Find the Exact Value pi/2-pi/3

$\frac{π}{2} - \frac{π}{3}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

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

Multiply $2$ by $3$ .

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

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

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

Multiply $3$ by $2$ .

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

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 3 - π \cdot 2}{6}$

Step 5

Simplify the numerator.

Move $3$ to the left of $π$ .

$\frac{3 \cdot π - π \cdot 2}{6}$

Multiply $2$ by $- 1$ .

$\frac{3 π - 2 π}{6}$

Subtract $2 π$ from $3 π$ .

$\frac{π}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{π}{6}$

Decimal Form:

$0.52359877 \dots$