Cherry3451 said:
... If I had to guess I would say number 1 has no property ...
Hi Cherry3451:
If you're thinking that number 1 has no property because the left side looks exactly like the right side, then you're on the right track. It's not correct to say "no property" because one of the four properties you listed describes an equation where the left and right sides are
identical. (Hint, hint.)
Cherry3451 said:
I would say ... number 3 is distributive and commutative
I would say that you're half correct.
When looked at
individually, the two equations in problem 3 are
each an example of the distributive property. However, I do not think that your instructor wants you to comment on a property exhibited by just one part of the problem. In other words, I think your instructor wants you to compare the two equations, find what's different between them, and then state the property that describes
this difference.
(I could be wrong, of course, since contemporary American English is the most ambiguous language in use on our planet today. :!
Either way, if you picked the commutative property because you recognize that the left and right sides switched places going from one equation to the other, then you're exactly correct!
Cherry3451 said:
2. If 5(3) + 7 = 15 + 7 and 15 + 7 + 22, then 5(3) + 7 + 22
It looks to me like you made two typographical errors because this statement does not make sense. Since the plus sign and the equals sign are both the same key on the keyboard, I'm going to assume that you mistakenly held down the shift key and thus typed some plus signs where you actually want equal signs. Is the following correct?
2. If 5(3) + 7 = 15 + 7 and 15 + 7 = 22, then 5(3) + 7 = 22
To me, this looks like an example of the transitive property of equality. Since the transitive property is not one of the four that you listed, I'm not sure what your instructor wants. (Loren? Elizabeth?
)
The transitive property goes something like this:
Let's say that you know your dad has exactly the same amount of money in his pocket as you have in yours. You then ask me how much money I have in my pocket, and I tell you that I have the same amount of money in my pocket as your dad has in his. At this point, you should realize that I have the same amount of money that you do.
Y =
D
(
Your money is the same amount as your
Dad's.)
D =
M
(Your
Dad's amount of money is the same amount as
Mine.)
Therefore,
Y =
M
(
You have the same amount of money as
Me.)
The transitive property of equality is usually stated using the symbols A, B, and C:
If A = B and B = C, then A = C
To see how this property relates to your problem number 2, make the replacements below.
If 5(3) + 7 = 15 + 7 and 15 + 7 = 22, then 5(3) + 7 = 22
Replace each of the two expressions
5(3) + 7 with the symbol
A.
Replace each of the two expressions
15 + 7 with the symbol
B.
Replace each of the two expressions
22 with the symbol
C.
Please post a response if you need more help.
Cheers,
~ Mark
EDIT: I had to do a quick search for this so-called "identity property of equations" because I don't remember it. I could not find such a property. I understand identities (eg: trig identities); I understand the additive and multiplicative identities (these are not equations).
I have to ask: Is every true equation an example of this so-called "identity property of equations" or does this identity only relate to equations for which the expressions on each side appear identical?