^-1

$$( 6.7 ) \frac { 2 + \frac { 1 } { 3 } } { 2 - \frac { 1 } { 5 } } : \frac { 1 } { 5 } + ( \frac { 1 } { 3 } ) ^ { - 1 }$$

Evaluate

$$\frac{2507}{54}\approx 46.425925926$$

Solution Steps

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

$$\frac{6.7\times \frac{\frac{7}{3}}{2-\frac{1}{5}}}{\frac{1}{5}}+\left(\frac{1}{3}\right)^{-1}$$

Subtract \frac{1}{5} from 2 to get \frac{9}{5}.

$$\frac{6.7\times \frac{\frac{7}{3}}{\frac{9}{5}}}{\frac{1}{5}}+\left(\frac{1}{3}\right)^{-1}$$

Divide \frac{7}{3} by \frac{9}{5} by multiplying \frac{7}{3} by the reciprocal of \frac{9}{5}.

$$\frac{6.7\times \frac{7}{3}\times \frac{5}{9}}{\frac{1}{5}}+\left(\frac{1}{3}\right)^{-1}$$

Multiply \frac{7}{3} and \frac{5}{9} to get \frac{35}{27}.

$$\frac{6.7\times \frac{35}{27}}{\frac{1}{5}}+\left(\frac{1}{3}\right)^{-1}$$

Multiply 6.7 and \frac{35}{27} to get \frac{469}{54}.

$$\frac{\frac{469}{54}}{\frac{1}{5}}+\left(\frac{1}{3}\right)^{-1}$$

Divide \frac{469}{54} by \frac{1}{5} by multiplying \frac{469}{54} by the reciprocal of \frac{1}{5}.

$$\frac{469}{54}\times 5+\left(\frac{1}{3}\right)^{-1}$$

Multiply \frac{469}{54} and 5 to get \frac{2345}{54}.

$$\frac{2345}{54}+\left(\frac{1}{3}\right)^{-1}$$

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

$$\frac{2345}{54}+3$$

Add \frac{2345}{54} and 3 to get \frac{2507}{54}.

$$\frac{2507}{54}$$

Factor

$$\frac{23 \cdot 109}{2 \cdot 3 ^ {3}} = 46\frac{23}{54} \approx 46.425925926$$