Basic Math Examples

$\frac{3 p - \frac{9}{8}}{8 p - \frac{24}{3}}$

Step 1

Cancel the common factor of $24$ and $3$ .

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Step 1.1

Factor $3$ out of $24$ .

$\frac{3 p - \frac{9}{8}}{8 p - \frac{3 \cdot 8}{3}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $3$ .

$\frac{3 p - \frac{9}{8}}{8 p - \frac{3 \cdot 8}{3 (1)}}$

Step 1.2.2

Cancel the common factor.

$\frac{3 p - \frac{9}{8}}{8 p - \frac{3 \cdot 8}{3 \cdot 1}}$

Step 1.2.3

Rewrite the expression.

$\frac{3 p - \frac{9}{8}}{8 p - \frac{8}{1}}$

Step 1.2.4

Divide $8$ by $1$ .

$\frac{3 p - \frac{9}{8}}{8 p - 1 \cdot 8}$

Step 2

Multiply the numerator and denominator of the fraction by $8$ .

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Step 2.1

Multiply $\frac{3 p - \frac{9}{8}}{8 p - 1 \cdot 8}$ by $\frac{8}{8}$ .

$\frac{8}{8} \cdot \frac{3 p - \frac{9}{8}}{8 p - 1 \cdot 8}$

Step 2.2

Combine.

$\frac{8 (3 p - \frac{9}{8})}{8 (8 p - 1 \cdot 8)}$

Step 3

Apply the distributive property.

$\frac{8 (3 p) + 8 (- \frac{9}{8})}{8 (8 p) + 8 (- 1 \cdot 8)}$

Step 4

Simplify terms.

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Step 4.1

Cancel the common factor of $8$ .

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Step 4.1.1

Move the leading negative in $- \frac{9}{8}$ into the numerator.

$\frac{8 (3 p) + 8 (\frac{- 9}{8})}{8 (8 p) + 8 (- 1 \cdot 8)}$

Step 4.1.2

Cancel the common factor.

$\frac{8 (3 p) + 8 (\frac{- 9}{8})}{8 (8 p) + 8 (- 1 \cdot 8)}$

Step 4.1.3

Rewrite the expression.

$\frac{8 (3 p) - 9}{8 (8 p) + 8 (- 1 \cdot 8)}$

Step 4.2

Factor $3$ out of $8 \cdot 3 p - 9$ .

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Step 4.2.1

Factor $3$ out of $8 \cdot 3 p$ .

$\frac{3 (8 p) - 9}{8 \cdot 8 p + 8 (- 1 \cdot 8)}$

Step 4.2.2

Factor $3$ out of $- 9$ .

$\frac{3 (8 p) + 3 \cdot - 3}{8 \cdot 8 p + 8 (- 1 \cdot 8)}$

Step 4.2.3

Factor $3$ out of $3 (8 p) + 3 \cdot - 3$ .

$\frac{3 (8 p - 3)}{8 \cdot 8 p + 8 (- 1 \cdot 8)}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $8$ by $8$ .

$\frac{3 (8 p - 3)}{64 p + 8 (- 1 \cdot 8)}$

Step 5.2

Multiply $8 (- 1 \cdot 8)$ .

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Step 5.2.1

Multiply $- 1$ by $8$ .

$\frac{3 (8 p - 3)}{64 p + 8 \cdot - 8}$

Step 5.2.2

Multiply $8$ by $- 8$ .

$\frac{3 (8 p - 3)}{64 p - 64}$

Step 5.3

Factor $64$ out of $64 p - 64$ .

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Step 5.3.1

Factor $64$ out of $64 p$ .

$\frac{3 (8 p - 3)}{64 (p) - 64}$

Step 5.3.2

Factor $64$ out of $- 64$ .

$\frac{3 (8 p - 3)}{64 (p) + 64 (- 1)}$

Step 5.3.3

Factor $64$ out of $64 (p) + 64 (- 1)$ .

$\frac{3 (8 p - 3)}{64 (p - 1)}$