Solve 4/3-(1/9-7/3)+(-3/2-1)+frac{17}{18}

$$\frac { 4 } { 3 } - ( \frac { 1 } { 9 } - \frac { 7 } { 3 } ) + ( - \frac { 3 } { 2 } - 1 ) + \frac { 17 } { 18 }$$

Evaluate

$$2$$

Solution Steps

Least common multiple of 9 and 3 is 9. Convert \frac{1}{9} and \frac{7}{3} to fractions with denominator 9.

$$\frac{4}{3}-\left(\frac{1}{9}-\frac{21}{9}\right)-\frac{3}{2}-1+\frac{17}{18}$$

Since \frac{1}{9} and \frac{21}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{3}-\frac{1-21}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Subtract 21 from 1 to get -20.

$$\frac{4}{3}-\left(-\frac{20}{9}\right)-\frac{3}{2}-1+\frac{17}{18}$$

The opposite of -\frac{20}{9} is \frac{20}{9}.

$$\frac{4}{3}+\frac{20}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Least common multiple of 3 and 9 is 9. Convert \frac{4}{3} and \frac{20}{9} to fractions with denominator 9.

$$\frac{12}{9}+\frac{20}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Since \frac{12}{9} and \frac{20}{9} have the same denominator, add them by adding their numerators.

$$\frac{12+20}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Add 12 and 20 to get 32.

$$\frac{32}{9}-\frac{3}{2}-1+\frac{17}{18}$$

Least common multiple of 9 and 2 is 18. Convert \frac{32}{9} and \frac{3}{2} to fractions with denominator 18.

$$\frac{64}{18}-\frac{27}{18}-1+\frac{17}{18}$$

Since \frac{64}{18} and \frac{27}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64-27}{18}-1+\frac{17}{18}$$

Subtract 27 from 64 to get 37.

$$\frac{37}{18}-1+\frac{17}{18}$$

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

$$\frac{37}{18}-\frac{18}{18}+\frac{17}{18}$$

Since \frac{37}{18} and \frac{18}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{37-18}{18}+\frac{17}{18}$$

Subtract 18 from 37 to get 19.

$$\frac{19}{18}+\frac{17}{18}$$

Since \frac{19}{18} and \frac{17}{18} have the same denominator, add them by adding their numerators.

$$\frac{19+17}{18}$$

Add 19 and 17 to get 36.

$$\frac{36}{18}$$

Divide 36 by 18 to get 2.

$$2$$

Factor

$$2$$