Basic Math Examples

$\frac{2}{5} + {(\frac{2}{5})}^{2} - \frac{3}{25}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{2}{5}$ by $\frac{5}{5}$ .

$\frac{2}{5} \cdot \frac{5}{5} + {(\frac{2}{5})}^{2} - \frac{3}{25}$

Step 1.2

Multiply $\frac{2}{5}$ by $\frac{5}{5}$ .

$\frac{2 \cdot 5}{5 \cdot 5} + {(\frac{2}{5})}^{2} - \frac{3}{25}$

Step 1.3

Write ${(\frac{2}{5})}^{2}$ as a fraction with denominator $1$ .

$\frac{2 \cdot 5}{5 \cdot 5} + \frac{{(\frac{2}{5})}^{2}}{1} - \frac{3}{25}$

Step 1.4

Multiply $\frac{{(\frac{2}{5})}^{2}}{1}$ by $\frac{25}{25}$ .

$\frac{2 \cdot 5}{5 \cdot 5} + \frac{{(\frac{2}{5})}^{2}}{1} \cdot \frac{25}{25} - \frac{3}{25}$

Step 1.5

Multiply $\frac{{(\frac{2}{5})}^{2}}{1}$ by $\frac{25}{25}$ .

$\frac{2 \cdot 5}{5 \cdot 5} + \frac{{(\frac{2}{5})}^{2} \cdot 25}{25} - \frac{3}{25}$

Step 1.6

Multiply $5$ by $5$ .

$\frac{2 \cdot 5}{25} + \frac{{(\frac{2}{5})}^{2} \cdot 25}{25} - \frac{3}{25}$

Step 2

Combine the numerators over the common denominator.

$\frac{2 \cdot 5 + {(\frac{2}{5})}^{2} \cdot 25 - 3}{25}$

Step 3

Simplify each term.

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Step 3.1

Multiply $2$ by $5$ .

$\frac{10 + {(\frac{2}{5})}^{2} \cdot 25 - 3}{25}$

Step 3.2

Apply the product rule to $\frac{2}{5}$ .

$\frac{10 + \frac{2^{2}}{5^{2}} \cdot 25 - 3}{25}$

Step 3.3

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

$\frac{10 + \frac{4}{5^{2}} \cdot 25 - 3}{25}$

Step 3.4

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

$\frac{10 + \frac{4}{25} \cdot 25 - 3}{25}$

Step 3.5

Cancel the common factor of $25$ .

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Step 3.5.1

Cancel the common factor.

$\frac{10 + \frac{4}{25} \cdot 25 - 3}{25}$

Step 3.5.2

Rewrite the expression.

$\frac{10 + 4 - 3}{25}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Add $10$ and $4$ .

$\frac{14 - 3}{25}$

Step 4.2

Subtract $3$ from $14$ .

$\frac{11}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{25}$

Decimal Form:

$0.44$