Pre-Algebra Examples

$\frac{\frac{b + 4}{\frac{8}{b - 2}}}{8}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{b + 4}{\frac{8}{b - 2}} \cdot \frac{1}{8}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$(b + 4) \frac{b - 2}{8} \frac{1}{8}$

Step 3

Apply the distributive property.

$(b \frac{b - 2}{8} + 4 \frac{b - 2}{8}) \frac{1}{8}$

Step 4

Combine $b$ and $\frac{b - 2}{8}$ .

$(\frac{b (b - 2)}{8} + 4 \frac{b - 2}{8}) \frac{1}{8}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Factor $4$ out of $8$ .

$(\frac{b (b - 2)}{8} + 4 \frac{b - 2}{4 (2)}) \frac{1}{8}$

Step 5.2

Cancel the common factor.

$(\frac{b (b - 2)}{8} + 4 \frac{b - 2}{4 \cdot 2}) \frac{1}{8}$

Step 5.3

Rewrite the expression.

$(\frac{b (b - 2)}{8} + \frac{b - 2}{2}) \frac{1}{8}$

Step 6

To write $\frac{b - 2}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{b (b - 2)}{8} + \frac{b - 2}{2} \cdot \frac{4}{4}) \frac{1}{8}$

Step 7

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{b - 2}{2}$ by $\frac{4}{4}$ .

$(\frac{b (b - 2)}{8} + \frac{(b - 2) \cdot 4}{2 \cdot 4}) \frac{1}{8}$

Step 7.2

Multiply $2$ by $4$ .

$(\frac{b (b - 2)}{8} + \frac{(b - 2) \cdot 4}{8}) \frac{1}{8}$

Step 8

Combine the numerators over the common denominator.

$\frac{b (b - 2) + (b - 2) \cdot 4}{8} \cdot \frac{1}{8}$

Step 9

Factor $b - 2$ out of $b (b - 2) + (b - 2) \cdot 4$ .

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Step 9.1

Factor $b - 2$ out of $b (b - 2)$ .

$\frac{(b - 2) b + (b - 2) \cdot 4}{8} \cdot \frac{1}{8}$

Step 9.2

Factor $b - 2$ out of $(b - 2) \cdot 4$ .

$\frac{(b - 2) b + (b - 2) (4)}{8} \cdot \frac{1}{8}$

Step 9.3

Factor $b - 2$ out of $(b - 2) b + (b - 2) (4)$ .

$\frac{(b - 2) (b + 4)}{8} \cdot \frac{1}{8}$

Step 10

Multiply $\frac{(b - 2) (b + 4)}{8} \cdot \frac{1}{8}$ .

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Step 10.1

Multiply $\frac{(b - 2) (b + 4)}{8}$ by $\frac{1}{8}$ .

$\frac{(b - 2) (b + 4)}{8 \cdot 8}$

Step 10.2

Multiply $8$ by $8$ .

$\frac{(b - 2) (b + 4)}{64}$

Step 11

Expand $(b - 2) (b + 4)$ using the FOIL Method.

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Step 11.1

Apply the distributive property.

$\frac{b (b + 4) - 2 (b + 4)}{64}$

Step 11.2

Apply the distributive property.

$\frac{b \cdot b + b \cdot 4 - 2 (b + 4)}{64}$

Step 11.3

Apply the distributive property.

$\frac{b \cdot b + b \cdot 4 - 2 b - 2 \cdot 4}{64}$

Step 12

Simplify and combine like terms.

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Step 12.1

Simplify each term.

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Step 12.1.1

Multiply $b$ by $b$ .

$\frac{b^{2} + b \cdot 4 - 2 b - 2 \cdot 4}{64}$

Step 12.1.2

Move $4$ to the left of $b$ .

$\frac{b^{2} + 4 \cdot b - 2 b - 2 \cdot 4}{64}$

Step 12.1.3

Multiply $- 2$ by $4$ .

$\frac{b^{2} + 4 b - 2 b - 8}{64}$

Step 12.2

Subtract $2 b$ from $4 b$ .

$\frac{b^{2} + 2 b - 8}{64}$

Step 13

Split the fraction $\frac{b^{2} + 2 b - 8}{64}$ into two fractions.

$\frac{b^{2} + 2 b}{64} + \frac{- 8}{64}$

Step 14

Split the fraction $\frac{b^{2} + 2 b}{64}$ into two fractions.

$\frac{b^{2}}{64} + \frac{2 b}{64} + \frac{- 8}{64}$

Step 15

Cancel the common factor of $2$ and $64$ .

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Step 15.1

Factor $2$ out of $2 b$ .

$\frac{b^{2}}{64} + \frac{2 (b)}{64} + \frac{- 8}{64}$

Step 15.2

Cancel the common factors.

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Step 15.2.1

Factor $2$ out of $64$ .

$\frac{b^{2}}{64} + \frac{2 b}{2 \cdot 32} + \frac{- 8}{64}$

Step 15.2.2

Cancel the common factor.

$\frac{b^{2}}{64} + \frac{2 b}{2 \cdot 32} + \frac{- 8}{64}$

Step 15.2.3

Rewrite the expression.

$\frac{b^{2}}{64} + \frac{b}{32} + \frac{- 8}{64}$

Step 16

Cancel the common factor of $- 8$ and $64$ .

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Step 16.1

Factor $8$ out of $- 8$ .

$\frac{b^{2}}{64} + \frac{b}{32} + \frac{8 (- 1)}{64}$

Step 16.2

Cancel the common factors.

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Step 16.2.1

Factor $8$ out of $64$ .

$\frac{b^{2}}{64} + \frac{b}{32} + \frac{8 \cdot - 1}{8 \cdot 8}$

Step 16.2.2

Cancel the common factor.

$\frac{b^{2}}{64} + \frac{b}{32} + \frac{8 \cdot - 1}{8 \cdot 8}$

Step 16.2.3

Rewrite the expression.

$\frac{b^{2}}{64} + \frac{b}{32} + \frac{- 1}{8}$

Step 17

Move the negative in front of the fraction.

$\frac{b^{2}}{64} + \frac{b}{32} - \frac{1}{8}$