Question

combine like terms to create an equivalent expression
`- (2)/(3)a + (5)/(6) a - (1)/(6)`

Answer 1

The equivalent expression when combining like terms is ⅔a - ⅖.

Step-by-step explanation:

To create an equivalent expression by combining like terms, we look at the coefficients of the variable 'a' and add them together. Here we have terms with 'a' which involve fractions with different denominators. To combine these, we find a common denominator, which in this case would be 6, because 6 is the least common multiple (LCM) of 3 and 6.

So, the expression will look like this:

- ⅓a + ⅔a = -⅔(2a) + ⅓(3a)

This gives us:

(-⅔*2 + ⅓*3)a = (-⅖ +⅒)a

When we combine the fractions, we get:

(-⅖ + ⅒) = ⅔

So the expression simplifies to:

⅔a - ⅖

Answer 2

Rewrite the terms as similar expressions. Since the least common denominator of the three fractions is 6, multiply the numerator and the denominator of the first term by 2.

`-(4)/(6)a+(5)/(6)a-(1)/(6)`

Combine like terms. Terms are considered like terms or similar terms if they both have the same literal coefficients. Thus, combine the first and the second term. Factor out the variable.

`(-(4)/(6)+(5)/(6))a-(1)/(6)`

Add the fractions. Add the numerators and then copy the common denominator.

`\begin{gathered} (-4+5)/(6)a-(1)/(6) \\ =(1)/(6)a-(1)/(6)\text{ or }(a)/(6)-(1)/(6) \end{gathered}`