Introduction:

To find the number by which we need to multiply 2/11 to get -2/3, we can set up an equation and solve for the unknown number. In this case, we can let the unknown number be represented by 'x'. So, we have the equation:

2/11 * x = -2/3

To solve for 'x', we can cross-multiply and then divide both sides of the equation by 2/11.

Steps:

1. Cross-multiply:
Multiply the numerator of the left-hand side with the denominator of the right-hand side and vice versa.

(2 * x) = (-2 * 11/3)

Simplifying the right-hand side:
(2 * x) = (-22/3)

2. Divide by 2:
Divide both sides of the equation by 2 to isolate 'x'.

(2 * x) / 2 = (-22/3) / 2

Simplifying:
x = -22/6

3. Simplify the fraction:
The fraction -22/6 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2 in this case.

-22 ÷ 2 = -11
6 ÷ 2 = 3

So, the simplified fraction is -11/3.

Answer:

Therefore, the number by which 2/11 should be multiplied to get -2/3 is -11/3.