Solve {-7/6+1-[(11/3-3/5-6)+(5/6-frac{8}{15}+frac{8}{3})]+frac{13}{10}}-frac{6}{5}

$$\{ - \frac { 7 } { 6 } + 1 - [ ( \frac { 11 } { 3 } - \frac { 3 } { 5 } - 6 ) + ( \frac { 5 } { 6 } - \frac { 8 } { 15 } + \frac { 8 } { 3 } ) ] + \frac { 13 } { 10 } \} - \frac { 6 } { 5 }$$

Evaluate

$$-\frac{1}{10}=-0.1$$

Solution Steps

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

$$-\frac{7}{6}+\frac{6}{6}-\left(\frac{11}{3}-\frac{3}{5}-6+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

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

$$\frac{-7+6}{6}-\left(\frac{11}{3}-\frac{3}{5}-6+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Add -7 and 6 to get -1.

$$-\frac{1}{6}-\left(\frac{11}{3}-\frac{3}{5}-6+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{11}{3} and \frac{3}{5} to fractions with denominator 15.

$$-\frac{1}{6}-\left(\frac{55}{15}-\frac{9}{15}-6+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Since \frac{55}{15} and \frac{9}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}-\left(\frac{55-9}{15}-6+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Subtract 9 from 55 to get 46.

$$-\frac{1}{6}-\left(\frac{46}{15}-6+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Convert 6 to fraction \frac{90}{15}.

$$-\frac{1}{6}-\left(\frac{46}{15}-\frac{90}{15}+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Since \frac{46}{15} and \frac{90}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}-\left(\frac{46-90}{15}+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Subtract 90 from 46 to get -44.

$$-\frac{1}{6}-\left(-\frac{44}{15}+\frac{5}{6}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Least common multiple of 15 and 6 is 30. Convert -\frac{44}{15} and \frac{5}{6} to fractions with denominator 30.

$$-\frac{1}{6}-\left(-\frac{88}{30}+\frac{25}{30}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Since -\frac{88}{30} and \frac{25}{30} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}-\left(\frac{-88+25}{30}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Add -88 and 25 to get -63.

$$-\frac{1}{6}-\left(\frac{-63}{30}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Reduce the fraction \frac{-63}{30} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{6}-\left(-\frac{21}{10}-\frac{8}{15}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Least common multiple of 10 and 15 is 30. Convert -\frac{21}{10} and \frac{8}{15} to fractions with denominator 30.

$$-\frac{1}{6}-\left(-\frac{63}{30}-\frac{16}{30}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Since -\frac{63}{30} and \frac{16}{30} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}-\left(\frac{-63-16}{30}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Subtract 16 from -63 to get -79.

$$-\frac{1}{6}-\left(-\frac{79}{30}+\frac{8}{3}\right)+\frac{13}{10}-\frac{6}{5}$$

Least common multiple of 30 and 3 is 30. Convert -\frac{79}{30} and \frac{8}{3} to fractions with denominator 30.

$$-\frac{1}{6}-\left(-\frac{79}{30}+\frac{80}{30}\right)+\frac{13}{10}-\frac{6}{5}$$

Since -\frac{79}{30} and \frac{80}{30} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}-\frac{-79+80}{30}+\frac{13}{10}-\frac{6}{5}$$

Add -79 and 80 to get 1.

$$-\frac{1}{6}-\frac{1}{30}+\frac{13}{10}-\frac{6}{5}$$

Least common multiple of 6 and 30 is 30. Convert -\frac{1}{6} and \frac{1}{30} to fractions with denominator 30.

$$-\frac{5}{30}-\frac{1}{30}+\frac{13}{10}-\frac{6}{5}$$

Since -\frac{5}{30} and \frac{1}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-1}{30}+\frac{13}{10}-\frac{6}{5}$$

Subtract 1 from -5 to get -6.

$$\frac{-6}{30}+\frac{13}{10}-\frac{6}{5}$$

Reduce the fraction \frac{-6}{30} to lowest terms by extracting and canceling out 6.

$$-\frac{1}{5}+\frac{13}{10}-\frac{6}{5}$$

Least common multiple of 5 and 10 is 10. Convert -\frac{1}{5} and \frac{13}{10} to fractions with denominator 10.

$$-\frac{2}{10}+\frac{13}{10}-\frac{6}{5}$$

Since -\frac{2}{10} and \frac{13}{10} have the same denominator, add them by adding their numerators.

$$\frac{-2+13}{10}-\frac{6}{5}$$

Add -2 and 13 to get 11.

$$\frac{11}{10}-\frac{6}{5}$$

Least common multiple of 10 and 5 is 10. Convert \frac{11}{10} and \frac{6}{5} to fractions with denominator 10.

$$\frac{11}{10}-\frac{12}{10}$$

Since \frac{11}{10} and \frac{12}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-12}{10}$$

Subtract 12 from 11 to get -1.

$$-\frac{1}{10}$$

Factor

$$-\frac{1}{10} = -0.1$$