Solve 3/2-4/9+7/3-7/6-frac{5}{3}

$$\frac { 3 } { 2 } - \frac { 4 } { 9 } + \frac { 7 } { 3 } - \frac { 7 } { 6 } - \frac { 5 } { 3 }$$

Evaluate

$$\frac{5}{9}\approx 0.555555556$$

Solution Steps

Least common multiple of 2 and 9 is 18. Convert \frac{3}{2} and \frac{4}{9} to fractions with denominator 18.

$$\frac{27}{18}-\frac{8}{18}+\frac{7}{3}-\frac{7}{6}-\frac{5}{3}$$

Since \frac{27}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-8}{18}+\frac{7}{3}-\frac{7}{6}-\frac{5}{3}$$

Subtract 8 from 27 to get 19.

$$\frac{19}{18}+\frac{7}{3}-\frac{7}{6}-\frac{5}{3}$$

Least common multiple of 18 and 3 is 18. Convert \frac{19}{18} and \frac{7}{3} to fractions with denominator 18.

$$\frac{19}{18}+\frac{42}{18}-\frac{7}{6}-\frac{5}{3}$$

Since \frac{19}{18} and \frac{42}{18} have the same denominator, add them by adding their numerators.

$$\frac{19+42}{18}-\frac{7}{6}-\frac{5}{3}$$

Add 19 and 42 to get 61.

$$\frac{61}{18}-\frac{7}{6}-\frac{5}{3}$$

Least common multiple of 18 and 6 is 18. Convert \frac{61}{18} and \frac{7}{6} to fractions with denominator 18.

$$\frac{61}{18}-\frac{21}{18}-\frac{5}{3}$$

Since \frac{61}{18} and \frac{21}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{61-21}{18}-\frac{5}{3}$$

Subtract 21 from 61 to get 40.

$$\frac{40}{18}-\frac{5}{3}$$

Reduce the fraction \frac{40}{18} to lowest terms by extracting and canceling out 2.

$$\frac{20}{9}-\frac{5}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{20}{9} and \frac{5}{3} to fractions with denominator 9.

$$\frac{20}{9}-\frac{15}{9}$$

Since \frac{20}{9} and \frac{15}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-15}{9}$$

Subtract 15 from 20 to get 5.

$$\frac{5}{9}$$

Factor

$$\frac{5}{3 ^ {2}} = 0.5555555555555556$$