Solve (7/6-1/12+1/36)*72/34

$$( \frac { 7 } { 6 } - \frac { 1 } { 12 } + \frac { 1 } { 36 } ) \cdot \frac { 72 } { 34 }$$

Evaluate

$$\frac{40}{17}\approx 2.352941176$$

Solution Steps

Least common multiple of 6 and 12 is 12. Convert \frac{7}{6} and \frac{1}{12} to fractions with denominator 12.

$$\left(\frac{14}{12}-\frac{1}{12}+\frac{1}{36}\right)\times \frac{72}{34}$$

Since \frac{14}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{14-1}{12}+\frac{1}{36}\right)\times \frac{72}{34}$$

Subtract 1 from 14 to get 13.

$$\left(\frac{13}{12}+\frac{1}{36}\right)\times \frac{72}{34}$$

Least common multiple of 12 and 36 is 36. Convert \frac{13}{12} and \frac{1}{36} to fractions with denominator 36.

$$\left(\frac{39}{36}+\frac{1}{36}\right)\times \frac{72}{34}$$

Since \frac{39}{36} and \frac{1}{36} have the same denominator, add them by adding their numerators.

$$\frac{39+1}{36}\times \frac{72}{34}$$

Add 39 and 1 to get 40.

$$\frac{40}{36}\times \frac{72}{34}$$

Reduce the fraction \frac{40}{36} to lowest terms by extracting and canceling out 4.

$$\frac{10}{9}\times \frac{72}{34}$$

Reduce the fraction \frac{72}{34} to lowest terms by extracting and canceling out 2.

$$\frac{10}{9}\times \frac{36}{17}$$

Multiply \frac{10}{9} times \frac{36}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 36}{9\times 17}$$

Do the multiplications in the fraction \frac{10\times 36}{9\times 17}.

$$\frac{360}{153}$$

Reduce the fraction \frac{360}{153} to lowest terms by extracting and canceling out 9.

$$\frac{40}{17}$$

Factor

$$\frac{2 ^ {3} \cdot 5}{17} = 2\frac{6}{17} = 2.3529411764705883$$