Pre-Algebra Examples

$(\frac{3}{4} - \frac{4}{9}) \div \frac{5}{6}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{4}$ by $\frac{9}{9}$ .

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

Step 4.2

Multiply $4$ by $9$ .

$(\frac{3 \cdot 9}{36} - \frac{4}{9} \cdot \frac{4}{4}) \frac{6}{5}$

Step 4.3

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

$(\frac{3 \cdot 9}{36} - \frac{4 \cdot 4}{9 \cdot 4}) \frac{6}{5}$

Step 4.4

Multiply $9$ by $4$ .

$(\frac{3 \cdot 9}{36} - \frac{4 \cdot 4}{36}) \frac{6}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \cdot 9 - 4 \cdot 4}{36} \cdot \frac{6}{5}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $9$ .

$\frac{27 - 4 \cdot 4}{36} \cdot \frac{6}{5}$

Step 6.2

Multiply $- 4$ by $4$ .

$\frac{27 - 16}{36} \cdot \frac{6}{5}$

Step 6.3

Subtract $16$ from $27$ .

$\frac{11}{36} \cdot \frac{6}{5}$

Step 7

Cancel the common factor of $6$ .

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Step 7.1

Factor $6$ out of $36$ .

$\frac{11}{6 (6)} \cdot \frac{6}{5}$

Step 7.2

Cancel the common factor.

$\frac{11}{6 \cdot 6} \cdot \frac{6}{5}$

Step 7.3

Rewrite the expression.

$\frac{11}{6} \cdot \frac{1}{5}$

Step 8

Multiply $\frac{11}{6}$ by $\frac{1}{5}$ .

$\frac{11}{6 \cdot 5}$

Step 9

Multiply $6$ by $5$ .

$\frac{11}{30}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{30}$

Decimal Form:

$0.3\overline{6}$