Basic Math Examples

$\frac{5 h^{3}}{2} \cdot \frac{12 g}{h^{4}} \div \frac{h^{2}}{6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 h^{3}}{2} \cdot \frac{12 g}{h^{4}} \frac{6}{h^{2}}$

Step 2

Combine.

$\frac{5 h^{3} (12 g)}{2 h^{4}} \cdot \frac{6}{h^{2}}$

Step 3

Combine.

$\frac{5 h^{3} (12 g) \cdot 6}{2 h^{4} h^{2}}$

Step 4

Multiply $h^{4}$ by $h^{2}$ by adding the exponents.

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Step 4.1

Move $h^{2}$ .

$\frac{5 h^{3} (12 g) \cdot 6}{2 (h^{2} h^{4})}$

Step 4.2

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

$\frac{5 h^{3} (12 g) \cdot 6}{2 h^{2 + 4}}$

Step 4.3

Add $2$ and $4$ .

$\frac{5 h^{3} (12 g) \cdot 6}{2 h^{6}}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $h^{3}$ and $h^{6}$ .

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Step 5.1.1

Factor $h^{3}$ out of $5 h^{3} (12 g) \cdot 6$ .

$\frac{h^{3} ((5 (12 g)) \cdot 6)}{2 h^{6}}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

Factor $h^{3}$ out of $2 h^{6}$ .

$\frac{h^{3} ((5 (12 g)) \cdot 6)}{h^{3} (2 h^{3})}$

Step 5.1.2.2

Cancel the common factor.

$\frac{h^{3} ((5 (12 g)) \cdot 6)}{h^{3} (2 h^{3})}$

Step 5.1.2.3

Rewrite the expression.

$\frac{(5 (12 g)) \cdot 6}{2 h^{3}}$

Step 5.2

Cancel the common factor of $12$ and $2$ .

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Step 5.2.1

Factor $2$ out of $(5 (12 g)) \cdot 6$ .

$\frac{2 (5 (6 g) \cdot 6)}{2 h^{3}}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $2$ out of $2 h^{3}$ .

$\frac{2 (5 (6 g) \cdot 6)}{2 (h^{3})}$

Step 5.2.2.2

Cancel the common factor.

$\frac{2 (5 (6 g) \cdot 6)}{2 h^{3}}$

Step 5.2.2.3

Rewrite the expression.

$\frac{5 (6 g) \cdot 6}{h^{3}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $5$ by $6$ .

$\frac{30 g \cdot 6}{h^{3}}$

Step 6.2

Multiply $6$ by $30$ .

$\frac{180 g}{h^{3}}$