Solve 21/4+5/6+31/2

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

Evaluate

$$\frac{79}{12}\approx 6.583333333$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\frac{8+1}{4}+\frac{5}{6}+\frac{3\times 2+1}{2}$$

Add 8 and 1 to get 9.

$$\frac{9}{4}+\frac{5}{6}+\frac{3\times 2+1}{2}$$

Least common multiple of 4 and 6 is 12. Convert \frac{9}{4} and \frac{5}{6} to fractions with denominator 12.

$$\frac{27}{12}+\frac{10}{12}+\frac{3\times 2+1}{2}$$

Since \frac{27}{12} and \frac{10}{12} have the same denominator, add them by adding their numerators.

$$\frac{27+10}{12}+\frac{3\times 2+1}{2}$$

Add 27 and 10 to get 37.

$$\frac{37}{12}+\frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{37}{12}+\frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{37}{12}+\frac{7}{2}$$

Least common multiple of 12 and 2 is 12. Convert \frac{37}{12} and \frac{7}{2} to fractions with denominator 12.

$$\frac{37}{12}+\frac{42}{12}$$

Since \frac{37}{12} and \frac{42}{12} have the same denominator, add them by adding their numerators.

$$\frac{37+42}{12}$$

Add 37 and 42 to get 79.

$$\frac{79}{12}$$

Factor

$$\frac{79}{2 ^ {2} \cdot 3} = 6\frac{7}{12} = 6.583333333333333$$