Solve 4/9+2/3/frac{5{9}-1/3}

$$\frac { \frac { 4 } { 9 } + \frac { 2 } { 3 } } { \frac { 5 } { 9 } - \frac { 1 } { 3 } }$$

Evaluate

$$5$$

Solution Steps

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

$$\frac{\frac{4}{9}+\frac{6}{9}}{\frac{5}{9}-\frac{1}{3}}$$

Since \frac{4}{9} and \frac{6}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+6}{9}}{\frac{5}{9}-\frac{1}{3}}$$

Add 4 and 6 to get 10.

$$\frac{\frac{10}{9}}{\frac{5}{9}-\frac{1}{3}}$$

Least common multiple of 9 and 3 is 9. Convert \frac{5}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{\frac{10}{9}}{\frac{5}{9}-\frac{3}{9}}$$

Since \frac{5}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10}{9}}{\frac{5-3}{9}}$$

Subtract 3 from 5 to get 2.

$$\frac{\frac{10}{9}}{\frac{2}{9}}$$

Divide \frac{10}{9} by \frac{2}{9} by multiplying \frac{10}{9} by the reciprocal of \frac{2}{9}.

$$\frac{10}{9}\times \frac{9}{2}$$

Multiply \frac{10}{9} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 9}{9\times 2}$$

Cancel out 9 in both numerator and denominator.

$$\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$5$$

Factor

$$5$$