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

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

Evaluate

$$-\frac{25}{12}\approx -2.083333333$$

Solution Steps

Convert 6 to fraction \frac{12}{2}.

$$\frac{5}{6}-\frac{2}{3}\left(\frac{12}{2}-\frac{1}{2}\right)+\frac{3}{4}$$

Since \frac{12}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}-\frac{2}{3}\times \frac{12-1}{2}+\frac{3}{4}$$

Subtract 1 from 12 to get 11.

$$\frac{5}{6}-\frac{2}{3}\times \frac{11}{2}+\frac{3}{4}$$

Multiply \frac{2}{3} times \frac{11}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{6}-\frac{2\times 11}{3\times 2}+\frac{3}{4}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5}{6}-\frac{11}{3}+\frac{3}{4}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{11}{3} to fractions with denominator 6.

$$\frac{5}{6}-\frac{22}{6}+\frac{3}{4}$$

Since \frac{5}{6} and \frac{22}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-22}{6}+\frac{3}{4}$$

Subtract 22 from 5 to get -17.

$$-\frac{17}{6}+\frac{3}{4}$$

Least common multiple of 6 and 4 is 12. Convert -\frac{17}{6} and \frac{3}{4} to fractions with denominator 12.

$$-\frac{34}{12}+\frac{9}{12}$$

Since -\frac{34}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{-34+9}{12}$$

Add -34 and 9 to get -25.

$$-\frac{25}{12}$$

Factor

$$-\frac{25}{12} = -2\frac{1}{12} = -2.0833333333333335$$