Solve (1:3/2):1/2+(5/6:5/4):frac{2}{3}

$$( 1 : \frac { 3 } { 2 } ) : \frac { 1 } { 2 } + ( \frac { 5 } { 6 } : \frac { 5 } { 4 } ) : \frac { 2 } { 3 }$$

Evaluate

$$\frac{7}{3}\approx 2.333333333$$

Solution Steps

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

$$\frac{2}{\frac{3}{2}}+\frac{\frac{\frac{5}{6}}{\frac{5}{4}}}{\frac{2}{3}}$$

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

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

Express 2\times \frac{2}{3} as a single fraction.

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

Multiply 2 and 2 to get 4.

$$\frac{4}{3}+\frac{\frac{\frac{5}{6}}{\frac{5}{4}}}{\frac{2}{3}}$$

Divide \frac{\frac{5}{6}}{\frac{5}{4}} by \frac{2}{3} by multiplying \frac{\frac{5}{6}}{\frac{5}{4}} by the reciprocal of \frac{2}{3}.

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

Express \frac{5}{6}\times 3 as a single fraction.

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

Multiply 5 and 3 to get 15.

$$\frac{4}{3}+\frac{\frac{15}{6}}{\frac{5}{4}\times 2}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

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

Express \frac{5}{4}\times 2 as a single fraction.

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

Multiply 5 and 2 to get 10.

$$\frac{4}{3}+\frac{\frac{5}{2}}{\frac{10}{4}}$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}+\frac{\frac{5}{2}}{\frac{5}{2}}$$

Divide \frac{5}{2} by \frac{5}{2} to get 1.

$$\frac{4}{3}+1$$

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

$$\frac{4}{3}+\frac{3}{3}$$

Since \frac{4}{3} and \frac{3}{3} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{3}$$

Add 4 and 3 to get 7.

$$\frac{7}{3}$$

Factor

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$