Solve =-4/9c+5/6-4/9c+2/5-frac{17}{2}+frac{3}{4}c

$$= \frac { - 4 } { 9 } c + \frac { 5 } { 6 } - \frac { 4 } { 9 } c + \frac { 2 } { 5 } - \frac { 17 } { 2 } + \frac { 3 } { 4 } c$$

Evaluate

$$-\frac{5c}{36}-\frac{109}{15}$$

Solution Steps

Fraction \frac{-4}{9} can be rewritten as -\frac{4}{9} by extracting the negative sign.

$$-\frac{4}{9}c+\frac{5}{6}-\frac{4}{9}c+\frac{2}{5}-\frac{17}{2}+\frac{3}{4}c$$

Combine -\frac{4}{9}c and -\frac{4}{9}c to get -\frac{8}{9}c.

$$-\frac{8}{9}c+\frac{5}{6}+\frac{2}{5}-\frac{17}{2}+\frac{3}{4}c$$

Least common multiple of 6 and 5 is 30. Convert \frac{5}{6} and \frac{2}{5} to fractions with denominator 30.

$$-\frac{8}{9}c+\frac{25}{30}+\frac{12}{30}-\frac{17}{2}+\frac{3}{4}c$$

Since \frac{25}{30} and \frac{12}{30} have the same denominator, add them by adding their numerators.

$$-\frac{8}{9}c+\frac{25+12}{30}-\frac{17}{2}+\frac{3}{4}c$$

Add 25 and 12 to get 37.

$$-\frac{8}{9}c+\frac{37}{30}-\frac{17}{2}+\frac{3}{4}c$$

Least common multiple of 30 and 2 is 30. Convert \frac{37}{30} and \frac{17}{2} to fractions with denominator 30.

$$-\frac{8}{9}c+\frac{37}{30}-\frac{255}{30}+\frac{3}{4}c$$

Since \frac{37}{30} and \frac{255}{30} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{8}{9}c+\frac{37-255}{30}+\frac{3}{4}c$$

Subtract 255 from 37 to get -218.

$$-\frac{8}{9}c+\frac{-218}{30}+\frac{3}{4}c$$

Reduce the fraction \frac{-218}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{8}{9}c-\frac{109}{15}+\frac{3}{4}c$$

Combine -\frac{8}{9}c and \frac{3}{4}c to get -\frac{5}{36}c.

$$-\frac{5}{36}c-\frac{109}{15}$$

Factor

$$\frac{-25c-1308}{180}$$

Solution Steps

Factor out \frac{1}{180}.

$$\frac{-25c-1308}{180}$$

Consider -80c+150-80c+72-1530+135c. Multiply and combine like terms.

$$-25c-1308$$

Rewrite the complete factored expression.

$$\frac{-25c-1308}{180}$$