Basic Math Examples

$(\frac{1}{5} + \frac{1}{2}) \div (\frac{7}{15} - \frac{2}{5})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{1}{5} + \frac{1}{2}}{\frac{7}{15} - \frac{2}{5}}$

Step 2

Multiply the numerator and denominator of the fraction by $30$ .

Tap for more steps...

Step 2.1

Multiply $\frac{\frac{1}{5} + \frac{1}{2}}{\frac{7}{15} - \frac{2}{5}}$ by $\frac{30}{30}$ .

$\frac{30}{30} \cdot \frac{\frac{1}{5} + \frac{1}{2}}{\frac{7}{15} - \frac{2}{5}}$

Step 2.2

Combine.

$\frac{30 (\frac{1}{5} + \frac{1}{2})}{30 (\frac{7}{15} - \frac{2}{5})}$

Step 3

Apply the distributive property.

$\frac{30 (\frac{1}{5}) + 30 (\frac{1}{2})}{30 (\frac{7}{15}) + 30 (- \frac{2}{5})}$

Step 4

Simplify by cancelling.

Tap for more steps...

Step 4.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.1.1

Factor $5$ out of $30$ .

$\frac{5 (6) \frac{1}{5} + 30 (\frac{1}{2})}{30 (\frac{7}{15}) + 30 (- \frac{2}{5})}$

Step 4.1.2

Cancel the common factor.

$\frac{5 \cdot 6 \frac{1}{5} + 30 (\frac{1}{2})}{30 (\frac{7}{15}) + 30 (- \frac{2}{5})}$

Step 4.1.3

Rewrite the expression.

$\frac{6 + 30 (\frac{1}{2})}{30 (\frac{7}{15}) + 30 (- \frac{2}{5})}$

Step 4.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1

Factor $2$ out of $30$ .

$\frac{6 + 2 (15) \frac{1}{2}}{30 (\frac{7}{15}) + 30 (- \frac{2}{5})}$

Step 4.2.2

Cancel the common factor.

$\frac{6 + 2 \cdot 15 \frac{1}{2}}{30 (\frac{7}{15}) + 30 (- \frac{2}{5})}$

Step 4.2.3

Rewrite the expression.

$\frac{6 + 15}{30 (\frac{7}{15}) + 30 (- \frac{2}{5})}$

Step 4.3

Cancel the common factor of $15$ .

Tap for more steps...

Step 4.3.1

Factor $15$ out of $30$ .

$\frac{6 + 15}{15 (2) \frac{7}{15} + 30 (- \frac{2}{5})}$

Step 4.3.2

Cancel the common factor.

$\frac{6 + 15}{15 \cdot 2 \frac{7}{15} + 30 (- \frac{2}{5})}$

Step 4.3.3

Rewrite the expression.

$\frac{6 + 15}{2 \cdot 7 + 30 (- \frac{2}{5})}$

Step 4.4

Multiply $2$ by $7$ .

$\frac{6 + 15}{14 + 30 (- \frac{2}{5})}$

Step 4.5

Cancel the common factor of $5$ .

Tap for more steps...

Step 4.5.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{6 + 15}{14 + 30 (\frac{- 2}{5})}$

Step 4.5.2

Factor $5$ out of $30$ .

$\frac{6 + 15}{14 + 5 (6) \frac{- 2}{5}}$

Step 4.5.3

Cancel the common factor.

$\frac{6 + 15}{14 + 5 \cdot 6 \frac{- 2}{5}}$

Step 4.5.4

Rewrite the expression.

$\frac{6 + 15}{14 + 6 \cdot - 2}$

Step 4.6

Multiply $6$ by $- 2$ .

$\frac{6 + 15}{14 - 12}$

Step 5

Simplify by adding and subtracting.

Tap for more steps...

Step 5.1

Add $6$ and $15$ .

$\frac{21}{14 - 12}$

Step 5.2

Subtract $12$ from $14$ .

$\frac{21}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{2}$

Decimal Form:

$10.5$

Mixed Number Form:

$10 \frac{1}{2}$