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### Course: Grade 7 (VA SOL)>Unit 1

Lesson 8: Properties of multiplication & division

# Equivalent expressions with negative numbers (multiplication and division)

In this video, we figure out whether or not some expressions are equivalent. To do this, we think about properties of multiplication and division.

## Want to join the conversation?

• I'm not sure I understand the different ways to break down the problems and do them differently. Can someone please help me?
• Hello kenbat2. You might find it helpful to go back and relearn/rewatch the video/s on the different properties, such as disttributive and commutative. There are always multiple ways of figuring out how to solve a problem. I hope this helps, and if anyone could point to these videos, please do so. Otherwise you will have to search here on KA.
Jennifer in AZ
(1 vote)
• I have a question with an answer suggestions:
-x*(-y*x) = x^2*y. The solution says that it's the same as x*x*y, but what about the -x? Shouldn't it be -x^2?
I just have no clue why and how that could work.

• -yx is a single term, so you won't need to use the distributive property. The term, -yx has a negative sign, so does -x. Multiplying the two negative terms will make the negatives cancel out, so we are left with x^2y.

Hope this helps!
• How did he get a positive six when it was (-2)x3
• It should be 6. 2 3-1=6*-1=-6
(1 vote)
• I don't understand why -x*(-y*x) is not equal to -x*x*xy when using the distributive property? Please help! Thank You
• The distributive property is used to distribute something outside the parentheses to each of the terms inside the parentheses. Since you are multiplying, -y*x is a single term, and while what you are doing does not appear to follow any pattern, it appears you are trying to look at -yx as two terms, not one. If you had -x(-y+x) then you would get xy-x*x or xy-x^2.
• -12(-3/4) how do you solve this poblem
• What you do is you place -12 over 1 to become a fraction, then multiply the numerators and denominators as usual.
• I don't get why this is any different than doing order of operations. Like, it's still solving it, but with more unnecessary steps
• why is the 2.2 in the equation 3.7 / 2.2 x (-9.4) turned into 1/2.2 when it is rewritten? (in the quiz)
• With your expression, to multiply fractions times whole numbers, you can divide whole number by 1, then you multiply the numerators and denominators, there are a variety of ways to write this. 3.7/2.2 * (-9.4) = -9.4/2.2 * 3.7 = (3.7 * -9.4)/2.2 = 1/2.2 (3.7*-9.4). Each way is equivalent to multiplying the numerators and denominators.
• What about fractions? How does -(x/-y)*(-z/-a) equal to x/a*(-(-z/y)?
• Doesn't x get distributed to both items in parentheses?
• Which of the following expressions are equivalent to 3.7/2.2 x (-9.4)?
Choose all answers that apply:

(Choice A)
3.7x(-2.2)/9.4

(Choice B)
B
-3.7/(-2.2)x(-9.4)

(Choice C)

None of the above

Help!
• A simple way to do it is to get a calculator, but let's not do it.

Let a = 3.7, b = 2.2, and c = 9.4.

So we have a / b * (-c)

A: a * -b / c
Obviously not this, since we had / b instead of * b.

B: -a / -b * (-c)
Note that negative divided by negative equals positive (Remember division is essentially multiplication, but just multiplying a reciprocal).
Therefore, -a / -b = a / b

Hence B is the correct answer.
(1 vote)