Basic Math Examples

$\frac{5 m + 30}{m} \div \frac{3 m + 18}{10}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 m + 30}{m} \cdot \frac{10}{3 m + 18}$

Step 2

Factor $5$ out of $5 m + 30$ .

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Step 2.1

Factor $5$ out of $5 m$ .

$\frac{5 (m) + 30}{m} \cdot \frac{10}{3 m + 18}$

Step 2.2

Factor $5$ out of $30$ .

$\frac{5 m + 5 \cdot 6}{m} \cdot \frac{10}{3 m + 18}$

Step 2.3

Factor $5$ out of $5 m + 5 \cdot 6$ .

$\frac{5 (m + 6)}{m} \cdot \frac{10}{3 m + 18}$

Step 3

Factor $3$ out of $3 m + 18$ .

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Step 3.1

Factor $3$ out of $3 m$ .

$\frac{5 (m + 6)}{m} \cdot \frac{10}{3 (m) + 18}$

Step 3.2

Factor $3$ out of $18$ .

$\frac{5 (m + 6)}{m} \cdot \frac{10}{3 m + 3 \cdot 6}$

Step 3.3

Factor $3$ out of $3 m + 3 \cdot 6$ .

$\frac{5 (m + 6)}{m} \cdot \frac{10}{3 (m + 6)}$

Step 4

Cancel the common factor of $m + 6$ .

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Step 4.1

Factor $m + 6$ out of $5 (m + 6)$ .

$\frac{(m + 6) \cdot 5}{m} \cdot \frac{10}{3 (m + 6)}$

Step 4.2

Factor $m + 6$ out of $3 (m + 6)$ .

$\frac{(m + 6) \cdot 5}{m} \cdot \frac{10}{(m + 6) \cdot 3}$

Step 4.3

Cancel the common factor.

$\frac{(m + 6) \cdot 5}{m} \cdot \frac{10}{(m + 6) \cdot 3}$

Step 4.4

Rewrite the expression.

$\frac{5}{m} \cdot \frac{10}{3}$

Step 5

Multiply $\frac{5}{m}$ by $\frac{10}{3}$ .

$\frac{5 \cdot 10}{m \cdot 3}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $5$ by $10$ .

$\frac{50}{m \cdot 3}$

Step 6.2

Move $3$ to the left of $m$ .

$\frac{50}{3 m}$