Solve 37/12-1/6+23/4

$$3 \frac { 7 } { 12 } - \frac { 1 } { 6 } + 2 \frac { 3 } { 4 }$$

Evaluate

$$\frac{37}{6}\approx 6.166666667$$

Solution Steps

Multiply 3 and 12 to get 36.

$$\frac{36+7}{12}-\frac{1}{6}+\frac{2\times 4+3}{4}$$

Add 36 and 7 to get 43.

$$\frac{43}{12}-\frac{1}{6}+\frac{2\times 4+3}{4}$$

Least common multiple of 12 and 6 is 12. Convert \frac{43}{12} and \frac{1}{6} to fractions with denominator 12.

$$\frac{43}{12}-\frac{2}{12}+\frac{2\times 4+3}{4}$$

Since \frac{43}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{43-2}{12}+\frac{2\times 4+3}{4}$$

Subtract 2 from 43 to get 41.

$$\frac{41}{12}+\frac{2\times 4+3}{4}$$

Multiply 2 and 4 to get 8.

$$\frac{41}{12}+\frac{8+3}{4}$$

Add 8 and 3 to get 11.

$$\frac{41}{12}+\frac{11}{4}$$

Least common multiple of 12 and 4 is 12. Convert \frac{41}{12} and \frac{11}{4} to fractions with denominator 12.

$$\frac{41}{12}+\frac{33}{12}$$

Since \frac{41}{12} and \frac{33}{12} have the same denominator, add them by adding their numerators.

$$\frac{41+33}{12}$$

Add 41 and 33 to get 74.

$$\frac{74}{12}$$

Reduce the fraction \frac{74}{12} to lowest terms by extracting and canceling out 2.

$$\frac{37}{6}$$

Factor

$$\frac{37}{2 \cdot 3} = 6\frac{1}{6} = 6.166666666666667$$