Algebra Examples

$(36 x \frac{5}{6}) \div (4 x \frac{2}{3})$

Step 1

Rewrite the division as a fraction.

$\frac{36 x (\frac{5}{6})}{4 x (\frac{2}{3})}$

Step 2

Cancel the common factor of $36$ and $4$ .

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Step 2.1

Factor $4$ out of $36 x (\frac{5}{6})$ .

$\frac{4 (9 x \frac{5}{6})}{4 x (\frac{2}{3})}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $4 x (\frac{2}{3})$ .

$\frac{4 (9 x \frac{5}{6})}{4 (x (\frac{2}{3}))}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (9 x \frac{5}{6})}{4 (x (\frac{2}{3}))}$

Step 2.2.3

Rewrite the expression.

$\frac{9 x \frac{5}{6}}{x (\frac{2}{3})}$

$\frac{9 x \frac{5}{6}}{x (\frac{2}{3})}$

$\frac{9 x \frac{5}{6}}{x (\frac{2}{3})}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{9 x \frac{5}{6}}{x \frac{2}{3}}$

Step 3.2

Rewrite the expression.

$\frac{9 (\frac{5}{6})}{\frac{2}{3}}$

$\frac{9 (\frac{5}{6})}{\frac{2}{3}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$9 (\frac{5}{6}) \frac{3}{2}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $9$ .

$3 (3) \frac{5}{6} \frac{3}{2}$

Step 5.2

Factor $3$ out of $6$ .

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

Step 5.3

Cancel the common factor.

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

Step 5.4

Rewrite the expression.

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

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

Step 6

Combine $3$ and $\frac{5}{2}$ .

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

Step 7

Multiply $3$ by $5$ .

$\frac{15}{2} \cdot \frac{3}{2}$

Step 8

Multiply $\frac{15}{2} \cdot \frac{3}{2}$ .

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Step 8.1

Multiply $\frac{15}{2}$ by $\frac{3}{2}$ .

$\frac{15 \cdot 3}{2 \cdot 2}$

Step 8.2

Multiply $15$ by $3$ .

$\frac{45}{2 \cdot 2}$

Step 8.3

Multiply $2$ by $2$ .

$\frac{45}{4}$

$\frac{45}{4}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{45}{4}$

Decimal Form:

$11.25$

Mixed Number Form:

$11 \frac{1}{4}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$