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Lesson 1: Multiply with negatives

# Why a negative times a negative is a positive

Use the distributive property to understand the products of negative numbers. Created by Sal Khan.

## Want to join the conversation?

• When you multiply a negative by a negative you get a positive, because the two negative signs are cancelled out. Why don't the positive signs cancel out? •   Good question. The trouble might be that the word "cancel" is misleading. Perhaps a better way to think about it is that multiplying by a negative number switches the sign of the number being multiplied. While multiplying by a positive does not.
• Why do we "distribute" the 5? •   That is one of the principle properties of multiplication: it is distributive.
• What will 5(-3-(-3)) be? •   What I always do is count the amount of lines. Even means plus, uneven means minus.
- = 1 line so minus
+ = 2 lines so plus
+- = 3 lines so minus
++ = 4 lines so plus

So 5 - 3 -- 3 =
5 - 3 + 3 =
The -3 and +3 cancel eachother out. So your answer is 5.

Do note that I assume you left out the + after the 5, otherwise it's 5 * 0 = 0
• I understand why negative multiplied by a negative is a positive, but why is a negative divided by a negative a positive? • If a positive thing happens to a positive person, then that is positive(good), like a good scientist winning the Nobel Prize.

If a negative thing happens to a positive person, like someone getting robbed that's negative (bad).

If a positive thing happens to a negative person, that's negative (bad) like a robber being decreed innocent.

If a negative thing happens to a negative person, that's positive(good) like a robber being caught.

Apply this into division and multiplication,

Positive/Positive= Positive

Negative/Positive=Negative

Positive/Negative=Negative

Negative/Negative=Positive

Same for multiplication.

Hope this helps!
• Two wrongs do make a right. • At , Sal uses a dot to represent multiplying in the problem of "5 times 0 = 0," when right before that, he used an actual multiplication sign in the problem "5 times -3 = ?"

Why is that? Shouldn't he use the same sign always for multiplication? It is kind of confusing to me.

Any answer would be greatly appreciated!

Thank you!
Gleam of Dawn • There are several ways to represent multiplication. The dot and the x mean the same thing, but in problems that involve a variable, especially if the the variable is x it can get confusing to use the x multiplication symbol, so the dot or parenthesis are typically used to avoid confusion with the variable x.
• What is the Distributive Property? • The distributive property is the property of mathematics that states that a number multiplied by something in parenthesis can be distributed to everything between those parenthesis.

EXAMPLE:
3(x + 4) is the same as 3x + 12 when you distribute the 3 to the x and the 4.   