Precalculus Examples

$\frac{2}{\frac{2}{5}} - \frac{2}{\frac{5}{2}}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

$5 - \frac{2}{\frac{5}{2}}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.4

Multiply $2 (\frac{2}{5})$ .

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Step 1.4.1

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

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

Step 1.4.2

Multiply $2$ by $2$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $5$ .

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

Step 5.2

Subtract $4$ from $25$ .

$\frac{21}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{21}{5}$

Decimal Form:

$4.2$

Mixed Number Form:

$4 \frac{1}{5}$