Algebra Examples

\frac{2}{9} \div \frac{5}{12}

$\frac{2}{9} \div \frac{5}{12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

\frac{2}{9} \cdot \frac{12}{5}

$\frac{2}{9} \cdot \frac{12}{5}$

Step 2

Cancel the common factor of

3

$3$ .

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Step 2.1

Factor

3

$3$ out of

9

$9$ .

\frac{2}{3 (3)} \cdot \frac{12}{5}

$\frac{2}{3 (3)} \cdot \frac{12}{5}$

Step 2.2

Factor

3

$3$ out of

12

$12$ .

\frac{2}{3 \cdot 3} \cdot \frac{3 \cdot 4}{5}

$\frac{2}{3 \cdot 3} \cdot \frac{3 \cdot 4}{5}$

Step 2.3

Cancel the common factor.

\frac{2}{3 \cdot 3} \cdot \frac{3 \cdot 4}{5}

$\frac{2}{3 \cdot 3} \cdot \frac{3 \cdot 4}{5}$

Step 2.4

Rewrite the expression.

\frac{2}{3} \cdot \frac{4}{5}

$\frac{2}{3} \cdot \frac{4}{5}$

\frac{2}{3} \cdot \frac{4}{5}

$\frac{2}{3} \cdot \frac{4}{5}$

Step 3

Multiply

\frac{2}{3}

$\frac{2}{3}$ by

\frac{4}{5}

$\frac{4}{5}$ .

\frac{2 \cdot 4}{3 \cdot 5}

$\frac{2 \cdot 4}{3 \cdot 5}$

Step 4

Multiply

2

$2$ by

4

$4$ .

\frac{8}{3 \cdot 5}

$\frac{8}{3 \cdot 5}$

Step 5

Multiply

3

$3$ by

5

$5$ .

\frac{8}{15}

$\frac{8}{15}$