Basic Math Examples

$\frac{1}{8} y - 12 = \frac{3}{8} - 4$

Step 1

Combine $\frac{1}{8}$ and $y$ .

$\frac{y}{8} - 12 = \frac{3}{8} - 4$

Step 2

Simplify $\frac{3}{8} - 4$ .

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Step 2.1

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{y}{8} - 12 = \frac{3}{8} - 4 \cdot \frac{8}{8}$

Step 2.2

Combine $- 4$ and $\frac{8}{8}$ .

$\frac{y}{8} - 12 = \frac{3}{8} + \frac{- 4 \cdot 8}{8}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{y}{8} - 12 = \frac{3 - 4 \cdot 8}{8}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $- 4$ by $8$ .

$\frac{y}{8} - 12 = \frac{3 - 32}{8}$

Step 2.4.2

Subtract $32$ from $3$ .

$\frac{y}{8} - 12 = \frac{- 29}{8}$

Step 2.5

Move the negative in front of the fraction.

$\frac{y}{8} - 12 = - \frac{29}{8}$

Step 3

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

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Step 3.1

Add $12$ to both sides of the equation.

$\frac{y}{8} = - \frac{29}{8} + 12$

Step 3.2

To write $12$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{y}{8} = - \frac{29}{8} + 12 \cdot \frac{8}{8}$

Step 3.3

Combine $12$ and $\frac{8}{8}$ .

$\frac{y}{8} = - \frac{29}{8} + \frac{12 \cdot 8}{8}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{y}{8} = \frac{- 29 + 12 \cdot 8}{8}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $12$ by $8$ .

$\frac{y}{8} = \frac{- 29 + 96}{8}$

Step 3.5.2

Add $- 29$ and $96$ .

$\frac{y}{8} = \frac{67}{8}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$y = 67$