Solve 4-[7/12-(-4/5+3/2-2)*(7/13+frac{5}{26}-1)]:(frac{11}{12}-frac{8}{5}+frac{17}{30})

$$4 - [ \frac { 7 } { 12 } - ( - \frac { 4 } { 5 } + \frac { 3 } { 2 } - 2 ) \cdot ( \frac { 7 } { 13 } + \frac { 5 } { 26 } - 1 ) ] : ( \frac { 11 } { 12 } - \frac { 8 } { 5 } + \frac { 17 } { 30 } )$$

Evaluate

$$6$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert -\frac{4}{5} and \frac{3}{2} to fractions with denominator 10.

$$4-\frac{\frac{7}{12}-\left(-\frac{8}{10}+\frac{15}{10}-2\right)\left(\frac{7}{13}+\frac{5}{26}-1\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Since -\frac{8}{10} and \frac{15}{10} have the same denominator, add them by adding their numerators.

$$4-\frac{\frac{7}{12}-\left(\frac{-8+15}{10}-2\right)\left(\frac{7}{13}+\frac{5}{26}-1\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Add -8 and 15 to get 7.

$$4-\frac{\frac{7}{12}-\left(\frac{7}{10}-2\right)\left(\frac{7}{13}+\frac{5}{26}-1\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Convert 2 to fraction \frac{20}{10}.

$$4-\frac{\frac{7}{12}-\left(\frac{7}{10}-\frac{20}{10}\right)\left(\frac{7}{13}+\frac{5}{26}-1\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Since \frac{7}{10} and \frac{20}{10} have the same denominator, subtract them by subtracting their numerators.

$$4-\frac{\frac{7}{12}-\frac{7-20}{10}\left(\frac{7}{13}+\frac{5}{26}-1\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Subtract 20 from 7 to get -13.

$$4-\frac{\frac{7}{12}-\left(-\frac{13}{10}\left(\frac{7}{13}+\frac{5}{26}-1\right)\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Least common multiple of 13 and 26 is 26. Convert \frac{7}{13} and \frac{5}{26} to fractions with denominator 26.

$$4-\frac{\frac{7}{12}-\left(-\frac{13}{10}\left(\frac{14}{26}+\frac{5}{26}-1\right)\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Since \frac{14}{26} and \frac{5}{26} have the same denominator, add them by adding their numerators.

$$4-\frac{\frac{7}{12}-\left(-\frac{13}{10}\left(\frac{14+5}{26}-1\right)\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Add 14 and 5 to get 19.

$$4-\frac{\frac{7}{12}-\left(-\frac{13}{10}\left(\frac{19}{26}-1\right)\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Convert 1 to fraction \frac{26}{26}.

$$4-\frac{\frac{7}{12}-\left(-\frac{13}{10}\left(\frac{19}{26}-\frac{26}{26}\right)\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Since \frac{19}{26} and \frac{26}{26} have the same denominator, subtract them by subtracting their numerators.

$$4-\frac{\frac{7}{12}-\left(-\frac{13}{10}\times \frac{19-26}{26}\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Subtract 26 from 19 to get -7.

$$4-\frac{\frac{7}{12}-\left(-\frac{13}{10}\left(-\frac{7}{26}\right)\right)}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Multiply -\frac{13}{10} times -\frac{7}{26} by multiplying numerator times numerator and denominator times denominator.

$$4-\frac{\frac{7}{12}-\frac{-13\left(-7\right)}{10\times 26}}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Do the multiplications in the fraction \frac{-13\left(-7\right)}{10\times 26}.

$$4-\frac{\frac{7}{12}-\frac{91}{260}}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Reduce the fraction \frac{91}{260} to lowest terms by extracting and canceling out 13.

$$4-\frac{\frac{7}{12}-\frac{7}{20}}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Least common multiple of 12 and 20 is 60. Convert \frac{7}{12} and \frac{7}{20} to fractions with denominator 60.

$$4-\frac{\frac{35}{60}-\frac{21}{60}}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Since \frac{35}{60} and \frac{21}{60} have the same denominator, subtract them by subtracting their numerators.

$$4-\frac{\frac{35-21}{60}}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Subtract 21 from 35 to get 14.

$$4-\frac{\frac{14}{60}}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Reduce the fraction \frac{14}{60} to lowest terms by extracting and canceling out 2.

$$4-\frac{\frac{7}{30}}{\frac{11}{12}-\frac{8}{5}+\frac{17}{30}}$$

Least common multiple of 12 and 5 is 60. Convert \frac{11}{12} and \frac{8}{5} to fractions with denominator 60.

$$4-\frac{\frac{7}{30}}{\frac{55}{60}-\frac{96}{60}+\frac{17}{30}}$$

Since \frac{55}{60} and \frac{96}{60} have the same denominator, subtract them by subtracting their numerators.

$$4-\frac{\frac{7}{30}}{\frac{55-96}{60}+\frac{17}{30}}$$

Subtract 96 from 55 to get -41.

$$4-\frac{\frac{7}{30}}{-\frac{41}{60}+\frac{17}{30}}$$

Least common multiple of 60 and 30 is 60. Convert -\frac{41}{60} and \frac{17}{30} to fractions with denominator 60.

$$4-\frac{\frac{7}{30}}{-\frac{41}{60}+\frac{34}{60}}$$

Since -\frac{41}{60} and \frac{34}{60} have the same denominator, add them by adding their numerators.

$$4-\frac{\frac{7}{30}}{\frac{-41+34}{60}}$$

Add -41 and 34 to get -7.

$$4-\frac{\frac{7}{30}}{-\frac{7}{60}}$$

Divide \frac{7}{30} by -\frac{7}{60} by multiplying \frac{7}{30} by the reciprocal of -\frac{7}{60}.

$$4-\frac{7}{30}\left(-\frac{60}{7}\right)$$

Multiply \frac{7}{30} times -\frac{60}{7} by multiplying numerator times numerator and denominator times denominator.

$$4-\frac{7\left(-60\right)}{30\times 7}$$

Cancel out 7 in both numerator and denominator.

$$4-\frac{-60}{30}$$

Divide -60 by 30 to get -2.

$$4-\left(-2\right)$$

The opposite of -2 is 2.

$$4+2$$

Add 4 and 2 to get 6.

$$6$$

Factor

$$2\times 3$$