Pre-Algebra Examples

$\frac{3}{4} - \frac{1}{2} \cdot \frac{8}{9}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{3}{4} + \frac{- 1}{2} \cdot \frac{8}{9}$

Step 1.1.2

Factor $2$ out of $8$ .

$\frac{3}{4} + \frac{- 1}{2} \cdot \frac{2 (4)}{9}$

Step 1.1.3

Cancel the common factor.

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

Step 1.1.4

Rewrite the expression.

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

Step 1.2

Rewrite $- 1 (\frac{4}{9})$ as $- (\frac{4}{9})$ .

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

Step 2

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

$\frac{3}{4} \cdot \frac{9}{9} - \frac{4}{9}$

Step 3

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

$\frac{3}{4} \cdot \frac{9}{9} - \frac{4}{9} \cdot \frac{4}{4}$

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 $\frac{9}{9}$ .

$\frac{3 \cdot 9}{4 \cdot 9} - \frac{4}{9} \cdot \frac{4}{4}$

Step 4.2

Multiply $4$ by $9$ .

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

Step 4.3

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

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

Step 4.4

Multiply $9$ by $4$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $9$ .

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

Step 6.2

Multiply $- 4$ by $4$ .

$\frac{27 - 16}{36}$

Step 6.3

Subtract $16$ from $27$ .

$\frac{11}{36}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{36}$

Decimal Form:

$0.30\overline{5}$