Solve 15/6*(5/6-1/3)*(12/9)

$$1 \frac { 5 } { 6 } \times ( \frac { 5 } { 6 } - \frac { 1 } { 3 } ) \times ( 1 \frac { 2 } { 9 } )$$

Evaluate

$$\frac{121}{108}\approx 1.12037037$$

Solution Steps

Multiply 1 and 6 to get 6.

$$\frac{6+5}{6}\left(\frac{5}{6}-\frac{1}{3}\right)\times \frac{1\times 9+2}{9}$$

Add 6 and 5 to get 11.

$$\frac{11}{6}\left(\frac{5}{6}-\frac{1}{3}\right)\times \frac{1\times 9+2}{9}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{11}{6}\left(\frac{5}{6}-\frac{2}{6}\right)\times \frac{1\times 9+2}{9}$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{6}\times \frac{5-2}{6}\times \frac{1\times 9+2}{9}$$

Subtract 2 from 5 to get 3.

$$\frac{11}{6}\times \frac{3}{6}\times \frac{1\times 9+2}{9}$$

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

$$\frac{11}{6}\times \frac{1}{2}\times \frac{1\times 9+2}{9}$$

Multiply \frac{11}{6} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 1}{6\times 2}\times \frac{1\times 9+2}{9}$$

Do the multiplications in the fraction \frac{11\times 1}{6\times 2}.

$$\frac{11}{12}\times \frac{1\times 9+2}{9}$$

Multiply 1 and 9 to get 9.

$$\frac{11}{12}\times \frac{9+2}{9}$$

Add 9 and 2 to get 11.

$$\frac{11}{12}\times \frac{11}{9}$$

Multiply \frac{11}{12} times \frac{11}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\times 11}{12\times 9}$$

Do the multiplications in the fraction \frac{11\times 11}{12\times 9}.

$$\frac{121}{108}$$

Factor

$$\frac{11 ^ {2}}{2 ^ {2} \cdot 3 ^ {3}} = 1\frac{13}{108} = 1.1203703703703705$$