Evaluate (3pi)/2-(2pi)/3

$\frac{3 π}{2} - \frac{2 π}{3}$

To write $\frac{3 π}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

To write $- \frac{2 π}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 π}{2}$ by $\frac{3}{3}$ .

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

Multiply $2$ by $3$ .

$\frac{3 π \cdot 3}{6} - \frac{2 π}{3} \cdot \frac{2}{2}$

Multiply $\frac{2 π}{3}$ by $\frac{2}{2}$ .

$\frac{3 π \cdot 3}{6} - \frac{2 π \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$\frac{3 π \cdot 3}{6} - \frac{2 π \cdot 2}{6}$

Combine the numerators over the common denominator.

$\frac{3 π \cdot 3 - 2 π \cdot 2}{6}$

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{9 π - 2 π \cdot 2}{6}$

Multiply $2$ by $- 2$ .

$\frac{9 π - 4 π}{6}$

Subtract $4 π$ from $9 π$ .

$\frac{5 π}{6}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5 π}{6}$

Decimal Form:

$2.61799387 \dots$