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

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

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{2}{9} to fractions with denominator 9.

$$\frac{\frac{12}{9}+\frac{2}{9}}{\frac{3}{1}-\frac{1}{3}}$$

Since \frac{12}{9} and \frac{2}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{12+2}{9}}{\frac{3}{1}-\frac{1}{3}}$$

Add 12 and 2 to get 14.

$$\frac{\frac{14}{9}}{\frac{3}{1}-\frac{1}{3}}$$

Anything divided by one gives itself.

$$\frac{\frac{14}{9}}{3-\frac{1}{3}}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{\frac{14}{9}}{\frac{9}{3}-\frac{1}{3}}$$

Since \frac{9}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14}{9}}{\frac{9-1}{3}}$$

Subtract 1 from 9 to get 8.

$$\frac{\frac{14}{9}}{\frac{8}{3}}$$

Divide \frac{14}{9} by \frac{8}{3} by multiplying \frac{14}{9} by the reciprocal of \frac{8}{3}.

$$\frac{14}{9}\times \frac{3}{8}$$

Multiply \frac{14}{9} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{14\times 3}{9\times 8}$$

Do the multiplications in the fraction \frac{14\times 3}{9\times 8}.

$$\frac{42}{72}$$

Reduce the fraction \frac{42}{72} to lowest terms by extracting and canceling out 6.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$