Solve |4/3-(3/8-1/6)|-|2/5-(frac{7}{8}-frac{3}{6})|

$$| \frac { 4 } { 3 } - ( \frac { 3 } { 8 } - \frac { 1 } { 6 } ) | - | \frac { 2 } { 5 } - ( \frac { 7 } { 8 } - \frac { 3 } { 6 } ) |$$

Evaluate

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

Solution Steps

Least common multiple of 8 and 6 is 24. Convert \frac{3}{8} and \frac{1}{6} to fractions with denominator 24.

$$|\frac{4}{3}-\left(\frac{9}{24}-\frac{4}{24}\right)|-|\frac{2}{5}-\left(\frac{7}{8}-\frac{3}{6}\right)|$$

Since \frac{9}{24} and \frac{4}{24} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{4}{3}-\frac{9-4}{24}|-|\frac{2}{5}-\left(\frac{7}{8}-\frac{3}{6}\right)|$$

Subtract 4 from 9 to get 5.

$$|\frac{4}{3}-\frac{5}{24}|-|\frac{2}{5}-\left(\frac{7}{8}-\frac{3}{6}\right)|$$

Least common multiple of 3 and 24 is 24. Convert \frac{4}{3} and \frac{5}{24} to fractions with denominator 24.

$$|\frac{32}{24}-\frac{5}{24}|-|\frac{2}{5}-\left(\frac{7}{8}-\frac{3}{6}\right)|$$

Since \frac{32}{24} and \frac{5}{24} have the same denominator, subtract them by subtracting their numerators.

$$|\frac{32-5}{24}|-|\frac{2}{5}-\left(\frac{7}{8}-\frac{3}{6}\right)|$$

Subtract 5 from 32 to get 27.

$$|\frac{27}{24}|-|\frac{2}{5}-\left(\frac{7}{8}-\frac{3}{6}\right)|$$

Reduce the fraction \frac{27}{24} to lowest terms by extracting and canceling out 3.

$$|\frac{9}{8}|-|\frac{2}{5}-\left(\frac{7}{8}-\frac{3}{6}\right)|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{9}{8} is \frac{9}{8}.

$$\frac{9}{8}-|\frac{2}{5}-\left(\frac{7}{8}-\frac{3}{6}\right)|$$

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

$$\frac{9}{8}-|\frac{2}{5}-\left(\frac{7}{8}-\frac{1}{2}\right)|$$

Least common multiple of 8 and 2 is 8. Convert \frac{7}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{9}{8}-|\frac{2}{5}-\left(\frac{7}{8}-\frac{4}{8}\right)|$$

Since \frac{7}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{8}-|\frac{2}{5}-\frac{7-4}{8}|$$

Subtract 4 from 7 to get 3.

$$\frac{9}{8}-|\frac{2}{5}-\frac{3}{8}|$$

Least common multiple of 5 and 8 is 40. Convert \frac{2}{5} and \frac{3}{8} to fractions with denominator 40.

$$\frac{9}{8}-|\frac{16}{40}-\frac{15}{40}|$$

Since \frac{16}{40} and \frac{15}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9}{8}-|\frac{16-15}{40}|$$

Subtract 15 from 16 to get 1.

$$\frac{9}{8}-|\frac{1}{40}|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of \frac{1}{40} is \frac{1}{40}.

$$\frac{9}{8}-\frac{1}{40}$$

Least common multiple of 8 and 40 is 40. Convert \frac{9}{8} and \frac{1}{40} to fractions with denominator 40.

$$\frac{45}{40}-\frac{1}{40}$$

Since \frac{45}{40} and \frac{1}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{45-1}{40}$$

Subtract 1 from 45 to get 44.

$$\frac{44}{40}$$

Reduce the fraction \frac{44}{40} to lowest terms by extracting and canceling out 4.

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

Factor

$$\frac{11}{2 \cdot 5} = 1\frac{1}{10} = 1.1$$