Solve (2-3/9)-(21/9-(12/9-(15/10-frac{3}{9}))-1+frac{3}{9})

$$( 2 - \frac { 3 } { 9 } ) - ( \frac { 21 } { 9 } - ( \frac { 12 } { 9 } - ( \frac { 15 } { 10 } - \frac { 3 } { 9 } ) ) - 1 + \frac { 3 } { 9 } )$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$2-\frac{1}{3}-\left(\frac{21}{9}-\left(\frac{12}{9}-\left(\frac{15}{10}-\frac{3}{9}\right)\right)-1+\frac{3}{9}\right)$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{6}{3}-\frac{1}{3}-\left(\frac{21}{9}-\left(\frac{12}{9}-\left(\frac{15}{10}-\frac{3}{9}\right)\right)-1+\frac{3}{9}\right)$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-1}{3}-\left(\frac{21}{9}-\left(\frac{12}{9}-\left(\frac{15}{10}-\frac{3}{9}\right)\right)-1+\frac{3}{9}\right)$$

Subtract 1 from 6 to get 5.

$$\frac{5}{3}-\left(\frac{21}{9}-\left(\frac{12}{9}-\left(\frac{15}{10}-\frac{3}{9}\right)\right)-1+\frac{3}{9}\right)$$

Reduce the fraction \frac{21}{9} to lowest terms by extracting and canceling out 3.

$$\frac{5}{3}-\left(\frac{7}{3}-\left(\frac{12}{9}-\left(\frac{15}{10}-\frac{3}{9}\right)\right)-1+\frac{3}{9}\right)$$

Reduce the fraction \frac{12}{9} to lowest terms by extracting and canceling out 3.

$$\frac{5}{3}-\left(\frac{7}{3}-\left(\frac{4}{3}-\left(\frac{15}{10}-\frac{3}{9}\right)\right)-1+\frac{3}{9}\right)$$

Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

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

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

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

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{1}{3} to fractions with denominator 6.

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

Since \frac{9}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 9 to get 7.

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

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{7}{6} to fractions with denominator 6.

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

Since \frac{8}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 7 from 8 to get 1.

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

Least common multiple of 3 and 6 is 6. Convert \frac{7}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{5}{3}-\left(\frac{14}{6}-\frac{1}{6}-1+\frac{3}{9}\right)$$

Since \frac{14}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}-\left(\frac{14-1}{6}-1+\frac{3}{9}\right)$$

Subtract 1 from 14 to get 13.

$$\frac{5}{3}-\left(\frac{13}{6}-1+\frac{3}{9}\right)$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{5}{3}-\left(\frac{13}{6}-\frac{6}{6}+\frac{3}{9}\right)$$

Since \frac{13}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{3}-\left(\frac{13-6}{6}+\frac{3}{9}\right)$$

Subtract 6 from 13 to get 7.

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

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

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

Least common multiple of 6 and 3 is 6. Convert \frac{7}{6} and \frac{1}{3} to fractions with denominator 6.

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

Since \frac{7}{6} and \frac{2}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{3}-\frac{7+2}{6}$$

Add 7 and 2 to get 9.

$$\frac{5}{3}-\frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{3}-\frac{3}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{3}{2} to fractions with denominator 6.

$$\frac{10}{6}-\frac{9}{6}$$

Since \frac{10}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-9}{6}$$

Subtract 9 from 10 to get 1.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$