Pre-Algebra Examples

$\frac{b}{4} = \frac{b}{12} + \frac{2}{3}$

Step 1

Multiply both sides by $4$ .

$\frac{b}{4} \cdot 4 = (\frac{b}{12} + \frac{2}{3}) \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{b}{4} \cdot 4 = (\frac{b}{12} + \frac{2}{3}) \cdot 4$

Step 2.1.1.2

Rewrite the expression.

$b = (\frac{b}{12} + \frac{2}{3}) \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{b}{12} + \frac{2}{3}) \cdot 4$ .

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Step 2.2.1.1

Apply the distributive property.

$b = \frac{b}{12} \cdot 4 + \frac{2}{3} \cdot 4$

Step 2.2.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.2.1

Factor $4$ out of $12$ .

$b = \frac{b}{4 (3)} \cdot 4 + \frac{2}{3} \cdot 4$

Step 2.2.1.2.2

Cancel the common factor.

$b = \frac{b}{4 \cdot 3} \cdot 4 + \frac{2}{3} \cdot 4$

Step 2.2.1.2.3

Rewrite the expression.

$b = \frac{b}{3} + \frac{2}{3} \cdot 4$

Step 2.2.1.3

Multiply $\frac{2}{3} \cdot 4$ .

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Step 2.2.1.3.1

Combine $\frac{2}{3}$ and $4$ .

$b = \frac{b}{3} + \frac{2 \cdot 4}{3}$

Step 2.2.1.3.2

Multiply $2$ by $4$ .

$b = \frac{b}{3} + \frac{8}{3}$

Step 3

Solve for $b$ .

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Step 3.1

Move all terms containing $b$ to the left side of the equation.

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Step 3.1.1

Subtract $\frac{b}{3}$ from both sides of the equation.

$b - \frac{b}{3} = \frac{8}{3}$

Step 3.1.2

To write $b$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$b \cdot \frac{3}{3} - \frac{b}{3} = \frac{8}{3}$

Step 3.1.3

Combine $b$ and $\frac{3}{3}$ .

$\frac{b \cdot 3}{3} - \frac{b}{3} = \frac{8}{3}$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{b \cdot 3 - b}{3} = \frac{8}{3}$

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

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

$\frac{3 \cdot b - b}{3} = \frac{8}{3}$

Step 3.1.5.2

Subtract $b$ from $3 b$ .

$\frac{2 b}{3} = \frac{8}{3}$

Step 3.2

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

$2 b = 8$

Step 3.3

Divide each term in $2 b = 8$ by $2$ and simplify.

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Step 3.3.1

Divide each term in $2 b = 8$ by $2$ .

$\frac{2 b}{2} = \frac{8}{2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{2 b}{2} = \frac{8}{2}$

Step 3.3.2.1.2

Divide $b$ by $1$ .

$b = \frac{8}{2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $8$ by $2$ .

$b = 4$