Basic Math Examples

$\frac{\frac{21 n^{5}}{3 p^{5} q^{2}}}{\frac{7 m n^{3}}{9 p^{2} q}}$

Step 1

Cancel the common factor of $21$ and $3$ .

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Step 1.1

Factor $3$ out of $21 n^{5}$ .

$\frac{\frac{3 (7 n^{5})}{3 p^{5} q^{2}}}{\frac{7 m n^{3}}{9 p^{2} q}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

$\frac{\frac{3 (7 n^{5})}{3 (p^{5} q^{2})}}{\frac{7 m n^{3}}{9 p^{2} q}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{3 (7 n^{5})}{3 (p^{5} q^{2})}}{\frac{7 m n^{3}}{9 p^{2} q}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{7 n^{5}}{p^{5} q^{2}}}{\frac{7 m n^{3}}{9 p^{2} q}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 n^{5}}{p^{5} q^{2}} \cdot \frac{9 p^{2} q}{7 m n^{3}}$

Step 3

Combine.

$\frac{7 n^{5} (9 p^{2} q)}{p^{5} q^{2} (7 m n^{3})}$

Step 4

Cancel the common factor of $7$ .

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Step 4.1

Cancel the common factor.

$\frac{7 n^{5} (9 p^{2} q)}{p^{5} q^{2} (7 m n^{3})}$

Step 4.2

Rewrite the expression.

$\frac{n^{5} (9 p^{2} q)}{p^{5} q^{2} (m n^{3})}$

Step 5

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

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Step 5.1

Factor $n^{3}$ out of $n^{5} (9 p^{2} q)$ .

$\frac{n^{3} (n^{2} (9 p^{2} q))}{p^{5} q^{2} (m n^{3})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{n^{3} (n^{2} (9 p^{2} q))}{n^{3} (p^{5} q^{2} (m))}$

Step 5.2.2

Cancel the common factor.

$\frac{n^{3} (n^{2} (9 p^{2} q))}{n^{3} (p^{5} q^{2} (m))}$

Step 5.2.3

Rewrite the expression.

$\frac{n^{2} (9 p^{2} q)}{p^{5} q^{2} (m)}$

Step 6

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

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Step 6.1

Factor $p^{2}$ out of $n^{2} (9 p^{2} q)$ .

$\frac{p^{2} (n^{2} (9 q))}{p^{5} q^{2} (m)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $p^{2}$ out of $p^{5} q^{2} (m)$ .

$\frac{p^{2} (n^{2} (9 q))}{p^{2} (p^{3} q^{2} m)}$

Step 6.2.2

Cancel the common factor.

$\frac{p^{2} (n^{2} (9 q))}{p^{2} (p^{3} q^{2} m)}$

Step 6.2.3

Rewrite the expression.

$\frac{n^{2} (9 q)}{p^{3} q^{2} m}$

Step 7

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

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Step 7.1

Factor $q$ out of $n^{2} (9 q)$ .

$\frac{q (n^{2} \cdot (9))}{p^{3} q^{2} m}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{q (n^{2} \cdot (9))}{q (p^{3} q m)}$

Step 7.2.2

Cancel the common factor.

$\frac{q (n^{2} \cdot (9))}{q (p^{3} q m)}$

Step 7.2.3

Rewrite the expression.

$\frac{n^{2} \cdot (9)}{p^{3} q m}$

Step 8

Move $9$ to the left of $n^{2}$ .

$\frac{9 n^{2}}{p^{3} q m}$