Basic Math Examples

$\frac{1}{10 + \frac{4}{20}}$

Step 1

Cancel the common factor of $4$ and $20$ .

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Step 1.1

Factor $4$ out of $4$ .

$\frac{1}{10 + \frac{4 (1)}{20}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $20$ .

$\frac{1}{10 + \frac{4 \cdot 1}{4 \cdot 5}}$

Step 1.2.2

Cancel the common factor.

$\frac{1}{10 + \frac{4 \cdot 1}{4 \cdot 5}}$

Step 1.2.3

Rewrite the expression.

$\frac{1}{10 + \frac{1}{5}}$

Step 2

Simplify the denominator.

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Step 2.1

To write $10$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{10 \cdot \frac{5}{5} + \frac{1}{5}}$

Step 2.2

Combine $10$ and $\frac{5}{5}$ .

$\frac{1}{\frac{10 \cdot 5}{5} + \frac{1}{5}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{1}{\frac{10 \cdot 5 + 1}{5}}$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Multiply $10$ by $5$ .

$\frac{1}{\frac{50 + 1}{5}}$

Step 2.4.2

Add $50$ and $1$ .

$\frac{1}{\frac{51}{5}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{5}{51})$

Step 4

Multiply $\frac{5}{51}$ by $1$ .

$\frac{5}{51}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{51}$

Decimal Form:

$0.09803921 \dots$