Basic Math Examples

${(\frac{5}{8})}^{2} - (\frac{1}{4} - \frac{1}{20}) \div \frac{8}{5}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{5}{8}$ .

$\frac{5^{2}}{8^{2}} - (\frac{1}{4} - \frac{1}{20}) \div \frac{8}{5}$

Step 1.2

Raise $5$ to the power of $2$ .

$\frac{25}{8^{2}} - (\frac{1}{4} - \frac{1}{20}) \div \frac{8}{5}$

Step 1.3

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

$\frac{25}{64} - (\frac{1}{4} - \frac{1}{20}) \div \frac{8}{5}$

Step 1.4

To divide by a fraction, multiply by its reciprocal.

$\frac{25}{64} - ((\frac{1}{4} - \frac{1}{20}) \frac{5}{8})$

Step 1.5

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{25}{64} - ((\frac{1}{4} \cdot \frac{5}{5} - \frac{1}{20}) \frac{5}{8})$

Step 1.6

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.6.1

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{25}{64} - ((\frac{5}{4 \cdot 5} - \frac{1}{20}) \frac{5}{8})$

Step 1.6.2

Multiply $4$ by $5$ .

$\frac{25}{64} - ((\frac{5}{20} - \frac{1}{20}) \frac{5}{8})$

Step 1.7

Combine the numerators over the common denominator.

$\frac{25}{64} - (\frac{5 - 1}{20} \cdot \frac{5}{8})$

Step 1.8

Subtract $1$ from $5$ .

$\frac{25}{64} - (\frac{4}{20} \cdot \frac{5}{8})$

Step 1.9

Cancel the common factor of $4$ .

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Step 1.9.1

Factor $4$ out of $8$ .

$\frac{25}{64} - (\frac{4}{20} \cdot \frac{5}{4 (2)})$

Step 1.9.2

Cancel the common factor.

$\frac{25}{64} - (\frac{4}{20} \cdot \frac{5}{4 \cdot 2})$

Step 1.9.3

Rewrite the expression.

$\frac{25}{64} - (\frac{1}{20} \cdot \frac{5}{2})$

Step 1.10

Cancel the common factor of $5$ .

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Step 1.10.1

Factor $5$ out of $20$ .

$\frac{25}{64} - (\frac{1}{5 (4)} \cdot \frac{5}{2})$

Step 1.10.2

Cancel the common factor.

$\frac{25}{64} - (\frac{1}{5 \cdot 4} \cdot \frac{5}{2})$

Step 1.10.3

Rewrite the expression.

$\frac{25}{64} - (\frac{1}{4} \cdot \frac{1}{2})$

Step 1.11

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

$\frac{25}{64} - \frac{1}{4 \cdot 2}$

Step 1.12

Multiply $4$ by $2$ .

$\frac{25}{64} - \frac{1}{8}$

Step 2

To write $- \frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{25}{64} - \frac{1}{8} \cdot \frac{8}{8}$

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

$\frac{25}{64} - \frac{8}{8 \cdot 8}$

Step 3.2

Multiply $8$ by $8$ .

$\frac{25}{64} - \frac{8}{64}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 - 8}{64}$

Step 5

Subtract $8$ from $25$ .

$\frac{17}{64}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{64}$

Decimal Form:

$0.265625$