Solve (67/12-317/36)*21/2-41/3

$$( 6 \frac { 7 } { 12 } - 3 \frac { 17 } { 36 } ) \cdot 2 \frac { 1 } { 2 } - 4 \frac { 1 } { 3 }$$

Evaluate

$$\frac{31}{9}\approx 3.444444444$$

Solution Steps

Multiply 6 and 12 to get 72.

$$\left(\frac{72+7}{12}-\frac{3\times 36+17}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}$$

Add 72 and 7 to get 79.

$$\left(\frac{79}{12}-\frac{3\times 36+17}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}$$

Multiply 3 and 36 to get 108.

$$\left(\frac{79}{12}-\frac{108+17}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}$$

Add 108 and 17 to get 125.

$$\left(\frac{79}{12}-\frac{125}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}$$

Least common multiple of 12 and 36 is 36. Convert \frac{79}{12} and \frac{125}{36} to fractions with denominator 36.

$$\left(\frac{237}{36}-\frac{125}{36}\right)\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}$$

Since \frac{237}{36} and \frac{125}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{237-125}{36}\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}$$

Subtract 125 from 237 to get 112.

$$\frac{112}{36}\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}$$

Reduce the fraction \frac{112}{36} to lowest terms by extracting and canceling out 4.

$$\frac{28}{9}\times \frac{2\times 2+1}{2}-\frac{4\times 3+1}{3}$$

Multiply 2 and 2 to get 4.

$$\frac{28}{9}\times \frac{4+1}{2}-\frac{4\times 3+1}{3}$$

Add 4 and 1 to get 5.

$$\frac{28}{9}\times \frac{5}{2}-\frac{4\times 3+1}{3}$$

Multiply \frac{28}{9} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28\times 5}{9\times 2}-\frac{4\times 3+1}{3}$$

Do the multiplications in the fraction \frac{28\times 5}{9\times 2}.

$$\frac{140}{18}-\frac{4\times 3+1}{3}$$

Reduce the fraction \frac{140}{18} to lowest terms by extracting and canceling out 2.

$$\frac{70}{9}-\frac{4\times 3+1}{3}$$

Multiply 4 and 3 to get 12.

$$\frac{70}{9}-\frac{12+1}{3}$$

Add 12 and 1 to get 13.

$$\frac{70}{9}-\frac{13}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{70}{9} and \frac{13}{3} to fractions with denominator 9.

$$\frac{70}{9}-\frac{39}{9}$$

Since \frac{70}{9} and \frac{39}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{70-39}{9}$$

Subtract 39 from 70 to get 31.

$$\frac{31}{9}$$

Factor

$$\frac{31}{3 ^ {2}} = 3\frac{4}{9} = 3.4444444444444446$$