Solve (-5/4)+(2/3-21/6)

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

Evaluate

$$-\frac{11}{4}=-2.75$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert -\frac{5}{4} and \frac{2}{3} to fractions with denominator 12.

$$-\frac{15}{12}+\frac{8}{12}-\frac{2\times 6+1}{6}$$

Since -\frac{15}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{-15+8}{12}-\frac{2\times 6+1}{6}$$

Add -15 and 8 to get -7.

$$-\frac{7}{12}-\frac{2\times 6+1}{6}$$

Multiply 2 and 6 to get 12.

$$-\frac{7}{12}-\frac{12+1}{6}$$

Add 12 and 1 to get 13.

$$-\frac{7}{12}-\frac{13}{6}$$

Least common multiple of 12 and 6 is 12. Convert -\frac{7}{12} and \frac{13}{6} to fractions with denominator 12.

$$-\frac{7}{12}-\frac{26}{12}$$

Since -\frac{7}{12} and \frac{26}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-7-26}{12}$$

Subtract 26 from -7 to get -33.

$$\frac{-33}{12}$$

Reduce the fraction \frac{-33}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{11}{4}$$

Factor

$$-\frac{11}{4} = -2\frac{3}{4} = -2.75$$