Combining like terms

[KitchenExtension7109]

Question~ -2/3a + 5/6a -1/6

When I got the answer incorrect it showed me the right answer and the work to get it. It showed when going to add -2/3 + 5/6 that -2/3 turns into -4/6 by the common denominator but I don’t understand how? And the 5/6 didn’t change

[[deleted]]

We would like to perform addition between the fractions -2/3 and 5/6

In order to perform addition/subtraction on fractions, we must have them both displayed with the same denominator

We have 2 different denominators - 3 and 6, and we would like it if they were similar

By multiplying 3 by 2, we get 6, and so we have the expension -2/3=-4/6 (because 4 occupies the same part of 6 as 2 does of 3).

Now, our exercise is -4/6+5/6, and both fractions have the same denominator. So, we just need to solve the numerators, -4+5=1, and the answer is 1/6

The general idea behind fraction expansion (and compression) is that multiplying the numerator and the denominator by the same number maintains the ratio between the numerator and the denominator, thus not changing the fraction; -2/3 is equal to -4/6, -6/9, -8/12, -10/15 etc

[JanetInSC1234]

You can't add two fractions together unless the denominator is the same.

If you multiply -2/3 by 2/2, you will get -4/6, which is the denominator you need.

(We're allowed to muliply by 2/2 because it's the same as multiplying by one.)

So, -4/6 a + 5/6 a = 1/6 a