Final answer:
To combine like terms in the expression -2/3a + 5/6a - 1/6, we add the coefficients of the like terms. The resulting expression is 1/6a - 1/6.
Step-by-step explanation:
To combine like terms, we add the coefficients of the like terms. In this expression, -2/3a and 5/6a are like terms because they have the same variable, which is 'a'. The coefficients of these terms are -2/3 and 5/6, respectively. We can add these coefficients to get a new coefficient for the combined term. The coefficient of 'a' in the combined term is -2/3 + 5/6. To add these fractions, we need a common denominator, which in this case is 6. We multiply -2/3 by 2/2 and 5/6 by 1/1 to create fractions with the same denominator:
-2/3 * 2/2 = -4/6
5/6 * 1/1 = 5/6
Now that the fractions have the same denominator of 6, we can add the numerators: -4/6 + 5/6 = 1/6. So, the equivalent expression is 1/6a - 1/6.