Solve 21/2+42/3+13/4=

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

Evaluate

$$\frac{107}{12}\approx 8.916666667$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Add 4 and 1 to get 5.

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

Multiply 4 and 3 to get 12.

$$\frac{5}{2}+\frac{12+2}{3}+\frac{1\times 4+3}{4}$$

Add 12 and 2 to get 14.

$$\frac{5}{2}+\frac{14}{3}+\frac{1\times 4+3}{4}$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{14}{3} to fractions with denominator 6.

$$\frac{15}{6}+\frac{28}{6}+\frac{1\times 4+3}{4}$$

Since \frac{15}{6} and \frac{28}{6} have the same denominator, add them by adding their numerators.

$$\frac{15+28}{6}+\frac{1\times 4+3}{4}$$

Add 15 and 28 to get 43.

$$\frac{43}{6}+\frac{1\times 4+3}{4}$$

Multiply 1 and 4 to get 4.

$$\frac{43}{6}+\frac{4+3}{4}$$

Add 4 and 3 to get 7.

$$\frac{43}{6}+\frac{7}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{43}{6} and \frac{7}{4} to fractions with denominator 12.

$$\frac{86}{12}+\frac{21}{12}$$

Since \frac{86}{12} and \frac{21}{12} have the same denominator, add them by adding their numerators.

$$\frac{86+21}{12}$$

Add 86 and 21 to get 107.

$$\frac{107}{12}$$

Factor

$$\frac{107}{2 ^ {2} \cdot 3} = 8\frac{11}{12} = 8.916666666666666$$