Basic Math Examples

$\frac{y + 2}{12} = \frac{5}{8}$

Step 1

Multiply both sides of the equation by $12$ .

$12 \frac{y + 2}{12} = 12 (\frac{5}{8})$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $12$ .

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Step 2.1.1.1

Cancel the common factor.

$12 \frac{y + 2}{12} = 12 (\frac{5}{8})$

Step 2.1.1.2

Rewrite the expression.

$y + 2 = 12 (\frac{5}{8})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $12 (\frac{5}{8})$ .

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Step 2.2.1.1

Cancel the common factor of $4$ .

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Step 2.2.1.1.1

Factor $4$ out of $12$ .

$y + 2 = 4 (3) \frac{5}{8}$

Step 2.2.1.1.2

Factor $4$ out of $8$ .

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

Step 2.2.1.1.3

Cancel the common factor.

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

Step 2.2.1.1.4

Rewrite the expression.

$y + 2 = 3 (\frac{5}{2})$

Step 2.2.1.2

Combine $3$ and $\frac{5}{2}$ .

$y + 2 = \frac{3 \cdot 5}{2}$

Step 2.2.1.3

Multiply $3$ by $5$ .

$y + 2 = \frac{15}{2}$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the equation.

$y = \frac{15}{2} - 2$

Step 3.2

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

$y = \frac{15}{2} - 2 \cdot \frac{2}{2}$

Step 3.3

Combine $- 2$ and $\frac{2}{2}$ .

$y = \frac{15}{2} + \frac{- 2 \cdot 2}{2}$

Step 3.4

Combine the numerators over the common denominator.

$y = \frac{15 - 2 \cdot 2}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 2$ by $2$ .

$y = \frac{15 - 4}{2}$

Step 3.5.2

Subtract $4$ from $15$ .

$y = \frac{11}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{11}{2}$

Decimal Form:

$y = 5.5$

Mixed Number Form:

$y = 5 \frac{1}{2}$