Pre-Algebra Examples

$\frac{5}{9} \div (\frac{4}{9} - \frac{3}{18})$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{5}{9}}{\frac{4}{9} - \frac{3}{18}}$

Step 2

Cancel the common factor of $3$ and $18$ .

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Step 2.1

Factor $3$ out of $3$ .

$\frac{\frac{5}{9}}{\frac{4}{9} - \frac{3 (1)}{18}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $18$ .

$\frac{\frac{5}{9}}{\frac{4}{9} - \frac{3 \cdot 1}{3 \cdot 6}}$

Step 2.2.2

Cancel the common factor.

$\frac{\frac{5}{9}}{\frac{4}{9} - \frac{3 \cdot 1}{3 \cdot 6}}$

Step 2.2.3

Rewrite the expression.

$\frac{\frac{5}{9}}{\frac{4}{9} - \frac{1}{6}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{9} \cdot \frac{1}{\frac{4}{9} - \frac{1}{6}}$

Step 4

Simplify the denominator.

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Step 4.1

To write $\frac{4}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5}{9} \cdot \frac{1}{\frac{4}{9} \cdot \frac{2}{2} - \frac{1}{6}}$

Step 4.2

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{9} \cdot \frac{1}{\frac{4}{9} \cdot \frac{2}{2} - \frac{1}{6} \cdot \frac{3}{3}}$

Step 4.3

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{4}{9}$ by $\frac{2}{2}$ .

$\frac{5}{9} \cdot \frac{1}{\frac{4 \cdot 2}{9 \cdot 2} - \frac{1}{6} \cdot \frac{3}{3}}$

Step 4.3.2

Multiply $9$ by $2$ .

$\frac{5}{9} \cdot \frac{1}{\frac{4 \cdot 2}{18} - \frac{1}{6} \cdot \frac{3}{3}}$

Step 4.3.3

Multiply $\frac{1}{6}$ by $\frac{3}{3}$ .

$\frac{5}{9} \cdot \frac{1}{\frac{4 \cdot 2}{18} - \frac{3}{6 \cdot 3}}$

Step 4.3.4

Multiply $6$ by $3$ .

$\frac{5}{9} \cdot \frac{1}{\frac{4 \cdot 2}{18} - \frac{3}{18}}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{5}{9} \cdot \frac{1}{\frac{4 \cdot 2 - 3}{18}}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $4$ by $2$ .

$\frac{5}{9} \cdot \frac{1}{\frac{8 - 3}{18}}$

Step 4.5.2

Subtract $3$ from $8$ .

$\frac{5}{9} \cdot \frac{1}{\frac{5}{18}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$\frac{5}{9} (1 (\frac{18}{5}))$

Step 6

Multiply $\frac{18}{5}$ by $1$ .

$\frac{5}{9} \cdot \frac{18}{5}$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Cancel the common factor.

$\frac{5}{9} \cdot \frac{18}{5}$

Step 7.2

Rewrite the expression.

$\frac{1}{9} \cdot 18$

Step 8

Cancel the common factor of $9$ .

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Step 8.1

Factor $9$ out of $18$ .

$\frac{1}{9} \cdot (9 (2))$

Step 8.2

Cancel the common factor.

$\frac{1}{9} \cdot (9 \cdot 2)$

Step 8.3

Rewrite the expression.

$2$