Basic Math Examples

$\frac{\frac{2}{p^{2}} - \frac{3}{5 p}}{\frac{4}{p} + \frac{1}{4 p}}$

Step 1

Multiply the numerator and denominator of the fraction by $20 p^{2}$ .

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Step 1.1

Multiply $\frac{\frac{2}{p^{2}} - \frac{3}{5 p}}{\frac{4}{p} + \frac{1}{4 p}}$ by $\frac{20 p^{2}}{20 p^{2}}$ .

$\frac{20 p^{2}}{20 p^{2}} \cdot \frac{\frac{2}{p^{2}} - \frac{3}{5 p}}{\frac{4}{p} + \frac{1}{4 p}}$

Step 1.2

Combine.

$\frac{20 p^{2} (\frac{2}{p^{2}} - \frac{3}{5 p})}{20 p^{2} (\frac{4}{p} + \frac{1}{4 p})}$

Step 2

Apply the distributive property.

$\frac{20 p^{2} \frac{2}{p^{2}} + 20 p^{2} (- \frac{3}{5 p})}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $p^{2}$ .

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Step 3.1.1

Factor $p^{2}$ out of $20 p^{2}$ .

$\frac{p^{2} \cdot 20 \frac{2}{p^{2}} + 20 p^{2} (- \frac{3}{5 p})}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.1.2

Cancel the common factor.

$\frac{p^{2} \cdot 20 \frac{2}{p^{2}} + 20 p^{2} (- \frac{3}{5 p})}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.1.3

Rewrite the expression.

$\frac{20 \cdot 2 + 20 p^{2} (- \frac{3}{5 p})}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.2

Multiply $20$ by $2$ .

$\frac{40 + 20 p^{2} (- \frac{3}{5 p})}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.3

Cancel the common factor of $5 p$ .

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Step 3.3.1

Move the leading negative in $- \frac{3}{5 p}$ into the numerator.

$\frac{40 + 20 p^{2} \frac{- 3}{5 p}}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.3.2

Factor $5 p$ out of $20 p^{2}$ .

$\frac{40 + 5 p (4 p) \frac{- 3}{5 p}}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.3.3

Cancel the common factor.

$\frac{40 + 5 p (4 p) \frac{- 3}{5 p}}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.3.4

Rewrite the expression.

$\frac{40 + 4 p \cdot - 3}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.4

Multiply $- 3$ by $4$ .

$\frac{40 - 12 p}{20 p^{2} \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.5

Cancel the common factor of $p$ .

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Step 3.5.1

Factor $p$ out of $20 p^{2}$ .

$\frac{40 - 12 p}{p (20 p) \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.5.2

Cancel the common factor.

$\frac{40 - 12 p}{p (20 p) \frac{4}{p} + 20 p^{2} \frac{1}{4 p}}$

Step 3.5.3

Rewrite the expression.

$\frac{40 - 12 p}{20 p \cdot 4 + 20 p^{2} \frac{1}{4 p}}$

Step 3.6

Multiply $4$ by $20$ .

$\frac{40 - 12 p}{80 p + 20 p^{2} \frac{1}{4 p}}$

Step 3.7

Cancel the common factor of $4 p$ .

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Step 3.7.1

Factor $4 p$ out of $20 p^{2}$ .

$\frac{40 - 12 p}{80 p + 4 p (5 p) \frac{1}{4 p}}$

Step 3.7.2

Cancel the common factor.

$\frac{40 - 12 p}{80 p + 4 p (5 p) \frac{1}{4 p}}$

Step 3.7.3

Rewrite the expression.

$\frac{40 - 12 p}{80 p + 5 p}$

Step 4

Simplify terms.

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Step 4.1

Factor $4$ out of $40 - 12 p$ .

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Step 4.1.1

Factor $4$ out of $40$ .

$\frac{4 (10) - 12 p}{80 p + 5 p}$

Step 4.1.2

Factor $4$ out of $- 12 p$ .

$\frac{4 (10) + 4 (- 3 p)}{80 p + 5 p}$

Step 4.1.3

Factor $4$ out of $4 (10) + 4 (- 3 p)$ .

$\frac{4 (10 - 3 p)}{80 p + 5 p}$

Step 4.2

Add $80 p$ and $5 p$ .

$\frac{4 (10 - 3 p)}{85 p}$