Reflexive Property vs Commutative Property of Addition?

[Cecil L Russell]

Self Teaching myself Machine Shop Math from book Technical Shop Math by Thomas Achatz. According to the examples given, a=a is a Reflexive Property while a+b=b+a is described as a Commutative Property of Addition. The quiz question is: Name the property illustrated in the example. a) x+1=x+1. My answer is this is a Commutative Property of Addition. The book claims the correct answer is a Reflexive Property. Can anyone explain why my answer is incorrect, Please. Thank you.

 

[symbolipoint]

Self Teaching myself Machine Shop Math from book Technical Shop Math by Thomas Achatz. According to the examples given, a=a is a Reflexive Property while a+b=b+a is described as a Commutative Property of Addition. The quiz question is: Name the property illustrated in the example. a) x+1=x+1. My answer is this is a Commutative Property of Addition. The book claims the correct answer is a Reflexive Property. Can anyone explain why my answer is incorrect, Please. Thank you.

Reason is self evident.
An expression written in an exact way is equal to itself. HOW would you pick the reason to be Commutative Property?

Think about the meaning of "commute". Things move.
But your example, the terms did not move; they are the same terms in the exact same places for the expression.

 

[Cecil L Russell]

Reason is self evident.
An expression written in an exact way is equal to itself. HOW would you pick the reason to be Commutative Property?

Think about the meaning of "commute". Things move.
But your example, the terms did not move; they are the same terms in the exact same places for the expression.

Ok, I can see that now-just didn't see it that way when I read the question in the book.

 

[symbolipoint]

Ok, I can see that now-just didn't see it that way when I read the question in the book.

Okay. Some of the ideas in beginning algebra need a good long bit of study and practice before one understands them. These properties you are studying will - YES, they WILL - make plain sense to you in a short time; but you need to read and think, and then do some exercise practice.

 

[Cecil L Russell]

Okay. Some of the ideas in beginning algebra need a good long bit of study and practice before one understands them. These properties you are studying will - YES, they WILL - make plain sense to you in a short time; but you need to read and think, and then do some exercise practice.

My biggest issue is that letters do not have a value therefore in most algebra equations, the answer must be 0 unless a value is given. a+b=0 absent an expressed value. Example: In a factoring exercise, I am given the equation: 16uv+24u^2+12av+18au. I'm told that the answer is 2(4u+3a)(2v+3u) My course instructor wasn't happy with my answer or my explanation which is, 80 a^2 u^4 v^2.

 

[symbolipoint]

My biggest issue is that letters do not have a value therefore in most algebra equations, the answer must be 0 unless a value is given. a+b=0 absent an expressed value. Example: In a factoring exercise, I am given the equation: 16uv+24u^2+12av+18au. I'm told that the answer is 2(4u+3a)(2v+3u) My course instructor wasn't happy with my answer or my explanation which is, 80 a^2 u^4 v^2.

The letters are variables; which means that each variable is either not a set value or is a set value. A variable is a place-holder for a number, without regard to to number being varied or being constant.A variable has a value of zero ONLY IF the person handling the expression ASSIGNS the value zero to the variable; or if solving a statement using the variable reveals the solution to be zero.

 

[Cecil L Russell]

The letters are variables; which means that each variable is either not a set value or is a set value. A variable is a place-holder for a number, without regard to to number being varied or being constant.A variable has a value of zero ONLY IF the person handling the expression ASSIGNS the value zero to the variable; or if solving a statement using the variable reveals the solution to be zero.

So what happens to the numbers in the equation?

 

[symbolipoint]

My biggest issue is that letters do not have a value therefore in most algebra equations, the answer must be 0 unless a value is given. a+b=0 absent an expressed value. Example: In a factoring exercise, I am given the equation: 16uv+24u^2+12av+18au. I'm told that the answer is 2(4u+3a)(2v+3u) My course instructor wasn't happy with my answer or my explanation which is, 80 a^2 u^4 v^2.

A possible reason that you are struggling with factorization is that you are rushing through your studies, and by so rushing, have not adequately learned what you have studied.

 

[Cecil L Russell]

A possible reason that you are struggling with factorization is that you are rushing through your studies, and by so rushing, have not adequately learned what you have studied.

That's why I started over and am doing each exercise until I get 100 on each; also searching various websites on algebra for similar exercises to practice.

 

[symbolipoint]

That's why I started over and am doing each exercise until I get 100 on each; also searching various websites on algebra for similar exercises to practice.

This is better sense than some people have.

 

[Cecil L Russell]

This is better sense than some people have.

Well, there are conflicting issues at work here. 1-My general overall derogatory opinion of algebra in general, especially given that the term translates back into Arabic as "Allah's Calculations;" isn't very polite, but 2-My desire to the best at what ever I engage in drives me to seek outside educational information so that I get the top score in my class in every exercise.

 

[Mark44]

My biggest issue is that letters do not have a value therefore in most algebra equations, the answer must be 0 unless a value is given. a+b=0 absent an expressed value.

No, that's not true.
The expression a + b can take any value, depending on the values of a and b. You can't just arbitrarily say that a + b = 0 unless that is given information.

Example: In a factoring exercise, I am given the equation: 16uv+24u^2+12av+18au.

This is NOT an equation. The tipoff in an equation is the presence of the = symbol.

I'm told that the answer is 2(4u+3a)(2v+3u) My course instructor wasn't happy with my answer or my explanation which is, 80 a^2 u^4 v^2.

I wouldn't be happy with it, either. What you did is akin to saying that a bag containing 23 apples, 15 buttons, and 35 xylophones adds up to 73applebuttonxylophones. Hopefully you'll see that this is a ridiculous answer.

, but 2-My desire to the best at what ever I engage in drives me to seek outside educational information so that I get the top score in my class in every exercise.

 

[Mark44]

My general overall derogatory opinion of algebra in general, especially given that the term translates back into Arabic as "Allah's Calculations;"

No, that's incorrect, and you're way off base. Our English word "algebra" comes from the Arabic al jabr, which means "reunion of broken parts." See https://en.wikipedia.org/wiki/Algebra.

 

[Mark44]

According to the examples given, a=a is a Reflexive Property while a+b=b+a is described as a Commutative Property of Addition.

It might be helpful to understand that the two properties listed here are properties of two completely different things. The reflexive property here is a property of the "equals" relation. A given expression is always equal to itself. Some other relations, such as <, do not have this property, as a number cannot be less than itself.

The commutative property of addition that you cited is a property of the operation of addition. The multiplication operation is another operation that is commutative. In other words, a * b = b * a, or with numbers, 3 * 7 = 7 * 3. The operations of subtraction and division are not commutative, as 5 - 2 ≠ 2 - 5, and 6 / 3 ≠ 3 / 6.