Solve 12(1/6-2/3+3/4)=

$$12 ( \frac { 1 } { 6 } - \frac { 2 } { 3 } + \frac { 3 } { 4 } ) =$$

Evaluate

$$3$$

Solution Steps

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

$$12\left(\frac{1}{6}-\frac{4}{6}+\frac{3}{4}\right)$$

Since \frac{1}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$12\left(\frac{1-4}{6}+\frac{3}{4}\right)$$

Subtract 4 from 1 to get -3.

$$12\left(\frac{-3}{6}+\frac{3}{4}\right)$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$12\left(-\frac{1}{2}+\frac{3}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert -\frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$12\left(-\frac{2}{4}+\frac{3}{4}\right)$$

Since -\frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$12\times \frac{-2+3}{4}$$

Add -2 and 3 to get 1.

$$12\times \frac{1}{4}$$

Multiply 12 and \frac{1}{4} to get \frac{12}{4}.

$$\frac{12}{4}$$

Divide 12 by 4 to get 3.

$$3$$

Factor

$$3$$