Evaluate (11pi)/12=(3pi)/4+pi/6

$\frac{11 π}{12} = \frac{3 π}{4} + \frac{π}{6}$

Step 1

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

$\frac{11 π}{12} = \frac{3 π}{4} \cdot \frac{3}{3} + \frac{π}{6}$

Step 2

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

$\frac{11 π}{12} = \frac{3 π}{4} \cdot \frac{3}{3} + \frac{π}{6} \cdot \frac{2}{2}$

Step 3

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

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

$\frac{11 π}{12} = \frac{3 π \cdot 3}{4 \cdot 3} + \frac{π}{6} \cdot \frac{2}{2}$

Multiply $4$ by $3$ .

$\frac{11 π}{12} = \frac{3 π \cdot 3}{12} + \frac{π}{6} \cdot \frac{2}{2}$

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

$\frac{11 π}{12} = \frac{3 π \cdot 3}{12} + \frac{π \cdot 2}{6 \cdot 2}$

Multiply $6$ by $2$ .

$\frac{11 π}{12} = \frac{3 π \cdot 3}{12} + \frac{π \cdot 2}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{11 π}{12} = \frac{3 π \cdot 3 + π \cdot 2}{12}$

Step 5

Simplify the numerator.

Multiply $3$ by $3$ .

$\frac{11 π}{12} = \frac{9 π + π \cdot 2}{12}$

Move $2$ to the left of $π$ .

$\frac{11 π}{12} = \frac{9 π + 2 \cdot π}{12}$

Add $9 π$ and $2 π$ .

$\frac{11 π}{12} = \frac{11 π}{12}$