Solve 1/12+y/4+1/4-1/2

$$\frac { 1 } { 12 } + \frac { y } { 4 } + \frac { 1 } { 4 } - \frac { 1 } { 2 }$$

Evaluate

$$\frac{y}{4}-\frac{1}{6}$$

Solution Steps

Least common multiple of 12 and 4 is 12. Convert \frac{1}{12} and \frac{1}{4} to fractions with denominator 12.

$$\frac{1}{12}+\frac{y}{4}+\frac{3}{12}-\frac{1}{2}$$

Since \frac{1}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{1+3}{12}+\frac{y}{4}-\frac{1}{2}$$

Add 1 and 3 to get 4.

$$\frac{4}{12}+\frac{y}{4}-\frac{1}{2}$$

Reduce the fraction \frac{4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{1}{3}+\frac{y}{4}-\frac{1}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{2}{6}+\frac{y}{4}-\frac{3}{6}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-3}{6}+\frac{y}{4}$$

Subtract 3 from 2 to get -1.

$$-\frac{1}{6}+\frac{y}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 4 is 12. Multiply -\frac{1}{6} times \frac{2}{2}. Multiply \frac{y}{4} times \frac{3}{3}.

$$-\frac{2}{12}+\frac{3y}{12}$$

Since -\frac{2}{12} and \frac{3y}{12} have the same denominator, add them by adding their numerators.

$$\frac{-2+3y}{12}$$

Factor

$$\frac{3y-2}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{-2+3y}{12}$$

Consider 1+3y+3-6. Multiply and combine like terms.

$$3y-2$$

Rewrite the complete factored expression.

$$\frac{3y-2}{12}$$