Simplify 4(3/4y-2+1/2y)

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

Simplify each term.

Combine $\frac{3}{4}$ and $y$ .

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

Combine $\frac{1}{2}$ and $y$ .

$4 (\frac{3 y}{4} - 2 + \frac{y}{2})$

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

$4 (\frac{3 y}{4} + \frac{y}{2} \cdot \frac{2}{2} - 2)$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{y}{2}$ by $\frac{2}{2}$ .

$4 (\frac{3 y}{4} + \frac{y \cdot 2}{2 \cdot 2} - 2)$

Multiply $2$ by $2$ .

$4 (\frac{3 y}{4} + \frac{y \cdot 2}{4} - 2)$

Combine the numerators over the common denominator.

$4 (\frac{3 y + y \cdot 2}{4} - 2)$

Add $3 y$ and $y \cdot 2$ .

Reorder $y$ and $2$ .

$4 (\frac{3 y + 2 \cdot y}{4} - 2)$

Add $3 y$ and $2 \cdot y$ .

$4 (\frac{5 y}{4} - 2)$

Apply the distributive property.

$4 \frac{5 y}{4} + 4 \cdot - 2$

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{5 y}{4} + 4 \cdot - 2$

Rewrite the expression.

$5 y + 4 \cdot - 2$

Multiply $4$ by $- 2$ .

$5 y - 8$