Solve 10/5|1/5-(2/3+5/6)|

$$\frac { 10 } { 5 } | \frac { 1 } { 5 } - ( \frac { 2 } { 3 } + \frac { 5 } { 6 } ) |$$

Evaluate

$$\frac{13}{5}=2.6$$

Solution Steps

Divide 10 by 5 to get 2.

$$2|\frac{1}{5}-\left(\frac{2}{3}+\frac{5}{6}\right)|$$

Least common multiple of 3 and 6 is 6. Convert \frac{2}{3} and \frac{5}{6} to fractions with denominator 6.

$$2|\frac{1}{5}-\left(\frac{4}{6}+\frac{5}{6}\right)|$$

Since \frac{4}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

$$2|\frac{1}{5}-\frac{4+5}{6}|$$

Add 4 and 5 to get 9.

$$2|\frac{1}{5}-\frac{9}{6}|$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$2|\frac{1}{5}-\frac{3}{2}|$$

Least common multiple of 5 and 2 is 10. Convert \frac{1}{5} and \frac{3}{2} to fractions with denominator 10.

$$2|\frac{2}{10}-\frac{15}{10}|$$

Since \frac{2}{10} and \frac{15}{10} have the same denominator, subtract them by subtracting their numerators.

$$2|\frac{2-15}{10}|$$

Subtract 15 from 2 to get -13.

$$2|-\frac{13}{10}|$$

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}{10} is \frac{13}{10}.

$$2\times \frac{13}{10}$$

Express 2\times \frac{13}{10} as a single fraction.

$$\frac{2\times 13}{10}$$

Multiply 2 and 13 to get 26.

$$\frac{26}{10}$$

Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.

$$\frac{13}{5}$$

Factor

$$\frac{13}{5} = 2\frac{3}{5} = 2.6$$