Question

Combine like terms -2/3p + 1/5 - 1 + 5/6p

Answer 1

1/6p - 4/5

Explanation: -2/3p needs to have the same denominator as 5/6p so they can combine. (Note, whatever sign is in front of a number determines if it is negative or positive. Your equation indicates that the bolded parts are negative and the other parts are positive: -2/3p + 1/5 - 1 + 5/6p. So what we are really doing in an equation like this is combining some numbers together)
-2/3p and 5/6p and the least common multiple of six, so we adjust the numbers to each have a denominator of 6. 5/6p is already there, so we need to adjust -2/3p.
We can multiply both the numerator and denominator by 2 to turn -2/3p into -4/6p. -4/6p has the same value as -2/3p, and now it also has the same denominator as 5/6p!
We then have to combine like terms, therefore combining -4/6p with 5/6p. When adding together fractions, the denominator does not change (this is why both numbers must have the same denominators). So our answer will be _/6p. So we combine -4 with 5, giving us one.
Therefore, -2/3p combined with 5/6p is 1/6p.
Now we have to combine our other set of like terms, 1/5 and -1. We can do this the same way that we combined the other numbers.
1/5 and -1 need the same denominator. This is simple because 1 can easily be figured out with any denominator, as long as the numerator and denominator are the same. This would make 1 = 5/5. But we need it negative, so it would be -5/5.
Now that we have common denominators, we can combine!
1/5 - 5/5
Remember what we said before, the solution will have the same denominator, so all we need to do is (in this case) subtract the numerators.
1 - 5 = 4
So that would be -4/5.
With the like terms combined, we just need to put our two combinations (1/6p and -4/5) together!

Our answer: 1/6p - 4/5

I hope that helps!