Solve 11/2-5/6+21/4

$$1 \frac { 1 } { 2 } - \frac { 5 } { 6 } + 2 \frac { 1 } { 4 }$$

Evaluate

$$\frac{35}{12}\approx 2.916666667$$

Solution Steps

Multiply 1 and 2 to get 2.

$$\frac{2+1}{2}-\frac{5}{6}+\frac{2\times 4+1}{4}$$

Add 2 and 1 to get 3.

$$\frac{3}{2}-\frac{5}{6}+\frac{2\times 4+1}{4}$$

Least common multiple of 2 and 6 is 6. Convert \frac{3}{2} and \frac{5}{6} to fractions with denominator 6.

$$\frac{9}{6}-\frac{5}{6}+\frac{2\times 4+1}{4}$$

Since \frac{9}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-5}{6}+\frac{2\times 4+1}{4}$$

Subtract 5 from 9 to get 4.

$$\frac{4}{6}+\frac{2\times 4+1}{4}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{2}{3}+\frac{2\times 4+1}{4}$$

Multiply 2 and 4 to get 8.

$$\frac{2}{3}+\frac{8+1}{4}$$

Add 8 and 1 to get 9.

$$\frac{2}{3}+\frac{9}{4}$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{9}{4} to fractions with denominator 12.

$$\frac{8}{12}+\frac{27}{12}$$

Since \frac{8}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{8+27}{12}$$

Add 8 and 27 to get 35.

$$\frac{35}{12}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2} \cdot 3} = 2\frac{11}{12} = 2.9166666666666665$$