Evaluate pi/6-pi/4

$\frac{π}{6} - \frac{π}{4}$

Step 1

To write $\frac{π}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{π}{6} \cdot \frac{2}{2} - \frac{π}{4}$

Step 2

To write $- \frac{π}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{π}{6} \cdot \frac{2}{2} - \frac{π}{4} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{π}{6}$ by $\frac{2}{2}$ .

$\frac{π \cdot 2}{6 \cdot 2} - \frac{π}{4} \cdot \frac{3}{3}$

Multiply $6$ by $2$ .

$\frac{π \cdot 2}{12} - \frac{π}{4} \cdot \frac{3}{3}$

Multiply $\frac{π}{4}$ by $\frac{3}{3}$ .

$\frac{π \cdot 2}{12} - \frac{π \cdot 3}{4 \cdot 3}$

Multiply $4$ by $3$ .

$\frac{π \cdot 2}{12} - \frac{π \cdot 3}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 2 - π \cdot 3}{12}$

Step 5

Simplify the numerator.

Move $2$ to the left of $π$ .

$\frac{2 \cdot π - π \cdot 3}{12}$

Multiply $3$ by $- 1$ .

$\frac{2 π - 3 π}{12}$

Subtract $3 π$ from $2 π$ .

$\frac{- π}{12}$

Step 6

Move the negative in front of the fraction.

$- \frac{π}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{12}$

Decimal Form:

$- 0.26179938 \dots$