Solve -1/10-1/6+41/18-7+27/2+frac{12}{5}-8=

$$\frac { - 1 } { 10 } - \frac { 1 } { 6 } + \frac { 41 } { 18 } - 7 + \frac { 27 } { 2 } + \frac { 12 } { 5 } - 8 =$$

Evaluate

$$\frac{131}{45}\approx 2.911111111$$

Solution Steps

Fraction \frac{-1}{10} can be rewritten as -\frac{1}{10} by extracting the negative sign.

$$-\frac{1}{10}-\frac{1}{6}+\frac{41}{18}-7+\frac{27}{2}+\frac{12}{5}-8$$

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

$$-\frac{3}{30}-\frac{5}{30}+\frac{41}{18}-7+\frac{27}{2}+\frac{12}{5}-8$$

Since -\frac{3}{30} and \frac{5}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-5}{30}+\frac{41}{18}-7+\frac{27}{2}+\frac{12}{5}-8$$

Subtract 5 from -3 to get -8.

$$\frac{-8}{30}+\frac{41}{18}-7+\frac{27}{2}+\frac{12}{5}-8$$

Reduce the fraction \frac{-8}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{4}{15}+\frac{41}{18}-7+\frac{27}{2}+\frac{12}{5}-8$$

Least common multiple of 15 and 18 is 90. Convert -\frac{4}{15} and \frac{41}{18} to fractions with denominator 90.

$$-\frac{24}{90}+\frac{205}{90}-7+\frac{27}{2}+\frac{12}{5}-8$$

Since -\frac{24}{90} and \frac{205}{90} have the same denominator, add them by adding their numerators.

$$\frac{-24+205}{90}-7+\frac{27}{2}+\frac{12}{5}-8$$

Add -24 and 205 to get 181.

$$\frac{181}{90}-7+\frac{27}{2}+\frac{12}{5}-8$$

Convert 7 to fraction \frac{630}{90}.

$$\frac{181}{90}-\frac{630}{90}+\frac{27}{2}+\frac{12}{5}-8$$

Since \frac{181}{90} and \frac{630}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{181-630}{90}+\frac{27}{2}+\frac{12}{5}-8$$

Subtract 630 from 181 to get -449.

$$-\frac{449}{90}+\frac{27}{2}+\frac{12}{5}-8$$

Least common multiple of 90 and 2 is 90. Convert -\frac{449}{90} and \frac{27}{2} to fractions with denominator 90.

$$-\frac{449}{90}+\frac{1215}{90}+\frac{12}{5}-8$$

Since -\frac{449}{90} and \frac{1215}{90} have the same denominator, add them by adding their numerators.

$$\frac{-449+1215}{90}+\frac{12}{5}-8$$

Add -449 and 1215 to get 766.

$$\frac{766}{90}+\frac{12}{5}-8$$

Reduce the fraction \frac{766}{90} to lowest terms by extracting and canceling out 2.

$$\frac{383}{45}+\frac{12}{5}-8$$

Least common multiple of 45 and 5 is 45. Convert \frac{383}{45} and \frac{12}{5} to fractions with denominator 45.

$$\frac{383}{45}+\frac{108}{45}-8$$

Since \frac{383}{45} and \frac{108}{45} have the same denominator, add them by adding their numerators.

$$\frac{383+108}{45}-8$$

Add 383 and 108 to get 491.

$$\frac{491}{45}-8$$

Convert 8 to fraction \frac{360}{45}.

$$\frac{491}{45}-\frac{360}{45}$$

Since \frac{491}{45} and \frac{360}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{491-360}{45}$$

Subtract 360 from 491 to get 131.

$$\frac{131}{45}$$

Factor

$$\frac{131}{3 ^ {2} \cdot 5} = 2\frac{41}{45} = 2.911111111111111$$