Solve 21/8-(21/6-17/8)=

$$2 \frac { 1 } { 8 } - ( 2 \frac { 1 } { 6 } - 1 \frac { 7 } { 8 } ) =$$

Evaluate

$$\frac{11}{6}\approx 1.833333333$$

Solution Steps

Multiply 2 and 8 to get 16.

$$\frac{16+1}{8}-\left(\frac{2\times 6+1}{6}-\frac{1\times 8+7}{8}\right)$$

Add 16 and 1 to get 17.

$$\frac{17}{8}-\left(\frac{2\times 6+1}{6}-\frac{1\times 8+7}{8}\right)$$

Multiply 2 and 6 to get 12.

$$\frac{17}{8}-\left(\frac{12+1}{6}-\frac{1\times 8+7}{8}\right)$$

Add 12 and 1 to get 13.

$$\frac{17}{8}-\left(\frac{13}{6}-\frac{1\times 8+7}{8}\right)$$

Multiply 1 and 8 to get 8.

$$\frac{17}{8}-\left(\frac{13}{6}-\frac{8+7}{8}\right)$$

Add 8 and 7 to get 15.

$$\frac{17}{8}-\left(\frac{13}{6}-\frac{15}{8}\right)$$

Least common multiple of 6 and 8 is 24. Convert \frac{13}{6} and \frac{15}{8} to fractions with denominator 24.

$$\frac{17}{8}-\left(\frac{52}{24}-\frac{45}{24}\right)$$

Since \frac{52}{24} and \frac{45}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{8}-\frac{52-45}{24}$$

Subtract 45 from 52 to get 7.

$$\frac{17}{8}-\frac{7}{24}$$

Least common multiple of 8 and 24 is 24. Convert \frac{17}{8} and \frac{7}{24} to fractions with denominator 24.

$$\frac{51}{24}-\frac{7}{24}$$

Since \frac{51}{24} and \frac{7}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{51-7}{24}$$

Subtract 7 from 51 to get 44.

$$\frac{44}{24}$$

Reduce the fraction \frac{44}{24} to lowest terms by extracting and canceling out 4.

$$\frac{11}{6}$$

Factor

$$\frac{11}{2 \cdot 3} = 1\frac{5}{6} = 1.8333333333333333$$