Solve c*1/3+2/9-6/5+12/10=

$$c \cdot \frac { 1 } { 3 } + \frac { 2 } { 9 } - \frac { 6 } { 5 } + \frac { 12 } { 10 } =$$

Evaluate

$$\frac{c}{3}+\frac{2}{9}$$

Solution Steps

Least common multiple of 9 and 5 is 45. Convert \frac{2}{9} and \frac{6}{5} to fractions with denominator 45.

$$c\times \frac{1}{3}+\frac{10}{45}-\frac{54}{45}+\frac{12}{10}$$

Since \frac{10}{45} and \frac{54}{45} have the same denominator, subtract them by subtracting their numerators.

$$c\times \frac{1}{3}+\frac{10-54}{45}+\frac{12}{10}$$

Subtract 54 from 10 to get -44.

$$c\times \frac{1}{3}-\frac{44}{45}+\frac{12}{10}$$

Reduce the fraction \frac{12}{10} to lowest terms by extracting and canceling out 2.

$$c\times \frac{1}{3}-\frac{44}{45}+\frac{6}{5}$$

Least common multiple of 45 and 5 is 45. Convert -\frac{44}{45} and \frac{6}{5} to fractions with denominator 45.

$$c\times \frac{1}{3}-\frac{44}{45}+\frac{54}{45}$$

Since -\frac{44}{45} and \frac{54}{45} have the same denominator, add them by adding their numerators.

$$c\times \frac{1}{3}+\frac{-44+54}{45}$$

Add -44 and 54 to get 10.

$$c\times \frac{1}{3}+\frac{10}{45}$$

Reduce the fraction \frac{10}{45} to lowest terms by extracting and canceling out 5.

$$c\times \frac{1}{3}+\frac{2}{9}$$

Factor

$$\frac{3c+2}{9}$$

Solution Steps

Factor out \frac{1}{45}.

$$\frac{15c+10}{45}$$

Consider 15c+10-54+54. Multiply and combine like terms.

$$15c+10$$

Consider 15c+10. Factor out 5.

$$5\left(3c+2\right)$$

Rewrite the complete factored expression.

$$\frac{3c+2}{9}$$