Solve 41/2+31/3+21/4=?

$$4 \frac { 1 } { 2 } + 3 \frac { 1 } { 3 } + 2 \frac { 1 } { 4 } = ?$$

Evaluate

$$\frac{121}{12}\approx 10.083333333$$

Solution Steps

Multiply 4 and 2 to get 8.

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

Add 8 and 1 to get 9.

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

Multiply 3 and 3 to get 9.

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

Add 9 and 1 to get 10.

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

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{10}{3} to fractions with denominator 6.

$$\frac{27}{6}+\frac{20}{6}+\frac{2\times 4+1}{4}$$

Since \frac{27}{6} and \frac{20}{6} have the same denominator, add them by adding their numerators.

$$\frac{27+20}{6}+\frac{2\times 4+1}{4}$$

Add 27 and 20 to get 47.

$$\frac{47}{6}+\frac{2\times 4+1}{4}$$

Multiply 2 and 4 to get 8.

$$\frac{47}{6}+\frac{8+1}{4}$$

Add 8 and 1 to get 9.

$$\frac{47}{6}+\frac{9}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{47}{6} and \frac{9}{4} to fractions with denominator 12.

$$\frac{94}{12}+\frac{27}{12}$$

Since \frac{94}{12} and \frac{27}{12} have the same denominator, add them by adding their numerators.

$$\frac{94+27}{12}$$

Add 94 and 27 to get 121.

$$\frac{121}{12}$$

Factor

$$\frac{11 ^ {2}}{2 ^ {2} \cdot 3} = 10\frac{1}{12} = 10.083333333333334$$