Solve 5/6*12/15/frac{1{3}+3/5}=

$$\frac { \frac { 5 } { 6 } \cdot \frac { 12 } { 15 } } { \frac { 1 } { 3 } + \frac { 3 } { 5 } } =$$

Evaluate

$$\frac{5}{7}\approx 0.714285714$$

Solution Steps

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{5}{6}\times \frac{4}{5}}{\frac{1}{3}+\frac{3}{5}}$$

Multiply \frac{5}{6} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5\times 4}{6\times 5}}{\frac{1}{3}+\frac{3}{5}}$$

Cancel out 5 in both numerator and denominator.

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

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{\frac{2}{3}}{\frac{5}{15}+\frac{9}{15}}$$

Since \frac{5}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2}{3}}{\frac{5+9}{15}}$$

Add 5 and 9 to get 14.

$$\frac{\frac{2}{3}}{\frac{14}{15}}$$

Divide \frac{2}{3} by \frac{14}{15} by multiplying \frac{2}{3} by the reciprocal of \frac{14}{15}.

$$\frac{2}{3}\times \frac{15}{14}$$

Multiply \frac{2}{3} times \frac{15}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 15}{3\times 14}$$

Do the multiplications in the fraction \frac{2\times 15}{3\times 14}.

$$\frac{30}{42}$$

Reduce the fraction \frac{30}{42} to lowest terms by extracting and canceling out 6.

$$\frac{5}{7}$$

Factor

$$\frac{5}{7} = 0.7142857142857143$$