Solve 5/9:(2/3+3/6)

$$\frac { 5 } { 9 } : ( \frac { 2 } { 3 } + \frac { 3 } { 6 } )$$

Evaluate

$$\frac{10}{21}\approx 0.476190476$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

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

Since \frac{4}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

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

Add 4 and 3 to get 7.

$$\frac{\frac{5}{9}}{\frac{7}{6}}$$

Divide \frac{5}{9} by \frac{7}{6} by multiplying \frac{5}{9} by the reciprocal of \frac{7}{6}.

$$\frac{5}{9}\times \frac{6}{7}$$

Multiply \frac{5}{9} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 6}{9\times 7}$$

Do the multiplications in the fraction \frac{5\times 6}{9\times 7}.

$$\frac{30}{63}$$

Reduce the fraction \frac{30}{63} to lowest terms by extracting and canceling out 3.

$$\frac{10}{21}$$

Factor

$$\frac{2 \cdot 5}{3 \cdot 7} = 0.47619047619047616$$