Solve 1-(1/10+7/6+1/8+7/12+frac{1}{8})=

$$1 - ( \frac { 1 } { 10 } + \frac { 7 } { 6 } + \frac { 1 } { 8 } + \frac { 7 } { 12 } + \frac { 1 } { 8 } ) =$$

Evaluate

$$-\frac{11}{10}=-1.1$$

Solution Steps

Least common multiple of 10 and 6 is 30. Convert \frac{1}{10} and \frac{7}{6} to fractions with denominator 30.

$$1-\left(\frac{3}{30}+\frac{35}{30}+\frac{1}{8}+\frac{7}{12}+\frac{1}{8}\right)$$

Since \frac{3}{30} and \frac{35}{30} have the same denominator, add them by adding their numerators.

$$1-\left(\frac{3+35}{30}+\frac{1}{8}+\frac{7}{12}+\frac{1}{8}\right)$$

Add 3 and 35 to get 38.

$$1-\left(\frac{38}{30}+\frac{1}{8}+\frac{7}{12}+\frac{1}{8}\right)$$

Reduce the fraction \frac{38}{30} to lowest terms by extracting and canceling out 2.

$$1-\left(\frac{19}{15}+\frac{1}{8}+\frac{7}{12}+\frac{1}{8}\right)$$

Least common multiple of 15 and 8 is 120. Convert \frac{19}{15} and \frac{1}{8} to fractions with denominator 120.

$$1-\left(\frac{152}{120}+\frac{15}{120}+\frac{7}{12}+\frac{1}{8}\right)$$

Since \frac{152}{120} and \frac{15}{120} have the same denominator, add them by adding their numerators.

$$1-\left(\frac{152+15}{120}+\frac{7}{12}+\frac{1}{8}\right)$$

Add 152 and 15 to get 167.

$$1-\left(\frac{167}{120}+\frac{7}{12}+\frac{1}{8}\right)$$

Least common multiple of 120 and 12 is 120. Convert \frac{167}{120} and \frac{7}{12} to fractions with denominator 120.

$$1-\left(\frac{167}{120}+\frac{70}{120}+\frac{1}{8}\right)$$

Since \frac{167}{120} and \frac{70}{120} have the same denominator, add them by adding their numerators.

$$1-\left(\frac{167+70}{120}+\frac{1}{8}\right)$$

Add 167 and 70 to get 237.

$$1-\left(\frac{237}{120}+\frac{1}{8}\right)$$

Reduce the fraction \frac{237}{120} to lowest terms by extracting and canceling out 3.

$$1-\left(\frac{79}{40}+\frac{1}{8}\right)$$

Least common multiple of 40 and 8 is 40. Convert \frac{79}{40} and \frac{1}{8} to fractions with denominator 40.

$$1-\left(\frac{79}{40}+\frac{5}{40}\right)$$

Since \frac{79}{40} and \frac{5}{40} have the same denominator, add them by adding their numerators.

$$1-\frac{79+5}{40}$$

Add 79 and 5 to get 84.

$$1-\frac{84}{40}$$

Reduce the fraction \frac{84}{40} to lowest terms by extracting and canceling out 4.

$$1-\frac{21}{10}$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{10}{10}-\frac{21}{10}$$

Since \frac{10}{10} and \frac{21}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-21}{10}$$

Subtract 21 from 10 to get -11.

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

Factor

$$-\frac{11}{10} = -1\frac{1}{10} = -1.1$$