Solve 5/6+2/3-(3/4+1/6)=

$$\frac{ 5 }{ 6 } + \frac{ 2 }{ 3 } -( \frac{ 3 }{ 4 } + \frac{ 1 }{ 6 } )=$$

Evaluate

$$\frac{7}{12}\approx 0.583333333$$

Solution Steps

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

$$\frac{5}{6}+\frac{4}{6}-\left(\frac{3}{4}+\frac{1}{6}\right)$$

Since \frac{5}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{5+4}{6}-\left(\frac{3}{4}+\frac{1}{6}\right)$$

Add 5 and 4 to get 9.

$$\frac{9}{6}-\left(\frac{3}{4}+\frac{1}{6}\right)$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{3}{2}-\left(\frac{3}{4}+\frac{1}{6}\right)$$

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{3}{2}-\left(\frac{9}{12}+\frac{2}{12}\right)$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$\frac{3}{2}-\frac{9+2}{12}$$

Add 9 and 2 to get 11.

$$\frac{3}{2}-\frac{11}{12}$$

Least common multiple of 2 and 12 is 12. Convert \frac{3}{2} and \frac{11}{12} to fractions with denominator 12.

$$\frac{18}{12}-\frac{11}{12}$$

Since \frac{18}{12} and \frac{11}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-11}{12}$$

Subtract 11 from 18 to get 7.

$$\frac{7}{12}$$

Factor

$$\frac{7}{2 ^ {2} \cdot 3} = 0.5833333333333334$$