Basic Math Examples

${(\frac{3}{2} + \frac{1}{8})}^{2} - (\frac{1}{4} + \frac{1}{8})$

Step 1

Simplify each term.

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Step 1.1

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

${(\frac{3}{2} \cdot \frac{4}{4} + \frac{1}{8})}^{2} - (\frac{1}{4} + \frac{1}{8})$

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 $\frac{3}{2}$ by $\frac{4}{4}$ .

${(\frac{3 \cdot 4}{2 \cdot 4} + \frac{1}{8})}^{2} - (\frac{1}{4} + \frac{1}{8})$

Step 1.2.2

Multiply $2$ by $4$ .

${(\frac{3 \cdot 4}{8} + \frac{1}{8})}^{2} - (\frac{1}{4} + \frac{1}{8})$

Step 1.3

Combine the numerators over the common denominator.

${(\frac{3 \cdot 4 + 1}{8})}^{2} - (\frac{1}{4} + \frac{1}{8})$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $3$ by $4$ .

${(\frac{12 + 1}{8})}^{2} - (\frac{1}{4} + \frac{1}{8})$

Step 1.4.2

Add $12$ and $1$ .

${(\frac{13}{8})}^{2} - (\frac{1}{4} + \frac{1}{8})$

Step 1.5

Apply the product rule to $\frac{13}{8}$ .

$\frac{13^{2}}{8^{2}} - (\frac{1}{4} + \frac{1}{8})$

Step 1.6

Raise $13$ to the power of $2$ .

$\frac{169}{8^{2}} - (\frac{1}{4} + \frac{1}{8})$

Step 1.7

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

$\frac{169}{64} - (\frac{1}{4} + \frac{1}{8})$

Step 1.8

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

$\frac{169}{64} - (\frac{1}{4} \cdot \frac{2}{2} + \frac{1}{8})$

Step 1.9

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

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Step 1.9.1

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

$\frac{169}{64} - (\frac{2}{4 \cdot 2} + \frac{1}{8})$

Step 1.9.2

Multiply $4$ by $2$ .

$\frac{169}{64} - (\frac{2}{8} + \frac{1}{8})$

Step 1.10

Combine the numerators over the common denominator.

$\frac{169}{64} - \frac{2 + 1}{8}$

Step 1.11

Add $2$ and $1$ .

$\frac{169}{64} - \frac{3}{8}$

Step 2

To write $- \frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{169}{64} - \frac{3}{8} \cdot \frac{8}{8}$

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 $\frac{3}{8}$ by $\frac{8}{8}$ .

$\frac{169}{64} - \frac{3 \cdot 8}{8 \cdot 8}$

Step 3.2

Multiply $8$ by $8$ .

$\frac{169}{64} - \frac{3 \cdot 8}{64}$

Step 4

Combine the numerators over the common denominator.

$\frac{169 - 3 \cdot 8}{64}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 3$ by $8$ .

$\frac{169 - 24}{64}$

Step 5.2

Subtract $24$ from $169$ .

$\frac{145}{64}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{145}{64}$

Decimal Form:

$2.265625$

Mixed Number Form:

$2 \frac{17}{64}$