Solve 4/3-(1/9-1/3)+(-3/2-1)+frac{17}{18}

$$\frac{ 4 }{ 3 } -( \frac{ 1 }{ 9 } - \frac{ 1 }{ 3 } )+(- \frac{ 3 }{ 2 } -1)+ \frac{ 17 }{ 18 }$$

Evaluate

$$0$$

Solution Steps

Least common multiple of 9 and 3 is 9. Convert \frac{1}{9} and \frac{1}{3} to fractions with denominator 9.

$$\frac{4}{3}-\left(\frac{1}{9}-\frac{3}{9}\right)-\frac{3}{2}-1+\frac{17}{18}$$

Since \frac{1}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}-\frac{1-3}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Subtract 3 from 1 to get -2.

$$\frac{4}{3}-\left(-\frac{2}{9}\right)-\frac{3}{2}-1+\frac{17}{18}$$

The opposite of -\frac{2}{9} is \frac{2}{9}.

$$\frac{4}{3}+\frac{2}{9}-\frac{3}{2}-1+\frac{17}{18}$$

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

$$\frac{12}{9}+\frac{2}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Since \frac{12}{9} and \frac{2}{9} have the same denominator, add them by adding their numerators.

$$\frac{12+2}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Add 12 and 2 to get 14.

$$\frac{14}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Least common multiple of 9 and 2 is 18. Convert \frac{14}{9} and \frac{3}{2} to fractions with denominator 18.

$$\frac{28}{18}-\frac{27}{18}-1+\frac{17}{18}$$

Since \frac{28}{18} and \frac{27}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{28-27}{18}-1+\frac{17}{18}$$

Subtract 27 from 28 to get 1.

$$\frac{1}{18}-1+\frac{17}{18}$$

Convert 1 to fraction \frac{18}{18}.

$$\frac{1}{18}-\frac{18}{18}+\frac{17}{18}$$

Since \frac{1}{18} and \frac{18}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-18}{18}+\frac{17}{18}$$

Subtract 18 from 1 to get -17.

$$-\frac{17}{18}+\frac{17}{18}$$

Add -\frac{17}{18} and \frac{17}{18} to get 0.

$$0$$

Factor

$$0$$