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

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

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{5}{3} and \frac{3}{4} to fractions with denominator 12.

$$\frac{3}{4}-\left(\frac{20}{12}+\frac{9}{12}\right)$$

Since \frac{20}{12} and \frac{9}{12} have the same denominator, add them by adding their numerators.

$$\frac{3}{4}-\frac{20+9}{12}$$

Add 20 and 9 to get 29.

$$\frac{3}{4}-\frac{29}{12}$$

Least common multiple of 4 and 12 is 12. Convert \frac{3}{4} and \frac{29}{12} to fractions with denominator 12.

$$\frac{9}{12}-\frac{29}{12}$$

Since \frac{9}{12} and \frac{29}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-29}{12}$$

Subtract 29 from 9 to get -20.

$$\frac{-20}{12}$$

Reduce the fraction \frac{-20}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{5}{3}$$

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$