Solve 21/4+51/2+32/3

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

Evaluate

$$\frac{137}{12}\approx 11.416666667$$

Solution Steps

Multiply 2 and 4 to get 8.

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

Add 8 and 1 to get 9.

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

Multiply 5 and 2 to get 10.

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

Add 10 and 1 to get 11.

$$\frac{9}{4}+\frac{11}{2}+\frac{3\times 3+2}{3}$$

Least common multiple of 4 and 2 is 4. Convert \frac{9}{4} and \frac{11}{2} to fractions with denominator 4.

$$\frac{9}{4}+\frac{22}{4}+\frac{3\times 3+2}{3}$$

Since \frac{9}{4} and \frac{22}{4} have the same denominator, add them by adding their numerators.

$$\frac{9+22}{4}+\frac{3\times 3+2}{3}$$

Add 9 and 22 to get 31.

$$\frac{31}{4}+\frac{3\times 3+2}{3}$$

Multiply 3 and 3 to get 9.

$$\frac{31}{4}+\frac{9+2}{3}$$

Add 9 and 2 to get 11.

$$\frac{31}{4}+\frac{11}{3}$$

Least common multiple of 4 and 3 is 12. Convert \frac{31}{4} and \frac{11}{3} to fractions with denominator 12.

$$\frac{93}{12}+\frac{44}{12}$$

Since \frac{93}{12} and \frac{44}{12} have the same denominator, add them by adding their numerators.

$$\frac{93+44}{12}$$

Add 93 and 44 to get 137.

$$\frac{137}{12}$$

Factor

$$\frac{137}{2 ^ {2} \cdot 3} = 11\frac{5}{12} = 11.416666666666666$$