Solve 5/4+[-7/3-(7/4-5/3)]

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

Evaluate

$$-\frac{7}{6}\approx -1.166666667$$

Solution Steps

Least common multiple of 4 and 3 is 12. Convert \frac{7}{4} and \frac{5}{3} to fractions with denominator 12.

$$\frac{5}{4}+-\frac{7}{3}-\left(\frac{21}{12}-\frac{20}{12}\right)$$

Since \frac{21}{12} and \frac{20}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}-\frac{7}{3}-\frac{21-20}{12}$$

Subtract 20 from 21 to get 1.

$$\frac{5}{4}-\frac{7}{3}-\frac{1}{12}$$

Least common multiple of 3 and 12 is 12. Convert -\frac{7}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{5}{4}-\frac{28}{12}-\frac{1}{12}$$

Since -\frac{28}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}+\frac{-28-1}{12}$$

Subtract 1 from -28 to get -29.

$$\frac{5}{4}-\frac{29}{12}$$

Least common multiple of 4 and 12 is 12. Convert \frac{5}{4} and \frac{29}{12} to fractions with denominator 12.

$$\frac{15}{12}-\frac{29}{12}$$

Since \frac{15}{12} and \frac{29}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-29}{12}$$

Subtract 29 from 15 to get -14.

$$\frac{-14}{12}$$

Reduce the fraction \frac{-14}{12} to lowest terms by extracting and canceling out 2.

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

Factor

$$-\frac{7}{6} = -1\frac{1}{6} = -1.1666666666666667$$