Solve 8/9-3/6-21/18+5/24

$$\frac { 8 } { 9 } - \frac { 3 } { 6 } - \frac { 21 } { 18 } + \frac { 5 } { 24 }$$

Evaluate

$$-\frac{41}{72}\approx -0.569444444$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{8}{9}-\frac{1}{2}-\frac{21}{18}+\frac{5}{24}$$

Least common multiple of 9 and 2 is 18. Convert \frac{8}{9} and \frac{1}{2} to fractions with denominator 18.

$$\frac{16}{18}-\frac{9}{18}-\frac{21}{18}+\frac{5}{24}$$

Since \frac{16}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-9}{18}-\frac{21}{18}+\frac{5}{24}$$

Subtract 9 from 16 to get 7.

$$\frac{7}{18}-\frac{21}{18}+\frac{5}{24}$$

Since \frac{7}{18} and \frac{21}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-21}{18}+\frac{5}{24}$$

Subtract 21 from 7 to get -14.

$$\frac{-14}{18}+\frac{5}{24}$$

Reduce the fraction \frac{-14}{18} to lowest terms by extracting and canceling out 2.

$$-\frac{7}{9}+\frac{5}{24}$$

Least common multiple of 9 and 24 is 72. Convert -\frac{7}{9} and \frac{5}{24} to fractions with denominator 72.

$$-\frac{56}{72}+\frac{15}{72}$$

Since -\frac{56}{72} and \frac{15}{72} have the same denominator, add them by adding their numerators.

$$\frac{-56+15}{72}$$

Add -56 and 15 to get -41.

$$-\frac{41}{72}$$

Factor

$$-\frac{41}{72} = -0.5694444444444444$$