Solve 105/6-71/2+1/4

$$10 \frac { 5 } { 6 } - 7 \frac { 1 } { 2 } + \frac { 1 } { 4 }$$

Evaluate

$$\frac{43}{12}\approx 3.583333333$$

Solution Steps

Multiply 10 and 6 to get 60.

$$\frac{60+5}{6}-\frac{7\times 2+1}{2}+\frac{1}{4}$$

Add 60 and 5 to get 65.

$$\frac{65}{6}-\frac{7\times 2+1}{2}+\frac{1}{4}$$

Multiply 7 and 2 to get 14.

$$\frac{65}{6}-\frac{14+1}{2}+\frac{1}{4}$$

Add 14 and 1 to get 15.

$$\frac{65}{6}-\frac{15}{2}+\frac{1}{4}$$

Least common multiple of 6 and 2 is 6. Convert \frac{65}{6} and \frac{15}{2} to fractions with denominator 6.

$$\frac{65}{6}-\frac{45}{6}+\frac{1}{4}$$

Since \frac{65}{6} and \frac{45}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-45}{6}+\frac{1}{4}$$

Subtract 45 from 65 to get 20.

$$\frac{20}{6}+\frac{1}{4}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$\frac{10}{3}+\frac{1}{4}$$

Least common multiple of 3 and 4 is 12. Convert \frac{10}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{40}{12}+\frac{3}{12}$$

Since \frac{40}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{40+3}{12}$$

Add 40 and 3 to get 43.

$$\frac{43}{12}$$

Factor

$$\frac{43}{2 ^ {2} \cdot 3} = 3\frac{7}{12} = 3.5833333333333335$$