Solve +18/6-3/2+8-6-1/5-2/3+frac{5}{3}+frac{6}{36}-1+frac{7}{14}-10-4+frac{4}{5}+frac{2}{3}

$$+ \frac { 18 } { 6 } - \frac { 3 } { 2 } + 8 - 6 - \frac { 1 } { 5 } - \frac { 2 } { 3 } + \frac { 5 } { 3 } + \frac { 6 } { 36 } - 1 + \frac { 7 } { 14 } - 10 - 4 + \frac { 4 } { 5 } + \frac { 2 } { 3 }$$

Evaluate

$$-\frac{257}{30}\approx -8.566666667$$

Solution Steps

Divide 18 by 6 to get 3.

$$3-\frac{3}{2}+8-6-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

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

$$\frac{6}{2}-\frac{3}{2}+8-6-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{6}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-3}{2}+8-6-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Subtract 3 from 6 to get 3.

$$\frac{3}{2}+8-6-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Convert 8 to fraction \frac{16}{2}.

$$\frac{3}{2}+\frac{16}{2}-6-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{3}{2} and \frac{16}{2} have the same denominator, add them by adding their numerators.

$$\frac{3+16}{2}-6-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Add 3 and 16 to get 19.

$$\frac{19}{2}-6-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{19}{2}-\frac{12}{2}-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{19}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{19-12}{2}-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Subtract 12 from 19 to get 7.

$$\frac{7}{2}-\frac{1}{5}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Least common multiple of 2 and 5 is 10. Convert \frac{7}{2} and \frac{1}{5} to fractions with denominator 10.

$$\frac{35}{10}-\frac{2}{10}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{35}{10} and \frac{2}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-2}{10}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Subtract 2 from 35 to get 33.

$$\frac{33}{10}-\frac{2}{3}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Least common multiple of 10 and 3 is 30. Convert \frac{33}{10} and \frac{2}{3} to fractions with denominator 30.

$$\frac{99}{30}-\frac{20}{30}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{99}{30} and \frac{20}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{99-20}{30}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Subtract 20 from 99 to get 79.

$$\frac{79}{30}+\frac{5}{3}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Least common multiple of 30 and 3 is 30. Convert \frac{79}{30} and \frac{5}{3} to fractions with denominator 30.

$$\frac{79}{30}+\frac{50}{30}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{79}{30} and \frac{50}{30} have the same denominator, add them by adding their numerators.

$$\frac{79+50}{30}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Add 79 and 50 to get 129.

$$\frac{129}{30}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Reduce the fraction \frac{129}{30} to lowest terms by extracting and canceling out 3.

$$\frac{43}{10}+\frac{6}{36}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Reduce the fraction \frac{6}{36} to lowest terms by extracting and canceling out 6.

$$\frac{43}{10}+\frac{1}{6}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Least common multiple of 10 and 6 is 30. Convert \frac{43}{10} and \frac{1}{6} to fractions with denominator 30.

$$\frac{129}{30}+\frac{5}{30}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{129}{30} and \frac{5}{30} have the same denominator, add them by adding their numerators.

$$\frac{129+5}{30}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Add 129 and 5 to get 134.

$$\frac{134}{30}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Reduce the fraction \frac{134}{30} to lowest terms by extracting and canceling out 2.

$$\frac{67}{15}-1+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Convert 1 to fraction \frac{15}{15}.

$$\frac{67}{15}-\frac{15}{15}+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{67}{15} and \frac{15}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{67-15}{15}+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Subtract 15 from 67 to get 52.

$$\frac{52}{15}+\frac{7}{14}-10-4+\frac{4}{5}+\frac{2}{3}$$

Reduce the fraction \frac{7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{52}{15}+\frac{1}{2}-10-4+\frac{4}{5}+\frac{2}{3}$$

Least common multiple of 15 and 2 is 30. Convert \frac{52}{15} and \frac{1}{2} to fractions with denominator 30.

$$\frac{104}{30}+\frac{15}{30}-10-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{104}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$\frac{104+15}{30}-10-4+\frac{4}{5}+\frac{2}{3}$$

Add 104 and 15 to get 119.

$$\frac{119}{30}-10-4+\frac{4}{5}+\frac{2}{3}$$

Convert 10 to fraction \frac{300}{30}.

$$\frac{119}{30}-\frac{300}{30}-4+\frac{4}{5}+\frac{2}{3}$$

Since \frac{119}{30} and \frac{300}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{119-300}{30}-4+\frac{4}{5}+\frac{2}{3}$$

Subtract 300 from 119 to get -181.

$$-\frac{181}{30}-4+\frac{4}{5}+\frac{2}{3}$$

Convert 4 to fraction \frac{120}{30}.

$$-\frac{181}{30}-\frac{120}{30}+\frac{4}{5}+\frac{2}{3}$$

Since -\frac{181}{30} and \frac{120}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-181-120}{30}+\frac{4}{5}+\frac{2}{3}$$

Subtract 120 from -181 to get -301.

$$-\frac{301}{30}+\frac{4}{5}+\frac{2}{3}$$

Least common multiple of 30 and 5 is 30. Convert -\frac{301}{30} and \frac{4}{5} to fractions with denominator 30.

$$-\frac{301}{30}+\frac{24}{30}+\frac{2}{3}$$

Since -\frac{301}{30} and \frac{24}{30} have the same denominator, add them by adding their numerators.

$$\frac{-301+24}{30}+\frac{2}{3}$$

Add -301 and 24 to get -277.

$$-\frac{277}{30}+\frac{2}{3}$$

Least common multiple of 30 and 3 is 30. Convert -\frac{277}{30} and \frac{2}{3} to fractions with denominator 30.

$$-\frac{277}{30}+\frac{20}{30}$$

Since -\frac{277}{30} and \frac{20}{30} have the same denominator, add them by adding their numerators.

$$\frac{-277+20}{30}$$

Add -277 and 20 to get -257.

$$-\frac{257}{30}$$

Factor

$$-\frac{257}{30} = -8\frac{17}{30} = -8.566666666666666$$