Pre-Algebra Examples

$\frac{3}{4} - \frac{7}{9} \cdot {(\frac{1}{2})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{1}{2}$ .

$\frac{3}{4} - \frac{7}{9} \cdot \frac{1^{2}}{2^{2}}$

Step 1.2

One to any power is one.

$\frac{3}{4} - \frac{7}{9} \cdot \frac{1}{2^{2}}$

Step 1.3

Raise $2$ to the power of $2$ .

$\frac{3}{4} - \frac{7}{9} \cdot \frac{1}{4}$

Step 1.4

Multiply $- \frac{7}{9} \cdot \frac{1}{4}$ .

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Step 1.4.1

Multiply $\frac{1}{4}$ by $\frac{7}{9}$ .

$\frac{3}{4} - \frac{7}{4 \cdot 9}$

Step 1.4.2

Multiply $4$ by $9$ .

$\frac{3}{4} - \frac{7}{36}$

Step 2

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

$\frac{3}{4} \cdot \frac{9}{9} - \frac{7}{36}$

Step 3

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

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Step 3.1

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

$\frac{3 \cdot 9}{4 \cdot 9} - \frac{7}{36}$

Step 3.2

Multiply $4$ by $9$ .

$\frac{3 \cdot 9}{36} - \frac{7}{36}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 9 - 7}{36}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $9$ .

$\frac{27 - 7}{36}$

Step 5.2

Subtract $7$ from $27$ .

$\frac{20}{36}$

Step 6

Cancel the common factor of $20$ and $36$ .

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Step 6.1

Factor $4$ out of $20$ .

$\frac{4 (5)}{36}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $36$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{5}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{9}$

Decimal Form:

$0.\overline{5}$