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Numbers & Operations - The Real & Complex Number Systems 222-226

Unit 2: Lesson 3

Understanding multiplying and dividing fractions

Negative signs in fractions

Sal finds equivalent expressions to -g/h.

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• Here's my understanding of this. There are 8 possible combinations: x/y, -x/y, x/-y, -x/-y, -(x/y), -(-x/y), -(x/-y), and -(-x/-y). They can all be simplified to either x/y or -(x/y), which is x/y positive or negative. When there's no negative sign before the whole expression (the first 4 combinations), normal rules apply (pos/pos = pos, pos/neg = neg, neg/pos = neg, neg/neg = pos). When there is a negative sign before the expression (the last 4 combinations), the opposite rules apply (i.e. evaluate the expression as if it wasn't there and then take the negative of the result you get).
• At , I still don't get why -(-e)/f is equal to e/f.
(1 vote)
• When there are 2 negatives, it equals to a positive. When someone says "Jump", it's a positive. When someone says "Don't eat", it is negative. Meanwhile, if someone says "Don't not eat", that's back to saying "Eat" which is a positive.
• just wondering is -6 / (-2) = 6 / 2?
• Yes, in multiplying/dividing positive and negative numbers, count number of - signs. If it is 0,2,4 or even numbers, answer is positive, and if 1,3,5,odd answer is snegative.
You have 2 negatives, so answer is positive. If you have (-6)^2/(-2) you end up with 3 negatives, so answer is -36/2=-18.
• Why did we learn this AFTER lessons that needed it?
• for the same reason that sal misspeaks
(1 vote)
• I am currently very confused.
• why?
(1 vote)
• At why can you put the negative sign on the top, bottom, or middle? Shouldn't it matter where it goes?
(1 vote)
• Okay, so we've got x/y. If x is negative, isn't the whole thing going to be negative? So we could have
-(x/y) for -x/y. Same thing with x/-y. I don't know if that was clear. If it wasn't, comment.
• This helped me understand this better.
• why are there so many combinations
• There are a lot of places to put the negative sign, if that's what you mean! They're all just ways of showing whether or not the number is negative. Depending on how you work with an operation, the negative number may end up in different spots.

Needless to say, sometimes I get mixed up as well. I just count the number of negative signs applying to the fraction and decide if it's a negative number with the rule that if there's an even number of "-" signs it's a positive; if there's an odd number, it's negative.
(1 vote)
• can anyone pls help me of summarising the whole thing in one sentence?
• I will put them into examples so that it will make sense.

Positives and negatives: fractions
1. -1/2 = Negative

2. -(-1/2) = Positive because: n / n = p and if part of fraction is negative, then it would be positive.

3. 1/2 = Positive
And that's all I can think of for now. Please use this information for help in case you are stuck. remind me if you still need any help.
(1 vote)
• It seems like conflicting information to say that you can multiply the negative sign that's in FRONT of an entire fraction by either the numerator (at ) or the denominator (at ). The contradiction is confusing.