Properties of Equations: name properties illustrated by eqns

I need to find the properties illustrated in the following equations:
1. (3 x 1/3) x 7 = (3 x 1/3) x 7
2. If 5(3) + 7 = 15 + 7 and 15 + 7 + 22, then 5(3) + 7 + 22
3. If (r+s)t = rt +st, then rt + st = (r+s)t

I am aware of the associative, commutative, distributive, and identity property, but I'm not sure which represents each of these problems. If I had to guess I would say number 1 has no property and number 3 is distributive and commutative, but I have no idea. Could someone please help me? Thanks so much!

Re: Properties of Equations

< am aware of the associative, commutative, distributive, and identity property, but...

I suggest that "being aware" of those properties is not enough. Your next step is to "understand" them. Once you learn their true meaning, you will be able to answer your questions with no difficulty. Read each property carefully and reread each until you can make up your own problem that demonstrates the principle. You will know when you "understand."

Cherry3451 said:

I am aware of the associative, commutative, distributive, and identity property, but I'm not sure which represents each of these problems.

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To amplify a bit on the (exactly right!) reply you received earlier, you need to understand what each of these properties does, what the names indicate. This isn't difficult, because each property contains clues within its name! :wink:

. . . . .associative: "associate" is "grouping together"
. . . . .commutative: to "commute" is to "move around"
. . . . .distributive: to "distribute" is to pair something(s) amongst other things
. . . . .identity: your "identity" is what makes you "you"; it is what doesn't change

So which property might relate to grouping, or re-grouping, factors or terms? Which might relate to moving factors or terms around, switching, say, the order of the first and second "place" numbers? Which might relate to taking a number that is multiplied on a sum, and pair it up with each of the terms of that sum? Which might relate to numbers which, when added (or multiplied), don't change what you'd started with? :idea:

Have fun!

Eliz.

for a quick review of number properties, with worked out examples, go to:

http://www.purplemath.com/modules/numbprop.htm

However, you are looking at "property of equality" - those are like reflexive, symmetric, transitive, etc. For reviewing those, for a start, go to:

http://en.wikipedia.org/wiki/Equality_(mathematics)

Cherry3451 said:

... If I had to guess I would say number 1 has no property ...

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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

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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

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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?

1. (3 x 1/3) x 7 = (3 x 1/3) x 7
Equivalent statement

A = A <--- Reflexive properties

2. If 5(3) + 7 = 15 + 7 and 15 + 7 = 22, then 5(3) + 7 = 22

Equivalent statement

If A = B and B = C then A = C <--- Transitive properties

3. If (r+s)t = rt +st, then rt + st = (r+s)t

Equivalent statement

If A = B then B = A <--- Symmetric properties

I am posting these answers - since some confusing answers are being given (confusion between properties of numbers and properties of equality)

Subhotosh Khan said:

... (confusion between properties of numbers and properties of equality)

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I can't say for sure that I ever learned the reflexive property of equality ... :?

I want to make sure that I understand it correctly. Both expressions in the equation must appear identical? (I looked around, and the only references I saw simply say, "a = a".)

And, yes, I see now that I confusingly tried to employ a commutative property (one of the properties of operations) to describe a property of equality. I need to pay closer attention to the terminology; especially since some instructions use equations to illustrate the properties of operations, and some texts take examples from each category and group them into a single topic (eg: the commutative, distributive and transitive properties). :|

Thanks for the post, Cherry. I re-learned something today.

~ Mark