Algebra Examples

$\frac{\frac{25}{4}}{\frac{1}{5} - \frac{4}{25}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{4} \cdot \frac{1}{\frac{1}{5} - \frac{4}{25}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{25}{4} \cdot \frac{1}{\frac{1}{5} \cdot \frac{5}{5} - \frac{4}{25}}$

Step 2.2

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1

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

$\frac{25}{4} \cdot \frac{1}{\frac{5}{5 \cdot 5} - \frac{4}{25}}$

Step 2.2.2

Multiply $5$ by $5$ .

$\frac{25}{4} \cdot \frac{1}{\frac{5}{25} - \frac{4}{25}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{25}{4} \cdot \frac{1}{\frac{5 - 4}{25}}$

Step 2.4

Subtract $4$ from $5$ .

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

Step 3

Simplify.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{25}{4} (1 \cdot 25)$

Step 3.2

Multiply $25$ by $1$ .

$\frac{25}{4} \cdot 25$

Step 4

Multiply $\frac{25}{4} \cdot 25$ .

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Step 4.1

Combine $\frac{25}{4}$ and $25$ .

$\frac{25 \cdot 25}{4}$

Step 4.2

Multiply $25$ by $25$ .

$\frac{625}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{625}{4}$

Decimal Form:

$156.25$

Mixed Number Form:

$156 \frac{1}{4}$