Precalculus Examples

$\frac{2}{\frac{2}{3}} - \frac{\frac{2}{3}}{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$2 (\frac{3}{2}) - \frac{\frac{2}{3}}{2}$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

$2 (\frac{3}{2}) - \frac{\frac{2}{3}}{2}$

Step 1.2.2

Rewrite the expression.

$3 - \frac{\frac{2}{3}}{2}$

Step 1.3

Multiply the numerator by the reciprocal of the denominator.

$3 - (\frac{2}{3} \cdot \frac{1}{2})$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

$3 - (\frac{2}{3} \cdot \frac{1}{2})$

Step 1.4.2

Rewrite the expression.

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

Step 2

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

Combine $3$ and $\frac{3}{3}$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 - 1}{3}$

Step 5.2

Subtract $1$ from $9$ .

$\frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{3}$

Decimal Form:

$2.\overline{6}$

Mixed Number Form:

$2 \frac{2}{3}$