Basic Math Examples

${(\frac{4}{3} + \frac{1}{12})}^{2} - (\frac{1}{6} + \frac{1}{12})$

Step 1

Simplify each term.

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Step 1.1

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

${(\frac{4}{3} \cdot \frac{4}{4} + \frac{1}{12})}^{2} - (\frac{1}{6} + \frac{1}{12})$

Step 1.2

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1

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

${(\frac{4 \cdot 4}{3 \cdot 4} + \frac{1}{12})}^{2} - (\frac{1}{6} + \frac{1}{12})$

Step 1.2.2

Multiply $3$ by $4$ .

${(\frac{4 \cdot 4}{12} + \frac{1}{12})}^{2} - (\frac{1}{6} + \frac{1}{12})$

Step 1.3

Combine the numerators over the common denominator.

${(\frac{4 \cdot 4 + 1}{12})}^{2} - (\frac{1}{6} + \frac{1}{12})$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $4$ by $4$ .

${(\frac{16 + 1}{12})}^{2} - (\frac{1}{6} + \frac{1}{12})$

Step 1.4.2

Add $16$ and $1$ .

${(\frac{17}{12})}^{2} - (\frac{1}{6} + \frac{1}{12})$

Step 1.5

Apply the product rule to $\frac{17}{12}$ .

$\frac{17^{2}}{12^{2}} - (\frac{1}{6} + \frac{1}{12})$

Step 1.6

Raise $17$ to the power of $2$ .

$\frac{289}{12^{2}} - (\frac{1}{6} + \frac{1}{12})$

Step 1.7

Raise $12$ to the power of $2$ .

$\frac{289}{144} - (\frac{1}{6} + \frac{1}{12})$

Step 1.8

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{289}{144} - (\frac{1}{6} \cdot \frac{2}{2} + \frac{1}{12})$

Step 1.9

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.9.1

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{289}{144} - (\frac{2}{6 \cdot 2} + \frac{1}{12})$

Step 1.9.2

Multiply $6$ by $2$ .

$\frac{289}{144} - (\frac{2}{12} + \frac{1}{12})$

Step 1.10

Combine the numerators over the common denominator.

$\frac{289}{144} - \frac{2 + 1}{12}$

Step 1.11

Add $2$ and $1$ .

$\frac{289}{144} - \frac{3}{12}$

Step 1.12

Cancel the common factor of $3$ and $12$ .

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Step 1.12.1

Factor $3$ out of $3$ .

$\frac{289}{144} - \frac{3 (1)}{12}$

Step 1.12.2

Cancel the common factors.

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Step 1.12.2.1

Factor $3$ out of $12$ .

$\frac{289}{144} - \frac{3 \cdot 1}{3 \cdot 4}$

Step 1.12.2.2

Cancel the common factor.

$\frac{289}{144} - \frac{3 \cdot 1}{3 \cdot 4}$

Step 1.12.2.3

Rewrite the expression.

$\frac{289}{144} - \frac{1}{4}$

Step 2

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{36}{36}$ .

$\frac{289}{144} - \frac{1}{4} \cdot \frac{36}{36}$

Step 3

Write each expression with a common denominator of $144$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{4}$ by $\frac{36}{36}$ .

$\frac{289}{144} - \frac{36}{4 \cdot 36}$

Step 3.2

Multiply $4$ by $36$ .

$\frac{289}{144} - \frac{36}{144}$

Step 4

Combine the numerators over the common denominator.

$\frac{289 - 36}{144}$

Step 5

Subtract $36$ from $289$ .

$\frac{253}{144}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{253}{144}$

Decimal Form:

$1.7569\overline{4}$

Mixed Number Form:

$1 \frac{109}{144}$