Pre-Algebra Examples

$\frac{10 p^{3} q^{3}}{2 p^{2} q} \div \frac{5 p q}{6 p q^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{10 p^{3} q^{3}}{2 p^{2} q} \cdot \frac{6 p q^{2}}{5 p q}$

Step 2

Combine.

$\frac{10 p^{3} q^{3} (6 p q^{2})}{2 p^{2} q (5 p q)}$

Step 3

Multiply $p^{3}$ by $p$ by adding the exponents.

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Step 3.1

Move $p$ .

$\frac{10 (p \cdot p^{3}) q^{3} (6 q^{2})}{2 p^{2} q (5 p q)}$

Step 3.2

Multiply $p$ by $p^{3}$ .

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Step 3.2.1

Raise $p$ to the power of $1$ .

$\frac{10 (p^{1} p^{3}) q^{3} (6 q^{2})}{2 p^{2} q (5 p q)}$

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10 p^{1 + 3} q^{3} (6 q^{2})}{2 p^{2} q (5 p q)}$

Step 3.3

Add $1$ and $3$ .

$\frac{10 p^{4} q^{3} (6 q^{2})}{2 p^{2} q (5 p q)}$

Step 4

Multiply $q^{3}$ by $q^{2}$ by adding the exponents.

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Step 4.1

Move $q^{2}$ .

$\frac{10 p^{4} (q^{2} q^{3}) \cdot 6}{2 p^{2} q (5 p q)}$

Step 4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10 p^{4} q^{2 + 3} \cdot 6}{2 p^{2} q (5 p q)}$

Step 4.3

Add $2$ and $3$ .

$\frac{10 p^{4} q^{5} \cdot 6}{2 p^{2} q (5 p q)}$

Step 5

Multiply $p^{2}$ by $p$ by adding the exponents.

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Step 5.1

Move $p$ .

$\frac{10 p^{4} q^{5} \cdot 6}{2 (p \cdot p^{2}) q (5 q)}$

Step 5.2

Multiply $p$ by $p^{2}$ .

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Step 5.2.1

Raise $p$ to the power of $1$ .

$\frac{10 p^{4} q^{5} \cdot 6}{2 (p^{1} p^{2}) q (5 q)}$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10 p^{4} q^{5} \cdot 6}{2 p^{1 + 2} q (5 q)}$

Step 5.3

Add $1$ and $2$ .

$\frac{10 p^{4} q^{5} \cdot 6}{2 p^{3} q (5 q)}$

Step 6

Multiply $q$ by $q$ by adding the exponents.

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Step 6.1

Move $q$ .

$\frac{10 p^{4} q^{5} \cdot 6}{2 p^{3} (q \cdot q) \cdot 5}$

Step 6.2

Multiply $q$ by $q$ .

$\frac{10 p^{4} q^{5} \cdot 6}{2 p^{3} q^{2} \cdot 5}$

Step 7

Cancel the common factor of $10$ and $2$ .

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Step 7.1

Factor $2$ out of $10 p^{4} q^{5} \cdot 6$ .

$\frac{2 (5 p^{4} q^{5} \cdot 6)}{2 p^{3} q^{2} \cdot 5}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $2 p^{3} q^{2} \cdot 5$ .

$\frac{2 (5 p^{4} q^{5} \cdot 6)}{2 (p^{3} q^{2} \cdot 5)}$

Step 7.2.2

Cancel the common factor.

$\frac{2 (5 p^{4} q^{5} \cdot 6)}{2 (p^{3} q^{2} \cdot 5)}$

Step 7.2.3

Rewrite the expression.

$\frac{5 p^{4} q^{5} \cdot 6}{p^{3} q^{2} \cdot 5}$

Step 8

Cancel the common factor of $5$ .

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Step 8.1

Cancel the common factor.

$\frac{5 p^{4} q^{5} \cdot 6}{p^{3} q^{2} \cdot 5}$

Step 8.2

Rewrite the expression.

$\frac{p^{4} q^{5} \cdot 6}{p^{3} q^{2}}$

Step 9

Cancel the common factor of $p^{4}$ and $p^{3}$ .

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Step 9.1

Factor $p^{3}$ out of $p^{4} q^{5} \cdot 6$ .

$\frac{p^{3} (p q^{5} \cdot 6)}{p^{3} q^{2}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $p^{3}$ out of $p^{3} q^{2}$ .

$\frac{p^{3} (p q^{5} \cdot 6)}{p^{3} (q^{2})}$

Step 9.2.2

Cancel the common factor.

$\frac{p^{3} (p q^{5} \cdot 6)}{p^{3} q^{2}}$

Step 9.2.3

Rewrite the expression.

$\frac{p q^{5} \cdot 6}{q^{2}}$

Step 10

Cancel the common factor of $q^{5}$ and $q^{2}$ .

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Step 10.1

Factor $q^{2}$ out of $p q^{5} \cdot 6$ .

$\frac{q^{2} (p q^{3} \cdot 6)}{q^{2}}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Multiply by $1$ .

$\frac{q^{2} (p q^{3} \cdot 6)}{q^{2} \cdot 1}$

Step 10.2.2

Cancel the common factor.

$\frac{q^{2} (p q^{3} \cdot 6)}{q^{2} \cdot 1}$

Step 10.2.3

Rewrite the expression.

$\frac{p q^{3} \cdot 6}{1}$

Step 10.2.4

Divide $p q^{3} \cdot 6$ by $1$ .

$p q^{3} \cdot 6$

Step 11

Move $6$ to the left of $p q^{3}$ .

$6 p q^{3}$