Algebra Examples

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

Step 1

Convert $6 \frac{1}{2}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.2

Add $6$ and $\frac{1}{2}$ .

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Step 1.2.1

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

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

Step 1.2.2

Combine $6$ and $\frac{2}{2}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $2$ .

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

Step 1.2.4.2

Add $12$ and $1$ .

${(\frac{13}{2} \cdot 4 \frac{1}{3})}^{2}$

Step 2

Convert $4 \frac{1}{3}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

${(\frac{13}{2} \cdot (4 + \frac{1}{3}))}^{2}$

Step 2.2

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

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Step 2.2.1

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

${(\frac{13}{2} \cdot (4 \cdot \frac{3}{3} + \frac{1}{3}))}^{2}$

Step 2.2.2

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

${(\frac{13}{2} \cdot (\frac{4 \cdot 3}{3} + \frac{1}{3}))}^{2}$

Step 2.2.3

Combine the numerators over the common denominator.

${(\frac{13}{2} \cdot \frac{4 \cdot 3 + 1}{3})}^{2}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $3$ .

${(\frac{13}{2} \cdot \frac{12 + 1}{3})}^{2}$

Step 2.2.4.2

Add $12$ and $1$ .

${(\frac{13}{2} \cdot \frac{13}{3})}^{2}$

Step 3

Multiply $\frac{13}{2} \cdot \frac{13}{3}$ .

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Step 3.1

Multiply $\frac{13}{2}$ by $\frac{13}{3}$ .

${(\frac{13 \cdot 13}{2 \cdot 3})}^{2}$

Step 3.2

Multiply $13$ by $13$ .

${(\frac{169}{2 \cdot 3})}^{2}$

Step 3.3

Multiply $2$ by $3$ .

${(\frac{169}{6})}^{2}$

Step 4

Apply the product rule to $\frac{169}{6}$ .

$\frac{169^{2}}{6^{2}}$

Step 5

Raise $169$ to the power of $2$ .

$\frac{28561}{6^{2}}$

Step 6

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

$\frac{28561}{36}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{28561}{36}$

Decimal Form:

$793.36\overline{1}$

Mixed Number Form:

$793 \frac{13}{36}$