Pre-Algebra Examples

$\frac{1}{2} + \frac{2}{3} \div \frac{3}{4} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{2} + \frac{2}{3} \cdot \frac{4}{3} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.2

Multiply $\frac{2}{3} \cdot \frac{4}{3}$ .

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Step 1.2.1

Multiply $\frac{2}{3}$ by $\frac{4}{3}$ .

$\frac{1}{2} + \frac{2 \cdot 4}{3 \cdot 3} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.2.2

Multiply $2$ by $4$ .

$\frac{1}{2} + \frac{8}{3 \cdot 3} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.2.3

Multiply $3$ by $3$ .

$\frac{1}{2} + \frac{8}{9} - (\frac{4}{5} \cdot \frac{5}{6})$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$\frac{1}{2} + \frac{8}{9} - (\frac{2 (2)}{5} \cdot \frac{5}{6})$

Step 1.3.2

Factor $2$ out of $6$ .

$\frac{1}{2} + \frac{8}{9} - (\frac{2 \cdot 2}{5} \cdot \frac{5}{2 \cdot 3})$

Step 1.3.3

Cancel the common factor.

$\frac{1}{2} + \frac{8}{9} - (\frac{2 \cdot 2}{5} \cdot \frac{5}{2 \cdot 3})$

Step 1.3.4

Rewrite the expression.

$\frac{1}{2} + \frac{8}{9} - (\frac{2}{5} \cdot \frac{5}{3})$

Step 1.4

Cancel the common factor of $5$ .

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Step 1.4.1

Cancel the common factor.

$\frac{1}{2} + \frac{8}{9} - (\frac{2}{5} \cdot \frac{5}{3})$

Step 1.4.2

Rewrite the expression.

$\frac{1}{2} + \frac{8}{9} - (2 \cdot \frac{1}{3})$

Step 1.5

Combine $2$ and $\frac{1}{3}$ .

$\frac{1}{2} + \frac{8}{9} - \frac{2}{3}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$\frac{1}{2} \cdot \frac{9}{9} + \frac{8}{9} - \frac{2}{3}$

Step 2.2

Multiply $\frac{1}{2}$ by $\frac{9}{9}$ .

$\frac{9}{2 \cdot 9} + \frac{8}{9} - \frac{2}{3}$

Step 2.3

Multiply $\frac{8}{9}$ by $\frac{2}{2}$ .

$\frac{9}{2 \cdot 9} + \frac{8}{9} \cdot \frac{2}{2} - \frac{2}{3}$

Step 2.4

Multiply $\frac{8}{9}$ by $\frac{2}{2}$ .

$\frac{9}{2 \cdot 9} + \frac{8 \cdot 2}{9 \cdot 2} - \frac{2}{3}$

Step 2.5

Multiply $\frac{2}{3}$ by $\frac{6}{6}$ .

$\frac{9}{2 \cdot 9} + \frac{8 \cdot 2}{9 \cdot 2} - (\frac{2}{3} \cdot \frac{6}{6})$

Step 2.6

Multiply $\frac{2}{3}$ by $\frac{6}{6}$ .

$\frac{9}{2 \cdot 9} + \frac{8 \cdot 2}{9 \cdot 2} - \frac{2 \cdot 6}{3 \cdot 6}$

Step 2.7

Multiply $2$ by $9$ .

$\frac{9}{18} + \frac{8 \cdot 2}{9 \cdot 2} - \frac{2 \cdot 6}{3 \cdot 6}$

Step 2.8

Reorder the factors of $9 \cdot 2$ .

$\frac{9}{18} + \frac{8 \cdot 2}{2 \cdot 9} - \frac{2 \cdot 6}{3 \cdot 6}$

Step 2.9

Multiply $2$ by $9$ .

$\frac{9}{18} + \frac{8 \cdot 2}{18} - \frac{2 \cdot 6}{3 \cdot 6}$

Step 2.10

Multiply $3$ by $6$ .

$\frac{9}{18} + \frac{8 \cdot 2}{18} - \frac{2 \cdot 6}{18}$

Step 3

Combine the numerators over the common denominator.

$\frac{9 + 8 \cdot 2 - 2 \cdot 6}{18}$

Step 4

Simplify each term.

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Step 4.1

Multiply $8$ by $2$ .

$\frac{9 + 16 - 2 \cdot 6}{18}$

Step 4.2

Multiply $- 2$ by $6$ .

$\frac{9 + 16 - 12}{18}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $9$ and $16$ .

$\frac{25 - 12}{18}$

Step 5.2

Subtract $12$ from $25$ .

$\frac{13}{18}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{18}$

Decimal Form:

$0.7\overline{2}$