Pre-Algebra Examples

$\frac{6 d^{2}}{4 c} \div \frac{c^{2} d^{3}}{18}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 d^{2}}{4 c} \cdot \frac{18}{c^{2} d^{3}}$

Step 2

Combine.

$\frac{6 d^{2} \cdot 18}{4 c (c^{2} d^{3})}$

Step 3

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

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Step 3.1

Move $c^{2}$ .

$\frac{6 d^{2} \cdot 18}{4 (c^{2} c) d^{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{6 d^{2} \cdot 18}{4 (c^{2} c^{1}) d^{3}}$

Step 3.2.2

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

$\frac{6 d^{2} \cdot 18}{4 c^{2 + 1} d^{3}}$

$\frac{6 d^{2} \cdot 18}{4 c^{2 + 1} d^{3}}$

Step 3.3

Add $2$ and $1$ .

$\frac{6 d^{2} \cdot 18}{4 c^{3} d^{3}}$

$\frac{6 d^{2} \cdot 18}{4 c^{3} d^{3}}$

Step 4

Cancel the common factor of $6$ and $4$ .

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Step 4.1

Factor $2$ out of $6 d^{2} \cdot 18$ .

$\frac{2 (3 d^{2} \cdot 18)}{4 c^{3} d^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $4 c^{3} d^{3}$ .

$\frac{2 (3 d^{2} \cdot 18)}{2 (2 c^{3} d^{3})}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (3 d^{2} \cdot 18)}{2 (2 c^{3} d^{3})}$

Step 4.2.3

Rewrite the expression.

$\frac{3 d^{2} \cdot 18}{2 c^{3} d^{3}}$

$\frac{3 d^{2} \cdot 18}{2 c^{3} d^{3}}$

$\frac{3 d^{2} \cdot 18}{2 c^{3} d^{3}}$

Step 5

Cancel the common factor of $d^{2}$ and $d^{3}$ .

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Step 5.1

Factor $d^{2}$ out of $3 d^{2} \cdot 18$ .

$\frac{d^{2} (3 \cdot 18)}{2 c^{3} d^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $d^{2}$ out of $2 c^{3} d^{3}$ .

$\frac{d^{2} (3 \cdot 18)}{d^{2} (2 c^{3} d)}$

Step 5.2.2

Cancel the common factor.

$\frac{d^{2} (3 \cdot 18)}{d^{2} (2 c^{3} d)}$

Step 5.2.3

Rewrite the expression.

$\frac{3 \cdot 18}{2 c^{3} d}$

$\frac{3 \cdot 18}{2 c^{3} d}$

$\frac{3 \cdot 18}{2 c^{3} d}$

Step 6

Cancel the common factor of $18$ and $2$ .

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Step 6.1

Factor $2$ out of $3 \cdot 18$ .

$\frac{2 (3 \cdot 9)}{2 c^{3} d}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2 c^{3} d$ .

$\frac{2 (3 \cdot 9)}{2 (c^{3} d)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (3 \cdot 9)}{2 (c^{3} d)}$

Step 6.2.3

Rewrite the expression.

$\frac{3 \cdot 9}{c^{3} d}$

$\frac{3 \cdot 9}{c^{3} d}$

$\frac{3 \cdot 9}{c^{3} d}$

Step 7

Multiply $3$ by $9$ .

$\frac{27}{c^{3} d}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$