Solve 2/3-(5/2+7/4)

$$\frac { 2 } { 3 } - ( \frac { 5 } { 2 } + \frac { 7 } { 4 } )$$

Evaluate

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

Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{5}{2} and \frac{7}{4} to fractions with denominator 4.

$$\frac{2}{3}-\left(\frac{10}{4}+\frac{7}{4}\right)$$

Since \frac{10}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}-\frac{10+7}{4}$$

Add 10 and 7 to get 17.

$$\frac{2}{3}-\frac{17}{4}$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{17}{4} to fractions with denominator 12.

$$\frac{8}{12}-\frac{51}{12}$$

Since \frac{8}{12} and \frac{51}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-51}{12}$$

Subtract 51 from 8 to get -43.

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

Factor

$$-\frac{43}{12} = -3\frac{7}{12} = -3.5833333333333335$$