Basic Math Examples

$\frac{5 m n^{3}}{21 p^{2} q} \div \frac{20 n^{5}}{7 p^{4} q^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 m n^{3}}{21 p^{2} q} \cdot \frac{7 p^{4} q^{4}}{20 n^{5}}$

Step 2

Combine.

$\frac{5 m n^{3} (7 p^{4} q^{4})}{21 p^{2} q (20 n^{5})}$

Step 3

Cancel the common factor of $5$ and $20$ .

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Step 3.1

Factor $5$ out of $5 m n^{3} (7 p^{4} q^{4})$ .

$\frac{5 (m n^{3} (7 p^{4} q^{4}))}{21 p^{2} q (20 n^{5})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $21 p^{2} q (20 n^{5})$ .

$\frac{5 (m n^{3} (7 p^{4} q^{4}))}{5 (21 p^{2} q (4 n^{5}))}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (m n^{3} (7 p^{4} q^{4}))}{5 (21 p^{2} q (4 n^{5}))}$

Step 3.2.3

Rewrite the expression.

$\frac{m n^{3} (7 p^{4} q^{4})}{21 p^{2} q (4 n^{5})}$

Step 4

Cancel the common factor of $n^{3}$ and $n^{5}$ .

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Step 4.1

Factor $n^{3}$ out of $m n^{3} (7 p^{4} q^{4})$ .

$\frac{n^{3} (m (7 p^{4} q^{4}))}{21 p^{2} q (4 n^{5})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $n^{3}$ out of $21 p^{2} q (4 n^{5})$ .

$\frac{n^{3} (m (7 p^{4} q^{4}))}{n^{3} (21 p^{2} q (4 n^{2}))}$

Step 4.2.2

Cancel the common factor.

$\frac{n^{3} (m (7 p^{4} q^{4}))}{n^{3} (21 p^{2} q (4 n^{2}))}$

Step 4.2.3

Rewrite the expression.

$\frac{m (7 p^{4} q^{4})}{21 p^{2} q (4 n^{2})}$

Step 5

Cancel the common factor of $7$ and $21$ .

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Step 5.1

Factor $7$ out of $m (7 p^{4} q^{4})$ .

$\frac{7 (m (p^{4} q^{4}))}{21 p^{2} q (4 n^{2})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $7$ out of $21 p^{2} q (4 n^{2})$ .

$\frac{7 (m (p^{4} q^{4}))}{7 (3 p^{2} q (4 n^{2}))}$

Step 5.2.2

Cancel the common factor.

$\frac{7 (m (p^{4} q^{4}))}{7 (3 p^{2} q (4 n^{2}))}$

Step 5.2.3

Rewrite the expression.

$\frac{m (p^{4} q^{4})}{3 p^{2} q (4 n^{2})}$

Step 6

Cancel the common factor of $p^{4}$ and $p^{2}$ .

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Step 6.1

Factor $p^{2}$ out of $m (p^{4} q^{4})$ .

$\frac{p^{2} (m (p^{2} q^{4}))}{3 p^{2} q (4 n^{2})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $p^{2}$ out of $3 p^{2} q (4 n^{2})$ .

$\frac{p^{2} (m (p^{2} q^{4}))}{p^{2} (3 q (4 n^{2}))}$

Step 6.2.2

Cancel the common factor.

$\frac{p^{2} (m (p^{2} q^{4}))}{p^{2} (3 q (4 n^{2}))}$

Step 6.2.3

Rewrite the expression.

$\frac{m (p^{2} q^{4})}{3 q (4 n^{2})}$

Step 7

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

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Step 7.1

Factor $q$ out of $m (p^{2} q^{4})$ .

$\frac{q (m (p^{2} q^{3}))}{3 q (4 n^{2})}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $q$ out of $3 q (4 n^{2})$ .

$\frac{q (m (p^{2} q^{3}))}{q (3 (4 n^{2}))}$

Step 7.2.2

Cancel the common factor.

$\frac{q (m (p^{2} q^{3}))}{q (3 (4 n^{2}))}$

Step 7.2.3

Rewrite the expression.

$\frac{m (p^{2} q^{3})}{3 (4 n^{2})}$

Step 8

Multiply $3$ by $4$ .

$\frac{m p^{2} q^{3}}{12 n^{2}}$