Basic Math Examples

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

Step 1

Convert $2 \frac{2}{5}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $2$ and $\frac{2}{5}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.2.2

Combine $2$ and $\frac{5}{5}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $5$ .

${(\frac{1}{2})}^{2} + \frac{1}{2} \cdot \frac{10 + 2}{5}$

Step 1.2.4.2

Add $10$ and $2$ .

${(\frac{1}{2})}^{2} + \frac{1}{2} \cdot \frac{12}{5}$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{2}}{2^{2}} + \frac{1}{2} \cdot \frac{12}{5}$

Step 2.2

One to any power is one.

$\frac{1}{2^{2}} + \frac{1}{2} \cdot \frac{12}{5}$

Step 2.3

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

$\frac{1}{4} + \frac{1}{2} \cdot \frac{12}{5}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Factor $2$ out of $12$ .

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

Step 2.4.2

Cancel the common factor.

$\frac{1}{4} + \frac{1}{2} \cdot \frac{2 \cdot 6}{5}$

Step 2.4.3

Rewrite the expression.

$\frac{1}{4} + \frac{6}{5}$

Step 3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{4} \cdot \frac{5}{5} + \frac{6}{5}$

Step 4

To write $\frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{4} \cdot \frac{5}{5} + \frac{6}{5} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$\frac{5}{4 \cdot 5} + \frac{6}{5} \cdot \frac{4}{4}$

Step 5.2

Multiply $4$ by $5$ .

$\frac{5}{20} + \frac{6}{5} \cdot \frac{4}{4}$

Step 5.3

Multiply $\frac{6}{5}$ by $\frac{4}{4}$ .

$\frac{5}{20} + \frac{6 \cdot 4}{5 \cdot 4}$

Step 5.4

Multiply $5$ by $4$ .

$\frac{5}{20} + \frac{6 \cdot 4}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{5 + 6 \cdot 4}{20}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $6$ by $4$ .

$\frac{5 + 24}{20}$

Step 7.2

Add $5$ and $24$ .

$\frac{29}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{29}{20}$

Decimal Form:

$1.45$

Mixed Number Form:

$1 \frac{9}{20}$