Pre-Algebra Examples

$\frac{8}{\frac{4}{9} + \frac{16}{9}}$

Step 1

Simplify the denominator.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{8}{\frac{4 + 16}{9}}$

Step 1.2

Add $4$ and $16$ .

$\frac{8}{\frac{20}{9}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$8 (\frac{9}{20})$

Step 3

Cancel the common factor of $4$ .

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Step 3.1

Factor $4$ out of $8$ .

$4 (2) \frac{9}{20}$

Step 3.2

Factor $4$ out of $20$ .

$4 \cdot 2 \frac{9}{4 \cdot 5}$

Step 3.3

Cancel the common factor.

$4 \cdot 2 \frac{9}{4 \cdot 5}$

Step 3.4

Rewrite the expression.

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

Step 4

Combine $2$ and $\frac{9}{5}$ .

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

Step 5

Multiply $2$ by $9$ .

$\frac{18}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{18}{5}$

Decimal Form:

$3.6$

Mixed Number Form:

$3 \frac{3}{5}$