PROBLEM #1:
As the problem is, we are adding a negative. I can change this to be a subtraction problem. It looks like this: [tex]2\frac{1}{3} - 1\frac{1}{5}[/tex].
To be able to add or subtract fractions/mixed numbers, we have to first get common denominators. A common denominator is a shared multiple between two numbers. So, we need to find the smallest number that both 3 and 5 (the denominators of each fraction) can do into evenly. In this case, that number is 15! To transform the fractions to have common denominators, we will multiply 1/3 by 5/5 and 1/5 by 3/3 (multiply the top and bottom by 5 or 3 so that the denominator is 15). Here is our new problem: [tex]2\frac{5}{15} - 1\frac{3}{15}[/tex].
All that's left to do now is subtract! Since our first fraction is larger (this is important!) we don't need to do any borrowing. So, we'll subtract 2 - 1 = 1, and 5/15 - 3/15 = 2/15. Therefore, if we put those pieces back together, we get 1 2/15 ([tex]1\frac{2}{15}[/tex]).
PROBLEM #2:
For this problem, we have two negative mixed numbers. In this case, we will simply be adding the negative numbers because both are negative. For example, -2 + -4 = -6. Here is the rewritten problem: [tex]-3\frac{1}{2} + -5\frac{1}{3}[/tex].
Our first step is to get common denominators. In this case, that common denominator will be 6: [tex]-3\frac{3}{6} + -5\frac{2}{6}[/tex].
Now, we have to add! -3 + -5 = -8, -3/6 + -2/6 = -5/6. Once we've added the parts, we can put them back together to form the answer: -8 5/6 ([tex]-8\frac{5}{6}[/tex]).
Hope this helps!! :)
