Basic Math Examples

$\frac{9}{y} + \frac{9}{4} + \frac{9}{4 y}$

Step 1

To write $\frac{9}{y}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{y} \cdot \frac{4}{4} + \frac{9}{4} + \frac{9}{4 y}$

Step 2

To write $\frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{9}{y} \cdot \frac{4}{4} + \frac{9}{4} \cdot \frac{y}{y} + \frac{9}{4 y}$

Step 3

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

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Step 3.1

Multiply $\frac{9}{y}$ by $\frac{4}{4}$ .

$\frac{9 \cdot 4}{y \cdot 4} + \frac{9}{4} \cdot \frac{y}{y} + \frac{9}{4 y}$

Step 3.2

Multiply $\frac{9}{4}$ by $\frac{y}{y}$ .

$\frac{9 \cdot 4}{y \cdot 4} + \frac{9 y}{4 y} + \frac{9}{4 y}$

Step 3.3

Reorder the factors of $y \cdot 4$ .

$\frac{9 \cdot 4}{4 y} + \frac{9 y}{4 y} + \frac{9}{4 y}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 4 + 9 y}{4 y} + \frac{9}{4 y}$

Step 5

Combine the numerators over the common denominator.

$\frac{9 \cdot 4 + 9 y + 9}{4 y}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $9$ by $4$ .

$\frac{36 + 9 y + 9}{4 y}$

Step 6.2

Add $36$ and $9$ .

$\frac{9 y + 45}{4 y}$

Step 7

Factor $9$ out of $9 y + 45$ .

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Step 7.1

Factor $9$ out of $9 y$ .

$\frac{9 (y) + 45}{4 y}$

Step 7.2

Factor $9$ out of $45$ .

$\frac{9 y + 9 \cdot 5}{4 y}$

Step 7.3

Factor $9$ out of $9 y + 9 \cdot 5$ .

$\frac{9 (y + 5)}{4 y}$