Solve 5/6-3/7+7-1/6-4/7+4

$$\frac { 5 } { 6 } - \frac { 3 } { 7 } + 7 - \frac { 1 } { 6 } - \frac { 4 } { 7 } + 4$$

Evaluate

$$\frac{32}{3}\approx 10.666666667$$

Solution Steps

Least common multiple of 6 and 7 is 42. Convert \frac{5}{6} and \frac{3}{7} to fractions with denominator 42.

$$\frac{35}{42}-\frac{18}{42}+7-\frac{1}{6}-\frac{4}{7}+4$$

Since \frac{35}{42} and \frac{18}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-18}{42}+7-\frac{1}{6}-\frac{4}{7}+4$$

Subtract 18 from 35 to get 17.

$$\frac{17}{42}+7-\frac{1}{6}-\frac{4}{7}+4$$

Convert 7 to fraction \frac{294}{42}.

$$\frac{17}{42}+\frac{294}{42}-\frac{1}{6}-\frac{4}{7}+4$$

Since \frac{17}{42} and \frac{294}{42} have the same denominator, add them by adding their numerators.

$$\frac{17+294}{42}-\frac{1}{6}-\frac{4}{7}+4$$

Add 17 and 294 to get 311.

$$\frac{311}{42}-\frac{1}{6}-\frac{4}{7}+4$$

Least common multiple of 42 and 6 is 42. Convert \frac{311}{42} and \frac{1}{6} to fractions with denominator 42.

$$\frac{311}{42}-\frac{7}{42}-\frac{4}{7}+4$$

Since \frac{311}{42} and \frac{7}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{311-7}{42}-\frac{4}{7}+4$$

Subtract 7 from 311 to get 304.

$$\frac{304}{42}-\frac{4}{7}+4$$

Reduce the fraction \frac{304}{42} to lowest terms by extracting and canceling out 2.

$$\frac{152}{21}-\frac{4}{7}+4$$

Least common multiple of 21 and 7 is 21. Convert \frac{152}{21} and \frac{4}{7} to fractions with denominator 21.

$$\frac{152}{21}-\frac{12}{21}+4$$

Since \frac{152}{21} and \frac{12}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{152-12}{21}+4$$

Subtract 12 from 152 to get 140.

$$\frac{140}{21}+4$$

Reduce the fraction \frac{140}{21} to lowest terms by extracting and canceling out 7.

$$\frac{20}{3}+4$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{20}{3}+\frac{12}{3}$$

Since \frac{20}{3} and \frac{12}{3} have the same denominator, add them by adding their numerators.

$$\frac{20+12}{3}$$

Add 20 and 12 to get 32.

$$\frac{32}{3}$$

Factor

$$\frac{2 ^ {5}}{3} = 10\frac{2}{3} = 10.666666666666666$$