Question

-7 2/3 + (-5 1/2) +8 3/4

Answer 1

`-4(5)/(12)`

Explanation:

Here we have three terms, none with matching denominators.

Now we have to find the least common multiple of 3, 2, and 4. We can ignore the 2 here because the 4 takes care of that. The least common multiple of 3 and 4 is 12. 12 is also divisible by 2, so we've fulfilled those terms.

Now, let's get to work. We have to convert all of those mixed numbers into fractions with a denominator of 12. I'll skip the explanation and just do the work step by step. Ask questions if you are unsure of something.

First, we'll just put them all in a row.

`-7(2)/(3) -5(1)/(2) +8(3)/(4)`

Next, I'm going to put them in the forms of improper fractions, just to make this a bit less cluttered.

`-(23)/(3) -(11)/(2) +(35)/(4)`

Then, I'll adjust the denominators of the fractions by multiplying the whole fraction by whatever it takes to make that denominator 12. Remember, multiply the numerator and the denominator by the same number.

`-(23)/(3)((4)/(4))-(11)/(2)((6)/(6))+(35)/(4)((3)/(3))`

`-(92)/(12) -(66)/(12) +(105)/(12)`

Now, let's add them together.

`-(53)/(12)`

You can leave this as an improper fraction, but I'm going to put this into mixed number form for you.

`-4(5)/(12)`