Solve 21/4+31/3-11/2+11/6

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

Evaluate

$$\frac{21}{4}=5.25$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+1}{4}+\frac{3\times 3+1}{3}-\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$

Add 8 and 1 to get 9.

$$\frac{9}{4}+\frac{3\times 3+1}{3}-\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$

Multiply 3 and 3 to get 9.

$$\frac{9}{4}+\frac{9+1}{3}-\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$

Add 9 and 1 to get 10.

$$\frac{9}{4}+\frac{10}{3}-\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$

Least common multiple of 4 and 3 is 12. Convert \frac{9}{4} and \frac{10}{3} to fractions with denominator 12.

$$\frac{27}{12}+\frac{40}{12}-\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$

Since \frac{27}{12} and \frac{40}{12} have the same denominator, add them by adding their numerators.

$$\frac{27+40}{12}-\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$

Add 27 and 40 to get 67.

$$\frac{67}{12}-\frac{1\times 2+1}{2}+\frac{1\times 6+1}{6}$$

Multiply 1 and 2 to get 2.

$$\frac{67}{12}-\frac{2+1}{2}+\frac{1\times 6+1}{6}$$

Add 2 and 1 to get 3.

$$\frac{67}{12}-\frac{3}{2}+\frac{1\times 6+1}{6}$$

Least common multiple of 12 and 2 is 12. Convert \frac{67}{12} and \frac{3}{2} to fractions with denominator 12.

$$\frac{67}{12}-\frac{18}{12}+\frac{1\times 6+1}{6}$$

Since \frac{67}{12} and \frac{18}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{67-18}{12}+\frac{1\times 6+1}{6}$$

Subtract 18 from 67 to get 49.

$$\frac{49}{12}+\frac{1\times 6+1}{6}$$

Multiply 1 and 6 to get 6.

$$\frac{49}{12}+\frac{6+1}{6}$$

Add 6 and 1 to get 7.

$$\frac{49}{12}+\frac{7}{6}$$

Least common multiple of 12 and 6 is 12. Convert \frac{49}{12} and \frac{7}{6} to fractions with denominator 12.

$$\frac{49}{12}+\frac{14}{12}$$

Since \frac{49}{12} and \frac{14}{12} have the same denominator, add them by adding their numerators.

$$\frac{49+14}{12}$$

Add 49 and 14 to get 63.

$$\frac{63}{12}$$

Reduce the fraction \frac{63}{12} to lowest terms by extracting and canceling out 3.

$$\frac{21}{4}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2}} = 5\frac{1}{4} = 5.25$$