Pre-Algebra Examples

$\frac{3 n}{2 m} \div \frac{5 n}{5 m}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{3 n}{2 m} \cdot \frac{5 m}{5 n}$

Step 2

Cancel the common factor of $n$ .

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Step 2.1

Factor $n$ out of $3 n$ .

$\frac{n \cdot 3}{2 m} \cdot \frac{5 m}{5 n}$

Step 2.2

Factor $n$ out of $5 n$ .

$\frac{n \cdot 3}{2 m} \cdot \frac{5 m}{n \cdot 5}$

Step 2.3

Cancel the common factor.

$\frac{n \cdot 3}{2 m} \cdot \frac{5 m}{n \cdot 5}$

Step 2.4

Rewrite the expression.

$\frac{3}{2 m} \cdot \frac{5 m}{5}$

Step 3

Cancel the common factor of $m$ .

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Step 3.1

Factor $m$ out of $2 m$ .

$\frac{3}{m \cdot 2} \cdot \frac{5 m}{5}$

Step 3.2

Factor $m$ out of $5 m$ .

$\frac{3}{m \cdot 2} \cdot \frac{m \cdot 5}{5}$

Step 3.3

Cancel the common factor.

$\frac{3}{m \cdot 2} \cdot \frac{m \cdot 5}{5}$

Step 3.4

Rewrite the expression.

$\frac{3}{2} \cdot \frac{5}{5}$

Step 4

Multiply $\frac{3}{2}$ by $\frac{5}{5}$ .

$\frac{3 \cdot 5}{2 \cdot 5}$

Step 5

Multiply $3$ by $5$ .

$\frac{15}{2 \cdot 5}$

Step 6

Multiply $2$ by $5$ .

$\frac{15}{10}$

Step 7

Cancel the common factor of $15$ and $10$ .

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Step 7.1

Factor $5$ out of $15$ .

$\frac{5 (3)}{10}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $5$ out of $10$ .

$\frac{5 \cdot 3}{5 \cdot 2}$

Step 7.2.2

Cancel the common factor.

$\frac{5 \cdot 3}{5 \cdot 2}$

Step 7.2.3

Rewrite the expression.

$\frac{3}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$