Solve 2/6-2/7-2/8/frac{8{2}-frac{7}{2}-frac{6}{2}}

$$\frac { \frac { 2 } { 6 } - \frac { 2 } { 7 } - \frac { 2 } { 8 } } { \frac { 8 } { 2 } - \frac { 7 } { 2 } - \frac { 6 } { 2 } }$$

Evaluate

$$\frac{17}{210}\approx 0.080952381$$

Solution Steps

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{3}-\frac{2}{7}-\frac{2}{8}}{\frac{8}{2}-\frac{7}{2}-\frac{6}{2}}$$

Least common multiple of 3 and 7 is 21. Convert \frac{1}{3} and \frac{2}{7} to fractions with denominator 21.

$$\frac{\frac{7}{21}-\frac{6}{21}-\frac{2}{8}}{\frac{8}{2}-\frac{7}{2}-\frac{6}{2}}$$

Since \frac{7}{21} and \frac{6}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-6}{21}-\frac{2}{8}}{\frac{8}{2}-\frac{7}{2}-\frac{6}{2}}$$

Subtract 6 from 7 to get 1.

$$\frac{\frac{1}{21}-\frac{2}{8}}{\frac{8}{2}-\frac{7}{2}-\frac{6}{2}}$$

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

$$\frac{\frac{1}{21}-\frac{1}{4}}{\frac{8}{2}-\frac{7}{2}-\frac{6}{2}}$$

Least common multiple of 21 and 4 is 84. Convert \frac{1}{21} and \frac{1}{4} to fractions with denominator 84.

$$\frac{\frac{4}{84}-\frac{21}{84}}{\frac{8}{2}-\frac{7}{2}-\frac{6}{2}}$$

Since \frac{4}{84} and \frac{21}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-21}{84}}{\frac{8}{2}-\frac{7}{2}-\frac{6}{2}}$$

Subtract 21 from 4 to get -17.

$$\frac{-\frac{17}{84}}{\frac{8}{2}-\frac{7}{2}-\frac{6}{2}}$$

Since \frac{8}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{17}{84}}{\frac{8-7}{2}-\frac{6}{2}}$$

Subtract 7 from 8 to get 1.

$$\frac{-\frac{17}{84}}{\frac{1}{2}-\frac{6}{2}}$$

Since \frac{1}{2} and \frac{6}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{17}{84}}{\frac{1-6}{2}}$$

Subtract 6 from 1 to get -5.

$$\frac{-\frac{17}{84}}{-\frac{5}{2}}$$

Divide -\frac{17}{84} by -\frac{5}{2} by multiplying -\frac{17}{84} by the reciprocal of -\frac{5}{2}.

$$-\frac{17}{84}\left(-\frac{2}{5}\right)$$

Multiply -\frac{17}{84} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-17\left(-2\right)}{84\times 5}$$

Do the multiplications in the fraction \frac{-17\left(-2\right)}{84\times 5}.

$$\frac{34}{420}$$

Reduce the fraction \frac{34}{420} to lowest terms by extracting and canceling out 2.

$$\frac{17}{210}$$

Factor

$$\frac{17}{2 \cdot 3 \cdot 5 \cdot 7} = 0.08095238095238096$$