Pre-Algebra Examples

${(\frac{7}{8})}^{2} \cdot (\frac{2}{7} - \frac{13}{49}) - \frac{1}{8} \cdot \frac{1}{16}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{7}{8}$ .

$\frac{7^{2}}{8^{2}} \cdot (\frac{2}{7} - \frac{13}{49}) - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.2

Raise $7$ to the power of $2$ .

$\frac{49}{8^{2}} \cdot (\frac{2}{7} - \frac{13}{49}) - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.3

Raise $8$ to the power of $2$ .

$\frac{49}{64} \cdot (\frac{2}{7} - \frac{13}{49}) - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.4

To write $\frac{2}{7}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{49}{64} \cdot (\frac{2}{7} \cdot \frac{7}{7} - \frac{13}{49}) - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.5

Write each expression with a common denominator of $49$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.5.1

Multiply $\frac{2}{7}$ by $\frac{7}{7}$ .

$\frac{49}{64} \cdot (\frac{2 \cdot 7}{7 \cdot 7} - \frac{13}{49}) - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.5.2

Multiply $7$ by $7$ .

$\frac{49}{64} \cdot (\frac{2 \cdot 7}{49} - \frac{13}{49}) - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.6

Combine the numerators over the common denominator.

$\frac{49}{64} \cdot \frac{2 \cdot 7 - 13}{49} - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.7

Simplify the numerator.

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Step 1.7.1

Multiply $2$ by $7$ .

$\frac{49}{64} \cdot \frac{14 - 13}{49} - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.7.2

Subtract $13$ from $14$ .

$\frac{49}{64} \cdot \frac{1}{49} - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.8

Cancel the common factor of $49$ .

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Step 1.8.1

Cancel the common factor.

$\frac{49}{64} \cdot \frac{1}{49} - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.8.2

Rewrite the expression.

$\frac{1}{64} - \frac{1}{8} \cdot \frac{1}{16}$

Step 1.9

Multiply $- \frac{1}{8} \cdot \frac{1}{16}$ .

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Step 1.9.1

Multiply $\frac{1}{16}$ by $\frac{1}{8}$ .

$\frac{1}{64} - \frac{1}{16 \cdot 8}$

Step 1.9.2

Multiply $16$ by $8$ .

$\frac{1}{64} - \frac{1}{128}$

Step 2

To write $\frac{1}{64}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{64} \cdot \frac{2}{2} - \frac{1}{128}$

Step 3

Write each expression with a common denominator of $128$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{64}$ by $\frac{2}{2}$ .

$\frac{2}{64 \cdot 2} - \frac{1}{128}$

Step 3.2

Multiply $64$ by $2$ .

$\frac{2}{128} - \frac{1}{128}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 - 1}{128}$

Step 5

Subtract $1$ from $2$ .

$\frac{1}{128}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{128}$

Decimal Form:

$0.0078125$