Solve 1/2*(2/3+3/5)*5/6

$$\frac { 1 } { 2 } \times ( \frac { 2 } { 3 } + \frac { 3 } { 5 } ) \times \frac { 5 } { 6 }$$

Evaluate

$$\frac{19}{36}\approx 0.527777778$$

Solution Steps

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{3}{5} to fractions with denominator 15.

$$\frac{1}{2}\left(\frac{10}{15}+\frac{9}{15}\right)\times \frac{5}{6}$$

Since \frac{10}{15} and \frac{9}{15} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\times \frac{10+9}{15}\times \frac{5}{6}$$

Add 10 and 9 to get 19.

$$\frac{1}{2}\times \frac{19}{15}\times \frac{5}{6}$$

Multiply \frac{1}{2} times \frac{19}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 19}{2\times 15}\times \frac{5}{6}$$

Do the multiplications in the fraction \frac{1\times 19}{2\times 15}.

$$\frac{19}{30}\times \frac{5}{6}$$

Multiply \frac{19}{30} times \frac{5}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 5}{30\times 6}$$

Do the multiplications in the fraction \frac{19\times 5}{30\times 6}.

$$\frac{95}{180}$$

Reduce the fraction \frac{95}{180} to lowest terms by extracting and canceling out 5.

$$\frac{19}{36}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 3 ^ {2}} = 0.5277777777777778$$