Solve 5/6+[-1/5-1-(-3/2+11/3-frac{4}{9})-2-(frac{7}{18}-1+frac{4}{9})]

$$\frac { 5 } { 6 } + [ - \frac { 1 } { 5 } - 1 - ( - \frac { 3 } { 2 } + 1 \frac { 1 } { 3 } - \frac { 4 } { 9 } ) - 2 - ( \frac { 7 } { 18 } - 1 + \frac { 4 } { 9 } ) ]$$

Evaluate

$$-\frac{143}{90}\approx -1.588888889$$

Solution Steps

Convert 1 to fraction \frac{5}{5}.

$$\frac{5}{6}+-\frac{1}{5}-\frac{5}{5}-\left(-\frac{3}{2}+\frac{1\times 3+1}{3}-\frac{4}{9}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Since -\frac{1}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}+\frac{-1-5}{5}-\left(-\frac{3}{2}+\frac{1\times 3+1}{3}-\frac{4}{9}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Subtract 5 from -1 to get -6.

$$\frac{5}{6}+-\frac{6}{5}-\left(-\frac{3}{2}+\frac{1\times 3+1}{3}-\frac{4}{9}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Multiply 1 and 3 to get 3.

$$\frac{5}{6}+-\frac{6}{5}-\left(-\frac{3}{2}+\frac{3+1}{3}-\frac{4}{9}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Add 3 and 1 to get 4.

$$\frac{5}{6}+-\frac{6}{5}-\left(-\frac{3}{2}+\frac{4}{3}-\frac{4}{9}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{5}{6}+-\frac{6}{5}-\left(-\frac{9}{6}+\frac{8}{6}-\frac{4}{9}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Since -\frac{9}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}+-\frac{6}{5}-\left(\frac{-9+8}{6}-\frac{4}{9}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Add -9 and 8 to get -1.

$$\frac{5}{6}+-\frac{6}{5}-\left(-\frac{1}{6}-\frac{4}{9}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Least common multiple of 6 and 9 is 18. Convert -\frac{1}{6} and \frac{4}{9} to fractions with denominator 18.

$$\frac{5}{6}+-\frac{6}{5}-\left(-\frac{3}{18}-\frac{8}{18}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Since -\frac{3}{18} and \frac{8}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}+-\frac{6}{5}-\frac{-3-8}{18}-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Subtract 8 from -3 to get -11.

$$\frac{5}{6}+-\frac{6}{5}-\left(-\frac{11}{18}\right)-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

The opposite of -\frac{11}{18} is \frac{11}{18}.

$$\frac{5}{6}+-\frac{6}{5}+\frac{11}{18}-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Least common multiple of 5 and 18 is 90. Convert -\frac{6}{5} and \frac{11}{18} to fractions with denominator 90.

$$\frac{5}{6}+-\frac{108}{90}+\frac{55}{90}-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Since -\frac{108}{90} and \frac{55}{90} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}+\frac{-108+55}{90}-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Add -108 and 55 to get -53.

$$\frac{5}{6}+-\frac{53}{90}-2-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Convert 2 to fraction \frac{180}{90}.

$$\frac{5}{6}+-\frac{53}{90}-\frac{180}{90}-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Since -\frac{53}{90} and \frac{180}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}+\frac{-53-180}{90}-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

Subtract 180 from -53 to get -233.

$$\frac{5}{6}+-\frac{233}{90}-\left(\frac{7}{18}-1+\frac{4}{9}\right)$$

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

$$\frac{5}{6}+-\frac{233}{90}-\left(\frac{7}{18}-\frac{18}{18}+\frac{4}{9}\right)$$

Since \frac{7}{18} and \frac{18}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}+-\frac{233}{90}-\left(\frac{7-18}{18}+\frac{4}{9}\right)$$

Subtract 18 from 7 to get -11.

$$\frac{5}{6}+-\frac{233}{90}-\left(-\frac{11}{18}+\frac{4}{9}\right)$$

Least common multiple of 18 and 9 is 18. Convert -\frac{11}{18} and \frac{4}{9} to fractions with denominator 18.

$$\frac{5}{6}+-\frac{233}{90}-\left(-\frac{11}{18}+\frac{8}{18}\right)$$

Since -\frac{11}{18} and \frac{8}{18} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}-\frac{233}{90}-\frac{-11+8}{18}$$

Add -11 and 8 to get -3.

$$\frac{5}{6}-\frac{233}{90}-\frac{-3}{18}$$

Reduce the fraction \frac{-3}{18} to lowest terms by extracting and canceling out 3.

$$\frac{5}{6}+-\frac{233}{90}-\left(-\frac{1}{6}\right)$$

The opposite of -\frac{1}{6} is \frac{1}{6}.

$$\frac{5}{6}-\frac{233}{90}+\frac{1}{6}$$

Least common multiple of 90 and 6 is 90. Convert -\frac{233}{90} and \frac{1}{6} to fractions with denominator 90.

$$\frac{5}{6}-\frac{233}{90}+\frac{15}{90}$$

Since -\frac{233}{90} and \frac{15}{90} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}+\frac{-233+15}{90}$$

Add -233 and 15 to get -218.

$$\frac{5}{6}+\frac{-218}{90}$$

Reduce the fraction \frac{-218}{90} to lowest terms by extracting and canceling out 2.

$$\frac{5}{6}-\frac{109}{45}$$

Least common multiple of 6 and 45 is 90. Convert \frac{5}{6} and \frac{109}{45} to fractions with denominator 90.

$$\frac{75}{90}-\frac{218}{90}$$

Since \frac{75}{90} and \frac{218}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-218}{90}$$

Subtract 218 from 75 to get -143.

$$-\frac{143}{90}$$

Factor

$$-\frac{143}{90} = -1\frac{53}{90} = -1.5888888888888888$$