Solve 12(m+2n/3-m-3n/6+m+n/2)

$$12( \frac{ m+2n }{ 3 } - \frac{ m-3n }{ 6 } + \frac{ m+n }{ 2 } )$$

Evaluate

$$8m+20n$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 6 is 6. Multiply \frac{m+2n}{3} times \frac{2}{2}.

$$12\left(\frac{2\left(m+2n\right)}{6}-\frac{m-3n}{6}+\frac{m+n}{2}\right)$$

Since \frac{2\left(m+2n\right)}{6} and \frac{m-3n}{6} have the same denominator, subtract them by subtracting their numerators.

$$12\left(\frac{2\left(m+2n\right)-\left(m-3n\right)}{6}+\frac{m+n}{2}\right)$$

Do the multiplications in 2\left(m+2n\right)-\left(m-3n\right).

$$12\left(\frac{2m+4n-m+3n}{6}+\frac{m+n}{2}\right)$$

Combine like terms in 2m+4n-m+3n.

$$12\left(\frac{m+7n}{6}+\frac{m+n}{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 2 is 6. Multiply \frac{m+n}{2} times \frac{3}{3}.

$$12\left(\frac{m+7n}{6}+\frac{3\left(m+n\right)}{6}\right)$$

Since \frac{m+7n}{6} and \frac{3\left(m+n\right)}{6} have the same denominator, add them by adding their numerators.

$$12\times \frac{m+7n+3\left(m+n\right)}{6}$$

Do the multiplications in m+7n+3\left(m+n\right).

$$12\times \frac{m+7n+3m+3n}{6}$$

Combine like terms in m+7n+3m+3n.

$$12\times \frac{4m+10n}{6}$$

Cancel out 6, the greatest common factor in 12 and 6.

$$2\left(4m+10n\right)$$

Use the distributive property to multiply 2 by 4m+10n.

$$8m+20n$$

Expand

$$8m+20n$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 6 is 6. Multiply \frac{m+2n}{3} times \frac{2}{2}.

$$12\left(\frac{2\left(m+2n\right)}{6}-\frac{m-3n}{6}+\frac{m+n}{2}\right)$$

Since \frac{2\left(m+2n\right)}{6} and \frac{m-3n}{6} have the same denominator, subtract them by subtracting their numerators.

$$12\left(\frac{2\left(m+2n\right)-\left(m-3n\right)}{6}+\frac{m+n}{2}\right)$$

Do the multiplications in 2\left(m+2n\right)-\left(m-3n\right).

$$12\left(\frac{2m+4n-m+3n}{6}+\frac{m+n}{2}\right)$$

Combine like terms in 2m+4n-m+3n.

$$12\left(\frac{m+7n}{6}+\frac{m+n}{2}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 2 is 6. Multiply \frac{m+n}{2} times \frac{3}{3}.

$$12\left(\frac{m+7n}{6}+\frac{3\left(m+n\right)}{6}\right)$$

Since \frac{m+7n}{6} and \frac{3\left(m+n\right)}{6} have the same denominator, add them by adding their numerators.

$$12\times \frac{m+7n+3\left(m+n\right)}{6}$$

Do the multiplications in m+7n+3\left(m+n\right).

$$12\times \frac{m+7n+3m+3n}{6}$$

Combine like terms in m+7n+3m+3n.

$$12\times \frac{4m+10n}{6}$$

Cancel out 6, the greatest common factor in 12 and 6.

$$2\left(4m+10n\right)$$

Use the distributive property to multiply 2 by 4m+10n.

$$8m+20n$$