Algebra Examples

$\frac{5 y - 3}{6 y} + \frac{y + 2}{4 y}$

Step 1

To write $\frac{5 y - 3}{6 y}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 y - 3}{6 y} \cdot \frac{2}{2} + \frac{y + 2}{4 y}$

Step 2

To write $\frac{y + 2}{4 y}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 y - 3}{6 y} \cdot \frac{2}{2} + \frac{y + 2}{4 y} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $12 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 y - 3}{6 y}$ by $\frac{2}{2}$ .

$\frac{(5 y - 3) \cdot 2}{6 y \cdot 2} + \frac{y + 2}{4 y} \cdot \frac{3}{3}$

Step 3.2

Multiply $2$ by $6$ .

$\frac{(5 y - 3) \cdot 2}{12 y} + \frac{y + 2}{4 y} \cdot \frac{3}{3}$

Step 3.3

Multiply $\frac{y + 2}{4 y}$ by $\frac{3}{3}$ .

$\frac{(5 y - 3) \cdot 2}{12 y} + \frac{(y + 2) \cdot 3}{4 y \cdot 3}$

Step 3.4

Multiply $3$ by $4$ .

$\frac{(5 y - 3) \cdot 2}{12 y} + \frac{(y + 2) \cdot 3}{12 y}$

Step 4

Combine the numerators over the common denominator.

$\frac{(5 y - 3) \cdot 2 + (y + 2) \cdot 3}{12 y}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{5 y \cdot 2 - 3 \cdot 2 + (y + 2) \cdot 3}{12 y}$

Step 5.2

Multiply $2$ by $5$ .

$\frac{10 y - 3 \cdot 2 + (y + 2) \cdot 3}{12 y}$

Step 5.3

Multiply $- 3$ by $2$ .

$\frac{10 y - 6 + (y + 2) \cdot 3}{12 y}$

Step 5.4

Apply the distributive property.

$\frac{10 y - 6 + y \cdot 3 + 2 \cdot 3}{12 y}$

Step 5.5

Move $3$ to the left of $y$ .

$\frac{10 y - 6 + 3 \cdot y + 2 \cdot 3}{12 y}$

Step 5.6

Multiply $2$ by $3$ .

$\frac{10 y - 6 + 3 \cdot y + 6}{12 y}$

Step 5.7

Add $10 y$ and $3 y$ .

$\frac{13 y - 6 + 6}{12 y}$

Step 5.8

Add $- 6$ and $6$ .

$\frac{13 y + 0}{12 y}$

Step 5.9

Add $13 y$ and $0$ .

$\frac{13 y}{12 y}$

Step 6

Cancel the common factor of $y$ .

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Step 6.1

Cancel the common factor.

$\frac{13 y}{12 y}$

Step 6.2

Rewrite the expression.

$\frac{13}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{12}$

Decimal Form:

$1.08\overline{3}$

Mixed Number Form:

$1 \frac{1}{12}$