1. You just find a common denominator. So it would be -15/20 + – 14/20 = – 29/20 (<-- improper fraction) or - 1 9/20 2. You have to change, change. -5/2 + 3/7. Find a common denominator again. -35/14 + 6/14 = -29/14 or -1 5/14 3. You have to change, change and find a common denominator again. -1/5 + -2/3, -3/15 + -10/15 = -13/15. None of these can be reduced, but if any of then can, please do.

Remember a long…. long…. long time ago… wen you were working with fractions? Remember a thing called a “Lowest Common Denominator” A what? In a fraction, the bottom number is called a “denominator.” The top number is called a “numerator.”

The lowest common denominator is the smallest number the denominators with which you’re working divide evenly into

Look at 3/4 and -3/5. What’s the smallest nmber both 4 and 5 divide into evenly? Hint 4 x 5 = ?

3/4 = x/20

multiply both sides by 20

(3)(20)/4 = (x)(20)/(20) — if you’ll concede that 20/20 = 1 and that x multiplied by 1 is equal to x, then you have…

60/4 = x

15 = x

So 3/4 = 15/20

-4/5 = x/20

same process

(-4)(20)/5 = x

-80/5 = x

-16 = x

So, -4/5 = -16/20

Now, since 3/4 = 15/20, and -4/5 = -16/20/

3/4 + -4/5 = 15/20 + -16/20 = 15/20 – 16/20 = ?

Come on, you can add fractions.. can’t you?

The rest are done exactly the same way.

to add and subtract fractions, you need the denominator (bottom number) to be the same for both fractions. So, using your first example of -3/4 + -3/5, you need to get these fractions stated with the same denominator. If you multiply the 2 bottom numbers together, you get 20, which will be a common denominator for both fractions. Now express both fractions in terms of the new denominator. The first one (-3/4) should be multiplied by 1 (which is 5/5) So multiplying -3 times 5 you get -15, and multiply 5 times 4 you get 20. So the first fraction can be expressed as -15/20. Do the same to the second fraction. Since you want it to also be expressed in 20ths, you multiply the top and bottom number by 4, so it converts to -12/20. Now, your new equation is -15/20 + -12/20. -15 plus -12 is -27, so your new fraction is -27/20. you can reduce this to negative one and seven twentieths (-1 7/20). See? the next one is -5/2 and -3/7, so the common denominator is 14 (2 x 7, right?). So multiply the top and bottom of the first fraction by 7, and the second one by 2, and solve like the ones above.

Hope this helps.