Can someone help me with this math problem?

Question

how is this problem worked out?
9/-2 + 5/3

I better understood Dave R explaination, I think I have it now, if I don't I will ask for help again....Thanks all and please feel free to help me further when i need it.

Answer 1

9/-2 + 5/3

9*3/-2*3 + 5*2/3*2

27/-6 + 10/6

-27/6 + 10/6

(-27 + 10)/6

-17/6

Answer 2

Find the lowest multiple of the denominators (the numbers below the line). In this case, it is 6.

Take the first number and multiply it by -3/-3 (this is equal to 1 and multiplying anything by 1 does not change its value, just its representation)

you'll get -27/6.

Second number, multiply by 2/2, you'll get 10/6.

Now that everything is in sixths, you just add the sixths:

-27 sixths + 10 sixths = -17 sixths = -17/6

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If you prefer, you can add a step at the beginning to flip the sign above the line: multiply by -1/-1
9/-2 becomes -9/2 (it is the same value, just written differently: all you did was multiply by 1)


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any value a/a (except 0/0) is equal to 1
so -17/-17 is 1; 4,293/4,293 is also 1.
Never use 0/0 (it does not work).

The trick is to have the same number for the denominator (below the fraction line) for all fractions. This makes additions and subtractions much easier.

You don't even have to worry about making it the lowest common multiple. We could have used -30/-30 and 20/20

9/-2 * -30/-30 = -270/60
5/3 * 20/20 = 100/60

-270/60 + 100/60 = -170/60 = -17*10 / 6*10
= -17/6 * 10/10 = -17/6
(10/10 = 1)
I'm using * for multiplication sign.

Answer 3

9/-2 + 5/3

Common denominator is 6
so

(-3*9 + 5*2)/6

(10-27)/6

(-17)/6

(-2 5/6)
.