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### Course: Arithmetic (all content) > Unit 4

Lesson 8: Multiplying & dividing negative numbers- Multiplying positive & negative numbers
- Multiplying numbers with different signs
- Why a negative times a negative makes sense
- Signs of expressions
- Dividing positive and negative numbers
- Multiplying and dividing negative numbers
- Multiplying negative numbers
- Why a negative times a negative is a positive
- Simplifying complex fractions
- Simplify complex fractions
- Multiplying negative numbers review
- Dividing negative numbers review

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# Multiplying numbers with different signs

Find the product of numbers with different signs. Created by Monterey Institute for Technology and Education.

## Want to join the conversation?

- Does -4 squared equal -16 or positive 16? I believe it is positive 16 but was told I was wrong.(0 votes)
- It is positive 16.

"Squared" means that number times itself, so -4 times -4 is positive 16. Any number squared, in fact is positive.

A lot of students find this difficult because they rely on the calculator too much and what might be happening is you're typing in -4^2. When you do this in the calculator it does 4^2 first, then makes it negative (because according to the calculator's order of operations it must do exponents first). When you type it in a calculator you MUST use parentheses and say (-4)^2, that will ensure that you are doing -4 * -4.(19 votes)

- Why do we even have negative numbers?(3 votes)
- There are so many uses for negative numbers!

If you are at a fair, and you win 30 cents for your race carrying cream pies, but you had to pay 45 cents to enter, you would use a negative number when figuring out whether it would be worth it to enter again.

If you are on a camping trip and the temperature starts out at 52 degrees, and the weather forecast on the radio says that the temperature will drop 45 degrees by midnight, will you need to thaw water for your canteen tomorrow? What about if the temperature is -4 degrees and the weather man says it will get 20 degrees warmer by afternoon. Will the birds be able to drink from the water fountain? Negative numbers would be useful here, too.

If you plan to help with a fundraiser for your school, and the tickets will bring in $5 each for all adults but the spaghetti feed will cost $420 to buy the pasta and sauce and paper plates, how much will the school have if 20 people sign up? Well, you would need some negative numbers to help you figure that out too.

Negative numbers are a pain at first, but they are very useful.(6 votes)

- Why is a positive times a negative always = negative.(2 votes)
- Think about how multiplying a number X by a number Y is just adding X together Y times. Any amount of negative numbers added together will always be negative.

2 * 3 = 2 + 2 + 2 = 6

-2 * 3 = -2 + -2 + -2 = -6(4 votes)

- It doesn't seem like Khan Academy covers this, but how come expressions like 4×(−3)+8×(−3) throw away the rules about positives and negatives and results in positives while also changing the addition to subtraction?(3 votes)
- it doesn't matter if you multiply from left to right or not you will still get the answer like (2)(4)(6) you don't have to do 2x4 you can start with 4x6 and still get the 48.(2 votes)
- How do you multiply a fraction with a negative number(2 votes)
- U can turn any number positive or negative into a fraction by putting it over 1, for example

-4 times 3/2 = -4/1 times 3/2 = -12/2

You can simplify that to -6(1 vote)

- If you can square a negative number, can you find the square root of a negative number? I looked it up but it was all really confusing algebra stuff.(2 votes)
- I don't think you can, because the square root of a number would either be two negatives or two positives.

neg x neg = pos

pos x pos = neg.

So to get a negative it would have to be a positive times a negative, which cant be a square number because the numbers aren't the same.(1 vote)

- How can negative*negative=positive?(2 votes)
- you should watch the video "Why a negative times a negative is a positive" on Khan Academy. it is really useful(1 vote)

- If negative times/divided by a negative is a positive, why is positive times/divided by a positive a positive?(2 votes)
- Some negative number divided by some negative number can be looked at this:
`- a / - b = c`

and it is allows you to do`c * - b = - a`

like`- 6 / - 3 = 2`

allows you to do this:`2 * - 3 = - 6`

With a positive number divided by a positive number you can use the same analogy:`a / b = c`

means you can do`c * b = a`

`6 / 2 = 3`

*______________*`2 * 3 = 6`

(1 vote)

- at1:20you said lets do 20 x 7.5 but then in the working out you did 7.5 x 20. Why did it change? Why would you do 7.5 x 20? Should the answer be the same despite the order of the numbers?(2 votes)
- When you multiply numbers, it does not matter what order you multiply them in. 20 x 7.5 will be the same as 7.5 x 20.(1 vote)

## Video transcript

Find the product 4 times
negative 5 times negative 7.5. So we're just multiplying
three numbers right here, some are positive,
some are negative. We could actually do
this in any order, but let's just go left to right. So let's start with the
4 times the negative 5. And then we'll multiply
whatever we get there times negative 7.5. So let's just
rewrite the problems. We have 4 times negative
5, times negative 7.5. I really don't have to
write that dot there. If you just have 4 and then
in parentheses a negative 5, that means 4 times negative 5. Now, the first thing
you need to realize is that a positive
times a positive is obviously a positive. A positive times a negative,
or a negative times a positive, when you have
different signs, you're going to end up with a negative. If you have same signs, even
if you have a negative times a negative, you're going
to have a positive as well. So let's just work that
out in this problem. So you have 4 times negative 5. 4 times 5 would be 20. Let me do this in
a different color. So 4 times 5 would be 20. But we have a positive
times a negative, so it's going to be a negative. Different signs mean we're
going to have a negative. So it becomes negative
20 times negative 7.5. So let's figure
out what that is. We have to multiply
20 times 7.5. We could do that out here. So 7.5 times 20. 0 times 5 is 0. 0 times 7 is 0. Put a 0 here, because
we're obviously not going to multiply by 2. We're actually
multiplying by 20. So 2 times 5 is 10. 2 times 7 is 14, plus 1 is 15. And we get a 0, we
get a 0, we get a 5. I'm just adding here. You get a 1. And then you count
the numbers you have behind the decimal point. We only have one digit
behind the decimal point in both numbers. So you only go one digit
behind the decimal point in our product. So the answer here is 150. So this is equal to 150. And now we just have
to think about is it going to be
positive or negative. We have a negative
times a negative. They are the same sign. So it's going to result
in a positive number. So our final answer is 150. And if we actually wanted
to keep the precision here, we could write 150.0.