Basic Math Examples

$\frac{28 q^{2}}{3 r^{4} s^{3}} \div \frac{7 p q^{2}}{9 r^{3} s}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{28 q^{2}}{3 r^{4} s^{3}} \cdot \frac{9 r^{3} s}{7 p q^{2}}$

Step 2

Simplify terms.

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Step 2.1

Combine.

$\frac{28 q^{2} (9 r^{3} s)}{3 r^{4} s^{3} (7 p q^{2})}$

Step 2.2

Cancel the common factor of $28$ and $7$ .

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Step 2.2.1

Factor $7$ out of $28 q^{2} (9 r^{3} s)$ .

$\frac{7 (4 q^{2} (9 r^{3} s))}{3 r^{4} s^{3} (7 p q^{2})}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $7$ out of $3 r^{4} s^{3} (7 p q^{2})$ .

$\frac{7 (4 q^{2} (9 r^{3} s))}{7 (3 r^{4} s^{3} (p q^{2}))}$

Step 2.2.2.2

Cancel the common factor.

$\frac{7 (4 q^{2} (9 r^{3} s))}{7 (3 r^{4} s^{3} (p q^{2}))}$

Step 2.2.2.3

Rewrite the expression.

$\frac{4 q^{2} (9 r^{3} s)}{3 r^{4} s^{3} (p q^{2})}$

Step 2.3

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

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Step 2.3.1

Cancel the common factor.

$\frac{4 q^{2} (9 r^{3} s)}{3 r^{4} s^{3} (p q^{2})}$

Step 2.3.2

Rewrite the expression.

$\frac{4 (9 r^{3} s)}{3 r^{4} s^{3} (p)}$

Step 2.4

Cancel the common factor of $9$ and $3$ .

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Step 2.4.1

Factor $3$ out of $4 (9 r^{3} s)$ .

$\frac{3 (4 (3 r^{3} s))}{3 r^{4} s^{3} (p)}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $3$ out of $3 r^{4} s^{3} (p)$ .

$\frac{3 (4 (3 r^{3} s))}{3 (r^{4} s^{3} (p))}$

Step 2.4.2.2

Cancel the common factor.

$\frac{3 (4 (3 r^{3} s))}{3 (r^{4} s^{3} (p))}$

Step 2.4.2.3

Rewrite the expression.

$\frac{4 (3 r^{3} s)}{r^{4} s^{3} (p)}$

Step 2.5

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

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Step 2.5.1

Factor $r^{3}$ out of $4 (3 r^{3} s)$ .

$\frac{r^{3} (4 (3 s))}{r^{4} s^{3} (p)}$

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $r^{3}$ out of $r^{4} s^{3} (p)$ .

$\frac{r^{3} (4 (3 s))}{r^{3} (r s^{3} p)}$

Step 2.5.2.2

Cancel the common factor.

$\frac{r^{3} (4 (3 s))}{r^{3} (r s^{3} p)}$

Step 2.5.2.3

Rewrite the expression.

$\frac{4 (3 s)}{r s^{3} p}$

Step 2.6

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

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Step 2.6.1

Factor $s$ out of $4 (3 s)$ .

$\frac{s (4 \cdot (3))}{r s^{3} p}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $s$ out of $r s^{3} p$ .

$\frac{s (4 \cdot (3))}{s (r s^{2} p)}$

Step 2.6.2.2

Cancel the common factor.

$\frac{s (4 \cdot (3))}{s (r s^{2} p)}$

Step 2.6.2.3

Rewrite the expression.

$\frac{4 \cdot (3)}{r s^{2} p}$

Step 3

Multiply $4$ by $3$ .

$\frac{12}{r s^{2} p}$