Solve 3+1/2/2+frac{1{3}}:2/3

$$\frac { 3 + \frac { 1 } { 2 } } { 2 + \frac { 1 } { 3 } } : \frac { 2 } { 3 }$$

Evaluate

$$\frac{9}{4}=2.25$$

Solution Steps

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

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

Convert 3 to fraction \frac{6}{2}.

$$\frac{\left(\frac{6}{2}+\frac{1}{2}\right)\times 3}{\left(2+\frac{1}{3}\right)\times 2}$$

Since \frac{6}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{6+1}{2}\times 3}{\left(2+\frac{1}{3}\right)\times 2}$$

Add 6 and 1 to get 7.

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

Express \frac{7}{2}\times 3 as a single fraction.

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

Multiply 7 and 3 to get 21.

$$\frac{\frac{21}{2}}{\left(2+\frac{1}{3}\right)\times 2}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{21}{2}}{\left(\frac{6}{3}+\frac{1}{3}\right)\times 2}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21}{2}}{\frac{6+1}{3}\times 2}$$

Add 6 and 1 to get 7.

$$\frac{\frac{21}{2}}{\frac{7}{3}\times 2}$$

Express \frac{7}{3}\times 2 as a single fraction.

$$\frac{\frac{21}{2}}{\frac{7\times 2}{3}}$$

Multiply 7 and 2 to get 14.

$$\frac{\frac{21}{2}}{\frac{14}{3}}$$

Divide \frac{21}{2} by \frac{14}{3} by multiplying \frac{21}{2} by the reciprocal of \frac{14}{3}.

$$\frac{21}{2}\times \frac{3}{14}$$

Multiply \frac{21}{2} times \frac{3}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{21\times 3}{2\times 14}$$

Do the multiplications in the fraction \frac{21\times 3}{2\times 14}.

$$\frac{63}{28}$$

Reduce the fraction \frac{63}{28} to lowest terms by extracting and canceling out 7.

$$\frac{9}{4}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2}} = 2\frac{1}{4} = 2.25$$