Solve 41/2-21/3+31/4

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

Evaluate

$$\frac{65}{12}\approx 5.416666667$$

Solution Steps

Multiply 4 and 2 to get 8.

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

Add 8 and 1 to get 9.

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

Multiply 2 and 3 to get 6.

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

Add 6 and 1 to get 7.

$$\frac{9}{2}-\frac{7}{3}+\frac{3\times 4+1}{4}$$

Least common multiple of 2 and 3 is 6. Convert \frac{9}{2} and \frac{7}{3} to fractions with denominator 6.

$$\frac{27}{6}-\frac{14}{6}+\frac{3\times 4+1}{4}$$

Since \frac{27}{6} and \frac{14}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-14}{6}+\frac{3\times 4+1}{4}$$

Subtract 14 from 27 to get 13.

$$\frac{13}{6}+\frac{3\times 4+1}{4}$$

Multiply 3 and 4 to get 12.

$$\frac{13}{6}+\frac{12+1}{4}$$

Add 12 and 1 to get 13.

$$\frac{13}{6}+\frac{13}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{13}{6} and \frac{13}{4} to fractions with denominator 12.

$$\frac{26}{12}+\frac{39}{12}$$

Since \frac{26}{12} and \frac{39}{12} have the same denominator, add them by adding their numerators.

$$\frac{26+39}{12}$$

Add 26 and 39 to get 65.

$$\frac{65}{12}$$

Factor

$$\frac{5 \cdot 13}{2 ^ {2} \cdot 3} = 5\frac{5}{12} = 5.416666666666667$$