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|\frac{9+1}{3}-\frac{4\times 3+2}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Multiply 3 and 3 to get 9.
|\frac{10}{3}-\frac{4\times 3+2}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Add 9 and 1 to get 10.
|\frac{10}{3}-\frac{12+2}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Multiply 4 and 3 to get 12.
|\frac{10}{3}-\frac{14}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Add 12 and 2 to get 14.
|\frac{10-14}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Since \frac{10}{3} and \frac{14}{3} have the same denominator, subtract them by subtracting their numerators.
|-\frac{4}{3}|-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Subtract 14 from 10 to get -4.
\frac{4}{3}-\left(-\frac{2\times 6+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{4}{3} is \frac{4}{3}.
\frac{4}{3}-\left(-\frac{12+5}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Multiply 2 and 6 to get 12.
\frac{4}{3}-\left(-\frac{17}{6}-\left(-1.5\right)-|-\frac{2\times 6+1}{6}|\right)
Add 12 and 5 to get 17.
\frac{4}{3}-\left(-\frac{17}{6}+1.5-|-\frac{2\times 6+1}{6}|\right)
The opposite of -1.5 is 1.5.
\frac{4}{3}-\left(-\frac{17}{6}+\frac{3}{2}-|-\frac{2\times 6+1}{6}|\right)
Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.
\frac{4}{3}-\left(-\frac{17}{6}+\frac{9}{6}-|-\frac{2\times 6+1}{6}|\right)
Least common multiple of 6 and 2 is 6. Convert -\frac{17}{6} and \frac{3}{2} to fractions with denominator 6.
\frac{4}{3}-\left(\frac{-17+9}{6}-|-\frac{2\times 6+1}{6}|\right)
Since -\frac{17}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.
\frac{4}{3}-\left(\frac{-8}{6}-|-\frac{2\times 6+1}{6}|\right)
Add -17 and 9 to get -8.
\frac{4}{3}-\left(-\frac{4}{3}-|-\frac{2\times 6+1}{6}|\right)
Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.
\frac{4}{3}-\left(-\frac{4}{3}-|-\frac{12+1}{6}|\right)
Multiply 2 and 6 to get 12.
\frac{4}{3}-\left(-\frac{4}{3}-|-\frac{13}{6}|\right)
Add 12 and 1 to get 13.
\frac{4}{3}-\left(-\frac{4}{3}-\frac{13}{6}\right)
The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{13}{6} is \frac{13}{6}.
\frac{4}{3}-\left(-\frac{8}{6}-\frac{13}{6}\right)
Least common multiple of 3 and 6 is 6. Convert -\frac{4}{3} and \frac{13}{6} to fractions with denominator 6.
\frac{4}{3}-\frac{-8-13}{6}
Since -\frac{8}{6} and \frac{13}{6} have the same denominator, subtract them by subtracting their numerators.
\frac{4}{3}-\frac{-21}{6}
Subtract 13 from -8 to get -21.
\frac{4}{3}-\left(-\frac{7}{2}\right)
Reduce the fraction \frac{-21}{6} to lowest terms by extracting and canceling out 3.
\frac{4}{3}+\frac{7}{2}
The opposite of -\frac{7}{2} is \frac{7}{2}.
\frac{8}{6}+\frac{21}{6}
Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{7}{2} to fractions with denominator 6.
\frac{8+21}{6}
Since \frac{8}{6} and \frac{21}{6} have the same denominator, add them by adding their numerators.
\frac{29}{6}
Add 8 and 21 to get 29.