Solve 3/4/frac{6{9}}+1/3/frac{3{2}}

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

Evaluate

$$\frac{97}{72}\approx 1.347222222$$

Solution Steps

Divide \frac{3}{4} by \frac{6}{9} by multiplying \frac{3}{4} by the reciprocal of \frac{6}{9}.

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

Cancel out 3 in both numerator and denominator.

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

Multiply 2 and 4 to get 8.

$$\frac{9}{8}+\frac{\frac{1}{3}}{\frac{3}{2}}$$

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

$$\frac{9}{8}+\frac{1}{3}\times \frac{2}{3}$$

Multiply \frac{1}{3} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{8}+\frac{1\times 2}{3\times 3}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 3}.

$$\frac{9}{8}+\frac{2}{9}$$

Least common multiple of 8 and 9 is 72. Convert \frac{9}{8} and \frac{2}{9} to fractions with denominator 72.

$$\frac{81}{72}+\frac{16}{72}$$

Since \frac{81}{72} and \frac{16}{72} have the same denominator, add them by adding their numerators.

$$\frac{81+16}{72}$$

Add 81 and 16 to get 97.

$$\frac{97}{72}$$

Factor

$$\frac{97}{2 ^ {3} \cdot 3 ^ {2}} = 1\frac{25}{72} = 1.3472222222222223$$