Basic Math Examples

$\frac{a}{b} \div \frac{a}{c} = \frac{c}{b}$

Step 1

Factor each term.

Tap for more steps...

Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{a}{b} \cdot \frac{c}{a} = \frac{c}{b}$

Step 1.2

Cancel the common factor of $a$ .

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$\frac{a}{b} \cdot \frac{c}{a} = \frac{c}{b}$

Step 1.2.2

Rewrite the expression.

$\frac{1}{b} c = \frac{c}{b}$

Step 1.3

Combine $\frac{1}{b}$ and $c$ .

$\frac{c}{b} = \frac{c}{b}$

Step 2

Solve the equation.

Tap for more steps...

Step 2.1

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$c = c$

Step 2.2

Move all terms containing $c$ to the left side of the equation.

Tap for more steps...

Step 2.2.1

Subtract $c$ from both sides of the equation.

$c - c = 0$

Step 2.2.2

Subtract $c$ from $c$ .

$0 = 0$

Step 2.3

Since $0 = 0$ , the equation will always be true.

Always true

Step 3

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$