Basic Math Examples

$5 {(\frac{4}{10})}^{2} + 4 (\frac{4}{10}) - 4$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $4$ and $10$ .

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Step 1.1.1

Factor $2$ out of $4$ .

$5 {(\frac{2 (2)}{10})}^{2} + 4 (\frac{4}{10}) - 4$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $10$ .

$5 {(\frac{2 \cdot 2}{2 \cdot 5})}^{2} + 4 (\frac{4}{10}) - 4$

Step 1.1.2.2

Cancel the common factor.

$5 {(\frac{2 \cdot 2}{2 \cdot 5})}^{2} + 4 (\frac{4}{10}) - 4$

Step 1.1.2.3

Rewrite the expression.

$5 {(\frac{2}{5})}^{2} + 4 (\frac{4}{10}) - 4$

Step 1.2

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

$5 \frac{2^{2}}{5^{2}} + 4 (\frac{4}{10}) - 4$

Step 1.3

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

$5 \frac{4}{5^{2}} + 4 (\frac{4}{10}) - 4$

Step 1.4

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

$5 (\frac{4}{25}) + 4 (\frac{4}{10}) - 4$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $25$ .

$5 \frac{4}{5 (5)} + 4 (\frac{4}{10}) - 4$

Step 1.5.2

Cancel the common factor.

$5 \frac{4}{5 \cdot 5} + 4 (\frac{4}{10}) - 4$

Step 1.5.3

Rewrite the expression.

$\frac{4}{5} + 4 (\frac{4}{10}) - 4$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Factor $2$ out of $4$ .

$\frac{4}{5} + 2 (2) \frac{4}{10} - 4$

Step 1.6.2

Factor $2$ out of $10$ .

$\frac{4}{5} + 2 \cdot 2 \frac{4}{2 \cdot 5} - 4$

Step 1.6.3

Cancel the common factor.

$\frac{4}{5} + 2 \cdot 2 \frac{4}{2 \cdot 5} - 4$

Step 1.6.4

Rewrite the expression.

$\frac{4}{5} + 2 (\frac{4}{5}) - 4$

Step 1.7

Combine $2$ and $\frac{4}{5}$ .

$\frac{4}{5} + \frac{2 \cdot 4}{5} - 4$

Step 1.8

Multiply $2$ by $4$ .

$\frac{4}{5} + \frac{8}{5} - 4$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$- 4 + \frac{4 + 8}{5}$

Step 2.2

Add $4$ and $8$ .

$- 4 + \frac{12}{5}$

Step 3

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

$- 4 \cdot \frac{5}{5} + \frac{12}{5}$

Step 4

Combine $- 4$ and $\frac{5}{5}$ .

$\frac{- 4 \cdot 5}{5} + \frac{12}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 4 \cdot 5 + 12}{5}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 4$ by $5$ .

$\frac{- 20 + 12}{5}$

Step 6.2

Add $- 20$ and $12$ .

$\frac{- 8}{5}$

Step 7

Move the negative in front of the fraction.

$- \frac{8}{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{5}$

Decimal Form:

$- 1.6$

Mixed Number Form:

$- 1 \frac{3}{5}$