Basic Math Examples

$4.5 + \frac{1}{4} \cdot {(\frac{1}{5})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{1}{5}$ .

$4.5 + \frac{1}{4} \cdot \frac{1^{2}}{5^{2}}$

Step 1.2

Combine.

$4.5 + \frac{1 \cdot 1^{2}}{4 \cdot 5^{2}}$

Step 1.3

Multiply $1$ by $1^{2}$ by adding the exponents.

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Step 1.3.1

Multiply $1$ by $1^{2}$ .

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Step 1.3.1.1

Raise $1$ to the power of $1$ .

$4.5 + \frac{1^{1} \cdot 1^{2}}{4 \cdot 5^{2}}$

Step 1.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4.5 + \frac{1^{1 + 2}}{4 \cdot 5^{2}}$

Step 1.3.2

Add $1$ and $2$ .

$4.5 + \frac{1^{3}}{4 \cdot 5^{2}}$

Step 1.4

One to any power is one.

$4.5 + \frac{1}{4 \cdot 5^{2}}$

Step 1.5

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

$4.5 + \frac{1}{4 \cdot 25}$

Step 1.6

Multiply $4$ by $25$ .

$4.5 + \frac{1}{100}$

Step 2

To write $4.5$ as a fraction with a common denominator, multiply by $\frac{100}{100}$ .

$4.5 \cdot \frac{100}{100} + \frac{1}{100}$

Step 3

Combine $4.5$ and $\frac{100}{100}$ .

$\frac{4.5 \cdot 100}{100} + \frac{1}{100}$

Step 4

Combine the numerators over the common denominator.

$\frac{4.5 \cdot 100 + 1}{100}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $4.5$ by $100$ .

$\frac{450 + 1}{100}$

Step 5.2

Add $450$ and $1$ .

$\frac{451}{100}$

Step 6

Cancel the common factor of $451$ and $100$ .

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Step 6.1

Rewrite $451$ as $1 (451)$ .

$\frac{1 (451)}{100}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Rewrite $100$ as $1 (100)$ .

$\frac{1 \cdot 451}{1 \cdot 100}$

Step 6.2.2

Cancel the common factor.

$\frac{1 \cdot 451}{1 \cdot 100}$

Step 6.2.3

Rewrite the expression.

$\frac{451}{100}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{451}{100}$

Decimal Form:

$4.51$

Mixed Number Form:

$4 \frac{51}{100}$