Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $3$ and $6$ .

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Step 1.1.1

Factor $3$ out of $3$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $6$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Step 1.4.2

Multiply $3$ by $2$ .

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

Step 1.4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

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

Step 1.4.4

Multiply $2$ by $3$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Add $2$ and $3$ .

${(\frac{5}{6})}^{2} + {(4 \cdot \frac{1}{3})}^{2}$

Step 1.7

Apply the product rule to $\frac{5}{6}$ .

$\frac{5^{2}}{6^{2}} + {(4 \cdot \frac{1}{3})}^{2}$

Step 1.8

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

$\frac{25}{6^{2}} + {(4 \cdot \frac{1}{3})}^{2}$

Step 1.9

Raise $6$ to the power of $2$ .

$\frac{25}{36} + {(4 \cdot \frac{1}{3})}^{2}$

Step 1.10

Combine $4$ and $\frac{1}{3}$ .

$\frac{25}{36} + {(\frac{4}{3})}^{2}$

Step 1.11

Apply the product rule to $\frac{4}{3}$ .

$\frac{25}{36} + \frac{4^{2}}{3^{2}}$

Step 1.12

Raise $4$ to the power of $2$ .

$\frac{25}{36} + \frac{16}{3^{2}}$

Step 1.13

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

$\frac{25}{36} + \frac{16}{9}$

Step 2

To write $\frac{16}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{25}{36} + \frac{16}{9} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{16}{9}$ by $\frac{4}{4}$ .

$\frac{25}{36} + \frac{16 \cdot 4}{9 \cdot 4}$

Step 3.2

Multiply $9$ by $4$ .

$\frac{25}{36} + \frac{16 \cdot 4}{36}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 + 16 \cdot 4}{36}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $16$ by $4$ .

$\frac{25 + 64}{36}$

Step 5.2

Add $25$ and $64$ .

$\frac{89}{36}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{89}{36}$

Decimal Form:

$2.47\overline{2}$

Mixed Number Form:

$2 \frac{17}{36}$