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

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

Evaluate

$$\frac{17}{12}\approx 1.416666667$$

Solution Steps

Multiply \frac{2}{3} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

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

The opposite of -\frac{1}{3} is \frac{1}{3}.

$$\frac{5}{6}+\frac{1}{3}+\frac{1}{4}$$

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{5}{6}+\frac{2}{6}+\frac{1}{4}$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{5+2}{6}+\frac{1}{4}$$

Add 5 and 2 to get 7.

$$\frac{7}{6}+\frac{1}{4}$$

Least common multiple of 6 and 4 is 12. Convert \frac{7}{6} and \frac{1}{4} to fractions with denominator 12.

$$\frac{14}{12}+\frac{3}{12}$$

Since \frac{14}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{14+3}{12}$$

Add 14 and 3 to get 17.

$$\frac{17}{12}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$