Basic Math Examples

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

Step 1

To write $\frac{2 m}{n}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2

Write each expression with a common denominator of $n \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{2 m}{n}$ by $\frac{3}{3}$ .

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

Step 2.2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Factor $m$ out of $2 m \cdot 3 - 5 m$ .

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Step 4.1.1

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

$\frac{m (2 \cdot 3) - 5 m}{3 n}$

Step 4.1.2

Factor $m$ out of $- 5 m$ .

$\frac{m (2 \cdot 3) + m \cdot - 5}{3 n}$

Step 4.1.3

Factor $m$ out of $m (2 \cdot 3) + m \cdot - 5$ .

$\frac{m (2 \cdot 3 - 5)}{3 n}$

Step 4.2

Multiply $2$ by $3$ .

$\frac{m (6 - 5)}{3 n}$

Step 4.3

Subtract $5$ from $6$ .

$\frac{m \cdot 1}{3 n}$

Step 5

Multiply $m$ by $1$ .

$\frac{m}{3 n}$