Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

${(\frac{7}{8} - \frac{1}{2} \cdot \frac{4}{4})}^{2} - \frac{1}{16}$

Step 1.2

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

Multiply $\frac{1}{2}$ by $\frac{4}{4}$ .

${(\frac{7}{8} - \frac{4}{2 \cdot 4})}^{2} - \frac{1}{16}$

Step 1.2.2

Multiply $2$ by $4$ .

${(\frac{7}{8} - \frac{4}{8})}^{2} - \frac{1}{16}$

Step 1.3

Combine the numerators over the common denominator.

${(\frac{7 - 4}{8})}^{2} - \frac{1}{16}$

Step 1.4

Subtract $4$ from $7$ .

${(\frac{3}{8})}^{2} - \frac{1}{16}$

Step 1.5

Apply the product rule to $\frac{3}{8}$ .

$\frac{3^{2}}{8^{2}} - \frac{1}{16}$

Step 1.6

Raise $3$ to the power of $2$ .

$\frac{9}{8^{2}} - \frac{1}{16}$

Step 1.7

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

$\frac{9}{64} - \frac{1}{16}$

Step 2

To write $- \frac{1}{16}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{9}{64} - \frac{1}{16} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $64$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{16}$ by $\frac{4}{4}$ .

$\frac{9}{64} - \frac{4}{16 \cdot 4}$

Step 3.2

Multiply $16$ by $4$ .

$\frac{9}{64} - \frac{4}{64}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 - 4}{64}$

Step 5

Subtract $4$ from $9$ .

$\frac{5}{64}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{64}$

Decimal Form:

$0.078125$