Question

"Compare and contrast the Multiplication Property of Equality and the Division Property of Equality and explain why they can be considered the same property."

I am literally not taught a thing about this in my textbook chapter. Can someone please explain it to me? I'd really really appreciate it!

Answer 1

@tkhunny

Answer 2

What are these mysterious properties. Can you provide examples of both?

Answer 3

Uh, well for the Multiplication Property of Equality a + b + c is equal to ab + ac...
right?
Or am I mixing something up?

Answer 4

Or no, its a = b?

Answer 5

That makes no sense.

If a = b, then ac = bc if c is NOT zero.

What can you say the other way?

If ac = bc, then ??

Answer 6

Then a + c = b + c ???

Answer 7

That looks like addition, to me. Why do we care about that?

Answer 8

Mm, I guess we don't.
Would, I do the same thing I did above except I'd multiply a * b = b * c
Or no?

Answer 9

I cannot answer your question because you have not defined what multiplication and division rules we are talking about. I gave it a guess.

Typically, we say, "multiply both sides of the equation by the same thing."

If we say , "multiply by 1/2", is that REALLY any different than saying "divide by 2"?

Answer 10

Well thats the thing, and this is why I needed both of these explained.
My textbook does not even mention them whatsoever, so I hardly even understand both of them. I vaguely remember something about a = b and this that and the other thing, but I do not know what to apply here in regards to definitions and also in regards to giving examples and comparing apples to apples.

Answer 11

@tkhunny

Answer 12

Not sure what to tell you.

Very often, a young math student will come how with a worksheet like this:

3x = 9
2y = 8
7z = 14

And the student is expected to DIVIDE to solve each one.

3x/3 = 9/3 ==> x = 3
2y/2 = 8/2 ==> y = 4
7z/7 = 14/7 ==> z = 2

It is odd and generally not discussed, that MULTIPLICATION can also be used to solve each one.

(1/3)3x = (1/3)9 ==> x = 9/3 = 3
(1/2)2y = (1/2)8 ==> y = 8/2 = 4
(1/7)7z = (1/7)14 ==> z = 14/7 = 2

Really, whether you multiply or divide, it is the same. Unique answers don't care how you find them.

Answer 13

@tkhunny
Well, everything you just said there basically (concept wise) is a perfect conclusion to this question, but I still have to compare two things that I don't even KNOW!
I'm baffled!!
Well, anyhow thanks for what you have done. I appreciate your time immensely. :)

Answer 14

@Whitemonsterbunny17
Heya!
Have you learned anything about this? If you could help out, I'd really appreciate it!

Answer 15

@SolomonZelman
Do you know anything about this? If so, could you add some insight? It'd mean a lot! :)

Answer 16

@pooja195
@mathmale
@Awolflover1
Please, someone. I don't mean to be a pain, but I'm lost. I need some help.

Answer 17

The Multiplication Property of Equality states that when you multiply both sides of an equation by the same number, the sides still remain equal.

The Division Property of Equality states that when you divide both sides of an equation by the same number, the sides still remain equal.

In both properties, the same action is performed to both sides of the equation. However, according to the properties, a different operation is performed (multiplication or division). They can be considered the same because as @tkhunny mentioned earlier, dividing by a whole number is the same as multiplying by a fraction.

Hope I helped clear things up :) If not, let me know and I'd be glad to clarify!

Answer 18

ooh! That makes some sense! I see now. Thank you very much!
I have to go atm, but if I have any other questions I'll go ahead and ask you.
Thanks again!! :)

Answer 19

" by the same number" should read " by the same NON-ZERO number"

Answer 20

Thats a good clarification! Thank you! @tkhunny