Basic Math Examples

$\frac{6 \frac{2}{7}}{{(3 + 2 \frac{1}{2})}^{2}}$

Step 1

Convert $6 \frac{2}{7}$ to an improper fraction.

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Step 1.1

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

$\frac{6 + \frac{2}{7}}{{(3 + 2 \frac{1}{2})}^{2}}$

Step 1.2

Add $6$ and $\frac{2}{7}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{6 \cdot \frac{7}{7} + \frac{2}{7}}{{(3 + 2 \frac{1}{2})}^{2}}$

Step 1.2.2

Combine $6$ and $\frac{7}{7}$ .

$\frac{\frac{6 \cdot 7}{7} + \frac{2}{7}}{{(3 + 2 \frac{1}{2})}^{2}}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{\frac{6 \cdot 7 + 2}{7}}{{(3 + 2 \frac{1}{2})}^{2}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $7$ .

$\frac{\frac{42 + 2}{7}}{{(3 + 2 \frac{1}{2})}^{2}}$

Step 1.2.4.2

Add $42$ and $2$ .

$\frac{\frac{44}{7}}{{(3 + 2 \frac{1}{2})}^{2}}$

Step 2

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

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Step 2.1

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

$\frac{\frac{44}{7}}{{(3 + 2 + \frac{1}{2})}^{2}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{\frac{44}{7}}{{(3 + 2 \cdot \frac{2}{2} + \frac{1}{2})}^{2}}$

Step 2.2.2

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

$\frac{\frac{44}{7}}{{(3 + \frac{2 \cdot 2}{2} + \frac{1}{2})}^{2}}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{\frac{44}{7}}{{(3 + \frac{2 \cdot 2 + 1}{2})}^{2}}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $2$ .

$\frac{\frac{44}{7}}{{(3 + \frac{4 + 1}{2})}^{2}}$

Step 2.2.4.2

Add $4$ and $1$ .

$\frac{\frac{44}{7}}{{(3 + \frac{5}{2})}^{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{44}{7} \cdot \frac{1}{{(3 + \frac{5}{2})}^{2}}$

Step 4

Combine fractions.

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Step 4.1

Combine.

$\frac{44 \cdot 1}{7 {(3 + \frac{5}{2})}^{2}}$

Step 4.2

Multiply $44$ by $1$ .

$\frac{44}{7 {(3 + \frac{5}{2})}^{2}}$

Step 5

Simplify the denominator.

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Step 5.1

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

$\frac{44}{7 {(3 \cdot \frac{2}{2} + \frac{5}{2})}^{2}}$

Step 5.2

Combine $3$ and $\frac{2}{2}$ .

$\frac{44}{7 {(\frac{3 \cdot 2}{2} + \frac{5}{2})}^{2}}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{44}{7 {(\frac{3 \cdot 2 + 5}{2})}^{2}}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply $3$ by $2$ .

$\frac{44}{7 {(\frac{6 + 5}{2})}^{2}}$

Step 5.4.2

Add $6$ and $5$ .

$\frac{44}{7 {(\frac{11}{2})}^{2}}$

Step 5.5

Apply the product rule to $\frac{11}{2}$ .

$\frac{44}{7 \frac{11^{2}}{2^{2}}}$

Step 5.6

Raise $11$ to the power of $2$ .

$\frac{44}{7 \frac{121}{2^{2}}}$

Step 5.7

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

$\frac{44}{7 (\frac{121}{4})}$

Step 6

Combine fractions.

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Step 6.1

Combine $7$ and $\frac{121}{4}$ .

$\frac{44}{\frac{7 \cdot 121}{4}}$

Step 6.2

Multiply $7$ by $121$ .

$\frac{44}{\frac{847}{4}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$44 (\frac{4}{847})$

Step 8

Cancel the common factor of $11$ .

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Step 8.1

Factor $11$ out of $44$ .

$11 (4) \frac{4}{847}$

Step 8.2

Factor $11$ out of $847$ .

$11 \cdot 4 \frac{4}{11 \cdot 77}$

Step 8.3

Cancel the common factor.

$11 \cdot 4 \frac{4}{11 \cdot 77}$

Step 8.4

Rewrite the expression.

$4 (\frac{4}{77})$

Step 9

Combine $4$ and $\frac{4}{77}$ .

$\frac{4 \cdot 4}{77}$

Step 10

Multiply $4$ by $4$ .

$\frac{16}{77}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{77}$

Decimal Form:

$0.\overline{207792}$