Solve 11/12quad12x(3/4-2/3)+(5/6-frac{1}{2})

$$1 \frac { 1 } { 12 } \quad 12 x ( \frac { 3 } { 4 } - \frac { 2 } { 3 } ) + ( \frac { 5 } { 6 } - \frac { 1 } { 2 } )$$

Evaluate

$$\frac{13x}{12}+\frac{1}{3}$$

Solution Steps

Multiply 1 and 12 to get 12.

$$\frac{12+1}{12}\times 12x\left(\frac{3}{4}-\frac{2}{3}\right)+\frac{5}{6}-\frac{1}{2}$$

Add 12 and 1 to get 13.

$$\frac{13}{12}\times 12x\left(\frac{3}{4}-\frac{2}{3}\right)+\frac{5}{6}-\frac{1}{2}$$

Cancel out 12 and 12.

$$13x\left(\frac{3}{4}-\frac{2}{3}\right)+\frac{5}{6}-\frac{1}{2}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$13x\left(\frac{9}{12}-\frac{8}{12}\right)+\frac{5}{6}-\frac{1}{2}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$13x\times \frac{9-8}{12}+\frac{5}{6}-\frac{1}{2}$$

Subtract 8 from 9 to get 1.

$$13x\times \frac{1}{12}+\frac{5}{6}-\frac{1}{2}$$

Multiply 13 and \frac{1}{12} to get \frac{13}{12}.

$$\frac{13}{12}x+\frac{5}{6}-\frac{1}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{13}{12}x+\frac{5}{6}-\frac{3}{6}$$

Since \frac{5}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{12}x+\frac{5-3}{6}$$

Subtract 3 from 5 to get 2.

$$\frac{13}{12}x+\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{13}{12}x+\frac{1}{3}$$

Expand

$$\frac{13x}{12}+\frac{1}{3}$$

Solution Steps

Multiply 1 and 12 to get 12.

$$\frac{12+1}{12}\times 12x\left(\frac{3}{4}-\frac{2}{3}\right)+\frac{5}{6}-\frac{1}{2}$$

Add 12 and 1 to get 13.

$$\frac{13}{12}\times 12x\left(\frac{3}{4}-\frac{2}{3}\right)+\frac{5}{6}-\frac{1}{2}$$

Cancel out 12 and 12.

$$13x\left(\frac{3}{4}-\frac{2}{3}\right)+\frac{5}{6}-\frac{1}{2}$$

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$13x\left(\frac{9}{12}-\frac{8}{12}\right)+\frac{5}{6}-\frac{1}{2}$$

Since \frac{9}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$13x\times \frac{9-8}{12}+\frac{5}{6}-\frac{1}{2}$$

Subtract 8 from 9 to get 1.

$$13x\times \frac{1}{12}+\frac{5}{6}-\frac{1}{2}$$

Multiply 13 and \frac{1}{12} to get \frac{13}{12}.

$$\frac{13}{12}x+\frac{5}{6}-\frac{1}{2}$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{13}{12}x+\frac{5}{6}-\frac{3}{6}$$

Since \frac{5}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{12}x+\frac{5-3}{6}$$

Subtract 3 from 5 to get 2.

$$\frac{13}{12}x+\frac{2}{6}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{13}{12}x+\frac{1}{3}$$