Evaluate 2(5/2-3)+6(1/3+5/2)

$2 (\frac{5}{2} - 3) + 6 (\frac{1}{3} + \frac{5}{2})$

Simplify each term.

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$2 (\frac{5}{2} - 3 \cdot \frac{2}{2}) + 6 (\frac{1}{3} + \frac{5}{2})$

Combine $- 3$ and $\frac{2}{2}$ .

$2 (\frac{5}{2} + \frac{- 3 \cdot 2}{2}) + 6 (\frac{1}{3} + \frac{5}{2})$

Combine the numerators over the common denominator.

$2 \frac{5 - 3 \cdot 2}{2} + 6 (\frac{1}{3} + \frac{5}{2})$

Simplify the numerator.

Multiply $- 3$ by $2$ .

$2 \frac{5 - 6}{2} + 6 (\frac{1}{3} + \frac{5}{2})$

Subtract $6$ from $5$ .

$2 (\frac{- 1}{2}) + 6 (\frac{1}{3} + \frac{5}{2})$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 (\frac{- 1}{2}) + 6 (\frac{1}{3} + \frac{5}{2})$

Rewrite the expression.

$- 1 + 6 (\frac{1}{3} + \frac{5}{2})$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 1 + 6 (\frac{1}{3} \cdot \frac{2}{2} + \frac{5}{2})$

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 1 + 6 (\frac{1}{3} \cdot \frac{2}{2} + \frac{5}{2} \cdot \frac{3}{3})$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$- 1 + 6 (\frac{2}{3 \cdot 2} + \frac{5}{2} \cdot \frac{3}{3})$

Multiply $3$ by $2$ .

$- 1 + 6 (\frac{2}{6} + \frac{5}{2} \cdot \frac{3}{3})$

Multiply $\frac{5}{2}$ by $\frac{3}{3}$ .

$- 1 + 6 (\frac{2}{6} + \frac{5 \cdot 3}{2 \cdot 3})$

Multiply $2$ by $3$ .

$- 1 + 6 (\frac{2}{6} + \frac{5 \cdot 3}{6})$

Combine the numerators over the common denominator.

$- 1 + 6 \frac{2 + 5 \cdot 3}{6}$

Simplify the numerator.

Multiply $5$ by $3$ .

$- 1 + 6 \frac{2 + 15}{6}$

Add $2$ and $15$ .

$- 1 + 6 (\frac{17}{6})$

Cancel the common factor of $6$ .

Cancel the common factor.

$- 1 + 6 (\frac{17}{6})$

Rewrite the expression.

$- 1 + 17$

Add $- 1$ and $17$ .

$16$