Answer:To add -2 1/6 to -2/3 and simplify the result, we need to first convert the mixed number -2 1/6 into an improper fraction.
To convert -2 1/6 to an improper fraction, we multiply the whole number (-2) by the denominator of the fraction (6) and add the numerator (1). Then, we put the result over the original denominator.
-2 * 6 + 1 = -12 + 1 = -11
-2 1/6 = -11/6
Now, we can add -11/6 to -2/3. To add fractions with different denominators, we need to find a common denominator.
The least common multiple (LCM) of 6 and 3 is 6. So, we can rewrite -11/6 as -11/6 * 2/2 to have the same denominator as -2/3.
-11/6 * 2/2 = -22/12
Now, we can add -22/12 and -2/3. Since the denominators are the same, we just need to add the numerators.
-22/12 + -2/3 = -22/12 + -8/12 = -30/12
The fraction -30/12 is not in simplest form because both the numerator and denominator can be divided by 6.
Dividing both the numerator and denominator by 6 gives us:
-30/12 ÷ 6/6 = -5/2
Therefore, -2 1/6 + (-2/3) in simplest form is equal to -5/2.