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

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

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

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

Since \frac{3}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

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

Add 3 and 2 to get 5.

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

Multiply 3 and 2 to get 6.

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

Add 6 and 3 to get 9.

$$\frac{\frac{5}{2}}{\frac{9}{2}+3}$$

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

$$\frac{\frac{5}{2}}{\frac{9}{2}+\frac{6}{2}}$$

Since \frac{9}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{2}}{\frac{9+6}{2}}$$

Add 9 and 6 to get 15.

$$\frac{\frac{5}{2}}{\frac{15}{2}}$$

Divide \frac{5}{2} by \frac{15}{2} by multiplying \frac{5}{2} by the reciprocal of \frac{15}{2}.

$$\frac{5}{2}\times \frac{2}{15}$$

Multiply \frac{5}{2} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 2}{2\times 15}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5}{15}$$

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$