Solve left(21/6+51/6/4frac{2{15}}right)3/82

$$\left( 2 \frac{ 1 }{ 6 } + \frac{ 5 \frac{ 1 }{ 6 } }{ 4 \frac{ 2 }{ 15 } } \right) \frac{ 3 }{ 82 }$$

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

Multiply 2 and 6 to get 12.

$$\left(\frac{12+1}{6}+\frac{\frac{5\times 6+1}{6}}{\frac{4\times 15+2}{15}}\right)\times \frac{3}{82}$$

Add 12 and 1 to get 13.

$$\left(\frac{13}{6}+\frac{\frac{5\times 6+1}{6}}{\frac{4\times 15+2}{15}}\right)\times \frac{3}{82}$$

Divide \frac{5\times 6+1}{6} by \frac{4\times 15+2}{15} by multiplying \frac{5\times 6+1}{6} by the reciprocal of \frac{4\times 15+2}{15}.

$$\left(\frac{13}{6}+\frac{\left(5\times 6+1\right)\times 15}{6\left(4\times 15+2\right)}\right)\times \frac{3}{82}$$

Cancel out 3 in both numerator and denominator.

$$\left(\frac{13}{6}+\frac{5\left(1+5\times 6\right)}{2\left(2+4\times 15\right)}\right)\times \frac{3}{82}$$

Multiply 5 and 6 to get 30.

$$\left(\frac{13}{6}+\frac{5\left(1+30\right)}{2\left(2+4\times 15\right)}\right)\times \frac{3}{82}$$

Add 1 and 30 to get 31.

$$\left(\frac{13}{6}+\frac{5\times 31}{2\left(2+4\times 15\right)}\right)\times \frac{3}{82}$$

Multiply 5 and 31 to get 155.

$$\left(\frac{13}{6}+\frac{155}{2\left(2+4\times 15\right)}\right)\times \frac{3}{82}$$

Multiply 4 and 15 to get 60.

$$\left(\frac{13}{6}+\frac{155}{2\left(2+60\right)}\right)\times \frac{3}{82}$$

Add 2 and 60 to get 62.

$$\left(\frac{13}{6}+\frac{155}{2\times 62}\right)\times \frac{3}{82}$$

Multiply 2 and 62 to get 124.

$$\left(\frac{13}{6}+\frac{155}{124}\right)\times \frac{3}{82}$$

Reduce the fraction \frac{155}{124} to lowest terms by extracting and canceling out 31.

$$\left(\frac{13}{6}+\frac{5}{4}\right)\times \frac{3}{82}$$

Least common multiple of 6 and 4 is 12. Convert \frac{13}{6} and \frac{5}{4} to fractions with denominator 12.

$$\left(\frac{26}{12}+\frac{15}{12}\right)\times \frac{3}{82}$$

Since \frac{26}{12} and \frac{15}{12} have the same denominator, add them by adding their numerators.

$$\frac{26+15}{12}\times \frac{3}{82}$$

Add 26 and 15 to get 41.

$$\frac{41}{12}\times \frac{3}{82}$$

Multiply \frac{41}{12} times \frac{3}{82} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41\times 3}{12\times 82}$$

Do the multiplications in the fraction \frac{41\times 3}{12\times 82}.

$$\frac{123}{984}$$

Reduce the fraction \frac{123}{984} to lowest terms by extracting and canceling out 123.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$