Solve (-11/4)-(-121/14)+(+5/3)-(-3/14)-frac{29}{4}+(-frac{16}{3})l

$$( - \frac { 11 } { 4 } ) - ( - \frac { 121 } { 14 } ) + ( + \frac { 5 } { 3 } ) - ( - \frac { 3 } { 14 } ) - \frac { 29 } { 4 } + ( - \frac { 16 } { 3 } ) l$$

Evaluate

$$-\frac{16l}{3}+\frac{11}{21}$$

Solution Steps

The opposite of -\frac{121}{14} is \frac{121}{14}.

$$-\frac{11}{4}+\frac{121}{14}+\frac{5}{3}-\left(-\frac{3}{14}\right)-\frac{29}{4}-\frac{16}{3}l$$

Least common multiple of 4 and 14 is 28. Convert -\frac{11}{4} and \frac{121}{14} to fractions with denominator 28.

$$-\frac{77}{28}+\frac{242}{28}+\frac{5}{3}-\left(-\frac{3}{14}\right)-\frac{29}{4}-\frac{16}{3}l$$

Since -\frac{77}{28} and \frac{242}{28} have the same denominator, add them by adding their numerators.

$$\frac{-77+242}{28}+\frac{5}{3}-\left(-\frac{3}{14}\right)-\frac{29}{4}-\frac{16}{3}l$$

Add -77 and 242 to get 165.

$$\frac{165}{28}+\frac{5}{3}-\left(-\frac{3}{14}\right)-\frac{29}{4}-\frac{16}{3}l$$

Least common multiple of 28 and 3 is 84. Convert \frac{165}{28} and \frac{5}{3} to fractions with denominator 84.

$$\frac{495}{84}+\frac{140}{84}-\left(-\frac{3}{14}\right)-\frac{29}{4}-\frac{16}{3}l$$

Since \frac{495}{84} and \frac{140}{84} have the same denominator, add them by adding their numerators.

$$\frac{495+140}{84}-\left(-\frac{3}{14}\right)-\frac{29}{4}-\frac{16}{3}l$$

Add 495 and 140 to get 635.

$$\frac{635}{84}-\left(-\frac{3}{14}\right)-\frac{29}{4}-\frac{16}{3}l$$

The opposite of -\frac{3}{14} is \frac{3}{14}.

$$\frac{635}{84}+\frac{3}{14}-\frac{29}{4}-\frac{16}{3}l$$

Least common multiple of 84 and 14 is 84. Convert \frac{635}{84} and \frac{3}{14} to fractions with denominator 84.

$$\frac{635}{84}+\frac{18}{84}-\frac{29}{4}-\frac{16}{3}l$$

Since \frac{635}{84} and \frac{18}{84} have the same denominator, add them by adding their numerators.

$$\frac{635+18}{84}-\frac{29}{4}-\frac{16}{3}l$$

Add 635 and 18 to get 653.

$$\frac{653}{84}-\frac{29}{4}-\frac{16}{3}l$$

Least common multiple of 84 and 4 is 84. Convert \frac{653}{84} and \frac{29}{4} to fractions with denominator 84.

$$\frac{653}{84}-\frac{609}{84}-\frac{16}{3}l$$

Since \frac{653}{84} and \frac{609}{84} have the same denominator, subtract them by subtracting their numerators.

$$\frac{653-609}{84}-\frac{16}{3}l$$

Subtract 609 from 653 to get 44.

$$\frac{44}{84}-\frac{16}{3}l$$

Reduce the fraction \frac{44}{84} to lowest terms by extracting and canceling out 4.

$$\frac{11}{21}-\frac{16}{3}l$$

Factor

$$\frac{11-112l}{21}$$

Solution Steps

Factor out \frac{1}{84}.

$$\frac{44-448l}{84}$$

Consider -231+726+140+18-609-448l. Multiply and combine like terms.

$$-448l+44$$

Consider -448l+44. Factor out 4.

$$4\left(-112l+11\right)$$

Rewrite the complete factored expression.

$$\frac{-112l+11}{21}$$