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# Multiplying positive & negative numbers

Learn some rules of thumb for multiplying positive and negative numbers. Created by Sal Khan.

## Want to join the conversation?

• what would -5 x 1 be? 1 x any other number is that number but i do not know if that works for negatives.
• Yes, it works for negatives, too. 1 is a pretty cool number.
• what happens if you have a negative times a positive times a positive or a negative times a negative times a positive?
• Good question. A negative times a negative times a positive will be a positive⏤the first two negatives cancel each other out to make a positive, so when you multiply them by a positive you will be multiplying a positive times a positive. Likewise a negative times a positive times a positive⏤the first two (neg. times pos.) will make a negative so when you multiply that by another positive you will end up with a negative. Does this make sense?
• Would two negatives being multiplied the same thing as thinking there both positive? Example: -a*-b = a*b true or false?
• stan is absolutely right, if you multiply or divide any two negative numbers, the answer will be positive. so yes your example is true. if you still cant figure it out, try to find a lesson about multiplying and dividing positive and negative integers
• Why is negative times a negative a positive while positive times a positive is not negative?
• A simpler algebraic proof
Using the fact multiplication is commutative, a negative times a positive is also negative. Similarly, we can prove that a negative times a negative is a positive. Since we know that −ab is negative, and the sum of these two terms is 0, therefore (−a) × (−b) is positive
(1 vote)
• If a=2

And the problem I'm solving for is -2^a

Then is this problem supposed to look like -(2 x 2) or (-2) (-2)?
I'm so confused.
• If 'a' is a positive 2 and we have a negative 2 we are multiplying it as -2 x 2 which also looks like -(2 x 2). If you had two negative numbers your example would be (-2)(-2).
• If you multiply six positive numbers,the products sign will be ?
• If there are an even amount of negatives, it's positive, if there are an odd amount of negatives, it's negative.
(1 vote)
• What if there are three factors and 2 out of the three are negative?
• If you are multiplying the factors, then the answer should come out as positive, because those two negatives when multiplied make a positive. Then it is just a positive times a positive.