Solve [(3/4)^-1+(1/2+1/3/2/3)/frac{3{9}+(1/5div1/3/4/9*3/2)}]

$$[ \frac { ( 3 / 4 ) ^ { - 1 } + ( \frac { 1 / 2 + 1 / 3 } { 2 / 3 } ) } { \frac { 3 } { 9 } + ( \frac { 1 / 5 \div 1 / 3 } { 4 / 9 * 3 / 2 } ) } ]$$

Evaluate

$$\frac{155}{74}\approx 2.094594595$$

Solution Steps

Calculate \frac{3}{4} to the power of -1 and get \frac{4}{3}.

$$\frac{\frac{4}{3}+\frac{\frac{1}{2}+\frac{1}{3}}{\frac{2}{3}}}{\frac{3}{9}+\frac{\frac{\frac{1}{5}}{\frac{1}{3}}}{\frac{4}{9}\times \frac{3}{2}}}$$

Add \frac{1}{2} and \frac{1}{3} to get \frac{5}{6}.

$$\frac{\frac{4}{3}+\frac{\frac{5}{6}}{\frac{2}{3}}}{\frac{3}{9}+\frac{\frac{\frac{1}{5}}{\frac{1}{3}}}{\frac{4}{9}\times \frac{3}{2}}}$$

Divide \frac{5}{6} by \frac{2}{3} by multiplying \frac{5}{6} by the reciprocal of \frac{2}{3}.

$$\frac{\frac{4}{3}+\frac{5}{6}\times \frac{3}{2}}{\frac{3}{9}+\frac{\frac{\frac{1}{5}}{\frac{1}{3}}}{\frac{4}{9}\times \frac{3}{2}}}$$

Multiply \frac{5}{6} and \frac{3}{2} to get \frac{5}{4}.

$$\frac{\frac{4}{3}+\frac{5}{4}}{\frac{3}{9}+\frac{\frac{\frac{1}{5}}{\frac{1}{3}}}{\frac{4}{9}\times \frac{3}{2}}}$$

Add \frac{4}{3} and \frac{5}{4} to get \frac{31}{12}.

$$\frac{\frac{31}{12}}{\frac{3}{9}+\frac{\frac{\frac{1}{5}}{\frac{1}{3}}}{\frac{4}{9}\times \frac{3}{2}}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{31}{12}}{\frac{1}{3}+\frac{\frac{\frac{1}{5}}{\frac{1}{3}}}{\frac{4}{9}\times \frac{3}{2}}}$$

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

$$\frac{\frac{31}{12}}{\frac{1}{3}+\frac{\frac{1}{5}\times 3}{\frac{4}{9}\times \frac{3}{2}}}$$

Multiply \frac{1}{5} and 3 to get \frac{3}{5}.

$$\frac{\frac{31}{12}}{\frac{1}{3}+\frac{\frac{3}{5}}{\frac{4}{9}\times \frac{3}{2}}}$$

Multiply \frac{4}{9} and \frac{3}{2} to get \frac{2}{3}.

$$\frac{\frac{31}{12}}{\frac{1}{3}+\frac{\frac{3}{5}}{\frac{2}{3}}}$$

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

$$\frac{\frac{31}{12}}{\frac{1}{3}+\frac{3}{5}\times \frac{3}{2}}$$

Multiply \frac{3}{5} and \frac{3}{2} to get \frac{9}{10}.

$$\frac{\frac{31}{12}}{\frac{1}{3}+\frac{9}{10}}$$

Add \frac{1}{3} and \frac{9}{10} to get \frac{37}{30}.

$$\frac{\frac{31}{12}}{\frac{37}{30}}$$

Divide \frac{31}{12} by \frac{37}{30} by multiplying \frac{31}{12} by the reciprocal of \frac{37}{30}.

$$\frac{31}{12}\times \frac{30}{37}$$

Multiply \frac{31}{12} and \frac{30}{37} to get \frac{155}{74}.

$$\frac{155}{74}$$

Factor

$$\frac{5 \cdot 31}{2 \cdot 37} = 2\frac{7}{74} = 2.0945945945945947$$