Basic Math Examples

$2 + \frac{4}{9} y + 5 = 12$

Step 1

Simplify $2 + \frac{4}{9} y + 5$ .

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Step 1.1

Combine $\frac{4}{9}$ and $y$ .

$2 + \frac{4 y}{9} + 5 = 12$

Step 1.2

Add $2$ and $5$ .

$\frac{4 y}{9} + 7 = 12$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Subtract $7$ from both sides of the equation.

$\frac{4 y}{9} = 12 - 7$

Step 2.2

Subtract $7$ from $12$ .

$\frac{4 y}{9} = 5$

Step 3

Multiply both sides of the equation by $\frac{9}{4}$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{9}{4} \cdot \frac{4 y}{9}$ .

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Step 4.1.1.1

Cancel the common factor of $9$ .

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Step 4.1.1.1.1

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 y) = \frac{9}{4} \cdot 5$

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $4 y$ .

$\frac{1}{4} (4 (y)) = \frac{9}{4} \cdot 5$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 y) = \frac{9}{4} \cdot 5$

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{9}{4} \cdot 5$ .

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Step 4.2.1.1

Combine $\frac{9}{4}$ and $5$ .

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

Step 4.2.1.2

Multiply $9$ by $5$ .

$y = \frac{45}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{45}{4}$

Decimal Form:

$y = 11.25$

Mixed Number Form:

$y = 11 \frac{1}{4}$