Basic Math Examples

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

Step 1

Convert $3 \frac{2}{7}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $3$ and $\frac{2}{7}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Step 1.2.2

Combine $3$ and $\frac{7}{7}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $7$ .

$\frac{1}{2} + \frac{1}{2} \cdot {(\frac{21 + 2}{7} + \frac{5}{7})}^{2}$

Step 1.2.4.2

Add $21$ and $2$ .

$\frac{1}{2} + \frac{1}{2} \cdot {(\frac{23}{7} + \frac{5}{7})}^{2}$

Step 2

Simplify each term.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1}{2} + \frac{1}{2} \cdot {(\frac{23 + 5}{7})}^{2}$

Step 2.2

Add $23$ and $5$ .

$\frac{1}{2} + \frac{1}{2} \cdot {(\frac{28}{7})}^{2}$

Step 2.3

Divide $28$ by $7$ .

$\frac{1}{2} + \frac{1}{2} \cdot 4^{2}$

Step 2.4

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

$\frac{1}{2} + \frac{1}{2} \cdot 16$

Step 2.5

Cancel the common factor of $2$ .

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Step 2.5.1

Factor $2$ out of $16$ .

$\frac{1}{2} + \frac{1}{2} \cdot (2 (8))$

Step 2.5.2

Cancel the common factor.

$\frac{1}{2} + \frac{1}{2} \cdot (2 \cdot 8)$

Step 2.5.3

Rewrite the expression.

$\frac{1}{2} + 8$

Step 3

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} + 8 \cdot \frac{2}{2}$

Step 4

Combine $8$ and $\frac{2}{2}$ .

$\frac{1}{2} + \frac{8 \cdot 2}{2}$

Step 5

Combine the numerators over the common denominator.

$\frac{1 + 8 \cdot 2}{2}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $8$ by $2$ .

$\frac{1 + 16}{2}$

Step 6.2

Add $1$ and $16$ .

$\frac{17}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{2}$

Decimal Form:

$8.5$

Mixed Number Form:

$8 \frac{1}{2}$