Solve 8/3-1/6+5/9+3/1=

$$\frac { 8 } { 3 } - \frac { 1 } { 6 } + \frac { 5 } { 9 } + \frac { 3 } { 1 } =$$

Evaluate

$$\frac{109}{18}\approx 6.055555556$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{8}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{16}{6}-\frac{1}{6}+\frac{5}{9}+\frac{3}{1}$$

Since \frac{16}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{16-1}{6}+\frac{5}{9}+\frac{3}{1}$$

Subtract 1 from 16 to get 15.

$$\frac{15}{6}+\frac{5}{9}+\frac{3}{1}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{2}+\frac{5}{9}+\frac{3}{1}$$

Least common multiple of 2 and 9 is 18. Convert \frac{5}{2} and \frac{5}{9} to fractions with denominator 18.

$$\frac{45}{18}+\frac{10}{18}+\frac{3}{1}$$

Since \frac{45}{18} and \frac{10}{18} have the same denominator, add them by adding their numerators.

$$\frac{45+10}{18}+\frac{3}{1}$$

Add 45 and 10 to get 55.

$$\frac{55}{18}+\frac{3}{1}$$

Anything divided by one gives itself.

$$\frac{55}{18}+3$$

Convert 3 to fraction \frac{54}{18}.

$$\frac{55}{18}+\frac{54}{18}$$

Since \frac{55}{18} and \frac{54}{18} have the same denominator, add them by adding their numerators.

$$\frac{55+54}{18}$$

Add 55 and 54 to get 109.

$$\frac{109}{18}$$

Factor

$$\frac{109}{2 \cdot 3 ^ {2}} = 6\frac{1}{18} = 6.055555555555555$$