Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Multiply $2$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

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

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Step 5.1

Reorder $y$ and $2$ .

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

Step 5.2

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

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

Step 6

Apply the distributive property.

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

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

$5 y + 4 \cdot - 2$

Step 8

Multiply $4$ by $- 2$ .

$5 y - 8$