Pre-Algebra Examples

$\frac{6}{5} \div (\frac{2}{3} + \frac{1}{6})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{6}{5}}{\frac{2}{3} + \frac{1}{6}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{6}{5} \cdot \frac{1}{\frac{2}{3} + \frac{1}{6}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

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

$\frac{6}{5} \cdot \frac{1}{\frac{2}{3} \cdot \frac{2}{2} + \frac{1}{6}}$

Step 3.2

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.2.1

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

$\frac{6}{5} \cdot \frac{1}{\frac{2 \cdot 2}{3 \cdot 2} + \frac{1}{6}}$

Step 3.2.2

Multiply $3$ by $2$ .

$\frac{6}{5} \cdot \frac{1}{\frac{2 \cdot 2}{6} + \frac{1}{6}}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{6}{5} \cdot \frac{1}{\frac{2 \cdot 2 + 1}{6}}$

Step 3.4

Simplify the numerator.

Tap for more steps...

Step 3.4.1

Multiply $2$ by $2$ .

$\frac{6}{5} \cdot \frac{1}{\frac{4 + 1}{6}}$

Step 3.4.2

Add $4$ and $1$ .

$\frac{6}{5} \cdot \frac{1}{\frac{5}{6}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{6}{5} (1 (\frac{6}{5}))$

Step 5

Multiply $\frac{6}{5}$ by $1$ .

$\frac{6}{5} \cdot \frac{6}{5}$

Step 6

Multiply $\frac{6}{5} \cdot \frac{6}{5}$ .

Tap for more steps...

Step 6.1

Multiply $\frac{6}{5}$ by $\frac{6}{5}$ .

$\frac{6 \cdot 6}{5 \cdot 5}$

Step 6.2

Multiply $6$ by $6$ .

$\frac{36}{5 \cdot 5}$

Step 6.3

Multiply $5$ by $5$ .

$\frac{36}{25}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{36}{25}$

Decimal Form:

$1.44$

Mixed Number Form:

$1 \frac{11}{25}$