Solve 3/5*(10/9+5/6)

$$\frac { 3 } { 5 } \cdot ( \frac { 10 } { 9 } + \frac { 5 } { 6 } )$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Least common multiple of 9 and 6 is 18. Convert \frac{10}{9} and \frac{5}{6} to fractions with denominator 18.

$$\frac{3}{5}\left(\frac{20}{18}+\frac{15}{18}\right)$$

Since \frac{20}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$\frac{3}{5}\times \frac{20+15}{18}$$

Add 20 and 15 to get 35.

$$\frac{3}{5}\times \frac{35}{18}$$

Multiply \frac{3}{5} times \frac{35}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 35}{5\times 18}$$

Do the multiplications in the fraction \frac{3\times 35}{5\times 18}.

$$\frac{105}{90}$$

Reduce the fraction \frac{105}{90} to lowest terms by extracting and canceling out 15.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$