Solve (4/2+7/6-4/7)-(2/6+frac{4}{10}-17)

$$( \frac { 4 } { 2 } + \frac { 7 } { 6 } - \frac { 4 } { 7 } ) - ( \frac { 2 } { 6 } + \frac { 4 } { 10 } - 17 )$$

Evaluate

$$\frac{3961}{210}\approx 18.861904762$$

Solution Steps

Divide 4 by 2 to get 2.

$$2+\frac{7}{6}-\frac{4}{7}-\left(\frac{2}{6}+\frac{4}{10}-17\right)$$

Convert 2 to fraction \frac{12}{6}.

$$\frac{12}{6}+\frac{7}{6}-\frac{4}{7}-\left(\frac{2}{6}+\frac{4}{10}-17\right)$$

Since \frac{12}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.

$$\frac{12+7}{6}-\frac{4}{7}-\left(\frac{2}{6}+\frac{4}{10}-17\right)$$

Add 12 and 7 to get 19.

$$\frac{19}{6}-\frac{4}{7}-\left(\frac{2}{6}+\frac{4}{10}-17\right)$$

Least common multiple of 6 and 7 is 42. Convert \frac{19}{6} and \frac{4}{7} to fractions with denominator 42.

$$\frac{133}{42}-\frac{24}{42}-\left(\frac{2}{6}+\frac{4}{10}-17\right)$$

Since \frac{133}{42} and \frac{24}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{133-24}{42}-\left(\frac{2}{6}+\frac{4}{10}-17\right)$$

Subtract 24 from 133 to get 109.

$$\frac{109}{42}-\left(\frac{2}{6}+\frac{4}{10}-17\right)$$

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

$$\frac{109}{42}-\left(\frac{1}{3}+\frac{4}{10}-17\right)$$

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{109}{42}-\left(\frac{1}{3}+\frac{2}{5}-17\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{109}{42}-\left(\frac{5}{15}+\frac{6}{15}-17\right)$$

Since \frac{5}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{109}{42}-\left(\frac{5+6}{15}-17\right)$$

Add 5 and 6 to get 11.

$$\frac{109}{42}-\left(\frac{11}{15}-17\right)$$

Convert 17 to fraction \frac{255}{15}.

$$\frac{109}{42}-\left(\frac{11}{15}-\frac{255}{15}\right)$$

Since \frac{11}{15} and \frac{255}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{109}{42}-\frac{11-255}{15}$$

Subtract 255 from 11 to get -244.

$$\frac{109}{42}-\left(-\frac{244}{15}\right)$$

The opposite of -\frac{244}{15} is \frac{244}{15}.

$$\frac{109}{42}+\frac{244}{15}$$

Least common multiple of 42 and 15 is 210. Convert \frac{109}{42} and \frac{244}{15} to fractions with denominator 210.

$$\frac{545}{210}+\frac{3416}{210}$$

Since \frac{545}{210} and \frac{3416}{210} have the same denominator, add them by adding their numerators.

$$\frac{545+3416}{210}$$

Add 545 and 3416 to get 3961.

$$\frac{3961}{210}$$

Factor

$$\frac{17 \cdot 233}{2 \cdot 3 \cdot 5 \cdot 7} = 18\frac{181}{210} = 18.86190476190476$$