Solve (x+5/9)-51/3div2

$$( x + \frac { 5 } { 9 } ) - 5 \frac { 1 } { 3 } \div 2$$

Evaluate

$$x = -\frac{19}{9} = -2\frac{1}{9} = -2.111111111111111$$

Solution Steps

Express \frac{\frac{5\times 3+1}{3}}{2} as a single fraction.

$$x+\frac{5}{9}-\frac{5\times 3+1}{3\times 2}$$

Multiply 5 and 3 to get 15.

$$x+\frac{5}{9}-\frac{15+1}{3\times 2}$$

Add 15 and 1 to get 16.

$$x+\frac{5}{9}-\frac{16}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x+\frac{5}{9}-\frac{16}{6}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$x+\frac{5}{9}-\frac{8}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{5}{9} and \frac{8}{3} to fractions with denominator 9.

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

Since \frac{5}{9} and \frac{24}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 24 from 5 to get -19.

$$x-\frac{19}{9}$$

Expand

$$x = -\frac{19}{9} = -2\frac{1}{9} = -2.111111111111111$$

Solution Steps

Express \frac{\frac{5\times 3+1}{3}}{2} as a single fraction.

$$x+\frac{5}{9}-\frac{5\times 3+1}{3\times 2}$$

Multiply 5 and 3 to get 15.

$$x+\frac{5}{9}-\frac{15+1}{3\times 2}$$

Add 15 and 1 to get 16.

$$x+\frac{5}{9}-\frac{16}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$x+\frac{5}{9}-\frac{16}{6}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$x+\frac{5}{9}-\frac{8}{3}$$

Least common multiple of 9 and 3 is 9. Convert \frac{5}{9} and \frac{8}{3} to fractions with denominator 9.

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

Since \frac{5}{9} and \frac{24}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 24 from 5 to get -19.

$$x-\frac{19}{9}$$