| Q. | Commutative and associative? Which one of these properties do you think is the most practical or useful? | Related Search:
Mathematics | | | The commutative and associative properties.
Which one of these properties do you think is the most practical or useful?
You may refer to math or everyday life. If you could explain the reasons for your opinion that would be great. Support your reasons with examples if possible.
| | A. | An interesting question. My answer depends quite a lot on the context.
If you mean in a mathematical research type of sense, then I would say associativity is more useful. We know of a good number of examples of systems which are non-commutative. For a few examples, consider matrices, quaternions, functions under composition, etc. In fact, the commutative (or "abelian") groups are somewhat boring to study in abstract algebra.
On the other hand, associativity is in every example I mentioned above. Almost all of the common sets and operations have associativity. Well, I suppose subtraction and division are nonassociative, but these are inverses of addition and multiplication, so they don't really count (so far as I'm concerned). One good example of a nonassociative operation is the cross product of vectors. But that's about all that I can think of. Notice that the cross product is also noncommutative.
If I think of this in a more everyday setting though, I think it's harder to say. They both play such an important role in my mental arithmetic. Really I don't think I could do most of that sort of thing without either of these properties, since they're so deeply ingrained in my mind as working for any real numbers I should happen to need to work with. | | | |
| Q. | How is the associative property different from the commutative property? | Related Search:
Homework Help | | | How is the associative property different from the commutative property?
| | A. | Number Properties
There are three basic number properties (or laws) that apply to arithmetic operations: Commutative Property, Associative Property and Distributive Property.
Commutative Property
An operation is commutative if a change in the order of the numbers does not change the results. This means the numbers can be swapped.
Numbers can be added in any order.
For example: 4 + 5 = 5 + 4
x + y = y + x
Numbers can be multiplied in any order.
For example: 5 × 3 = 3 × 5
a × b = b × a
Numbers that are subtracted are NOT commutative.
For example: 4 – 5 ≠ 5 – 4
x – y ≠ y –x
Numbers that are divided are NOT commutative.
For example: 4 ÷ 5 ≠ 5 ÷ 4
x ÷ y ≠ y ÷ x
Associative Property
An operation is associative if a change in grouping does not change the results. This means the parenthesis (or brackets) can be moved.
Numbers that are added can be grouped in any order.
For example: (4 + 5) + 6 = 5 + (4 + 6)
(x + y) + z = x + (y + z)
Numbers that are multiplied can be grouped in any order.
For example: (4 × 5) × 6 = 5 × (4 × 6)
(x × y) × z = x × (y × z)
Numbers that are subtracted are NOT associative.
For example: (4 – 5) – 6 ≠ 4 – (5– 6)
(x – y) – z ≠ x – (y – z)
Numbers that are divided are NOT associative.
For example: (4 ÷ 5) ÷ 6 ≠ 4 ÷ (5÷ 6)
(x ÷ y ) ÷ z ≠ x ÷ ( y ÷ z) | | | |
| Q. | Can anyone tell me anything about selectivity in associative learning? | Related Search:
Psychology | | | I'm writing a psychology report on selectivity in associative learning but am struggling to find anything on selective associative learning on the internet. Does anyone know any good websites? I've tried googling it, and all that comes up is examples of how a certain drug affects it, I need something on the main principles and theory of it.
Thanks.
| | A. | Associative Learning
Associative learning takes place whenever an animal learns to associate an external event with a change in its own internal state, or a change in its behavior. In addition, an animal can also learn to associate an act that it performs with some kind of reward. The first form of learning is classical conditioning, the second form of learning is operant or instrument conditioning.
A chicken with a bird feeder that comes on at night, may happen to create a shadow on the sensor that turns on the feeder in daylight. That chicken may then learn to place its head or body in a position to repeat that shadow when it is hungry and feed all the time when it is hungry.
Yes, the horrible, and deadly myth of permanence in ability is killing many students and adults. We need desperately to remove this false and deadly myth of fixed intelligences and abilities and replace it with tools to continually improve and change our lives. Please Please read learning theory and Grand Hope, and also Little Girl Innocence from profile and my blogs, and also on request to all by e-mail.
By showing students how their individual environments greatly affect their ability to think, learn, long-term motivation to learn, and grow mentally and emotionally, students will have much more respect and esteem for themselves and for others. By providing students with tools to approach their lives more delicately and differently to continually change and improve their lives, students will then have a continuous hope of developing in time, many if not all of the qualities they admire in others over time. Students will then have a continuous hope of changing and becoming better, newer persons with each passing day. This will reduce much hopelessness, many harmful escapes and other problems created by our horrible teachings of fixed intelligences in school such as dropouts, drug/alcohol abuse, catharsis of violence, and suicide.
I would like for all students though to be more thoughtful of seeing our minds as capable of much more thinking, learning, and motivation to learn by seeing how they can approach their more delicately to greatly improve from within their ability to think and learn.
Imagine a child who is able to learn more effectively. Try to see an upright rectangle representing our full ability. The young child has few if any layers of mental frictions so he has almost of all of his ability to learn. As we get older, we accumulate more layers of mental frictions. The trick we as humans need to learn is how to approach our lives more delicately to more permanently reduce layers of mental frictions to continually improve our thinking, learning, and mental/emotional health. Please read learning theory on profile, my blogs, and to all on request. | | | |
| Q. | How do I found out which problem is the distributive property and which is the associative property? | Related Search:
Homework Help | | | It's asking me which it the distributive property and associative property in these Algebra problems. Help please.
1. (a+b)+c=a+(b+c)
2. a(b+c)=a*b+a*c
3. a*1=a
4. a+b+c=a+c=b
Ah, thank you!
| | A. | Associative property states that the change in grouping of three or more addends or factors does not change their sum or product
Examples of Associative Property
Addition
(2 + 3) + 5 = 2 + (3 + 5)
Whether you add 2 & 3 first or 3 & 5 first does not matter as you get the the same sum (10) both ways.
Multiplication
(4 . 5) . 10 = 4 . (5 . 10)
Whether you multiply 4 & 5 first or 5 & 10 first does not matter as you get the the same product (200) both ways.
Distributive Property states that the product of a number and a sum is equal to the sum of the individual products of the addends and the number.
That is, a(b + c) = ab + ac.
Examples of Distributive Property
5(3 + 1) = 5 × 3 + 5 × 1
Consider LHS: 5(3 + 1) = 5(4) = 20
Consider RHS: 5 × 3 + 5 × 1 = 15 + 5 = 20
LHS = RHS
HOPE THIS HELPS!! GOOD LUCK!
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| Q. | what are the differences between the commutative and associative properties? | Related Search:
Homework Help | | | i need to know the difference for math
here is one of the questions
is the property associative or commutative?
| | A. | associative:
x+y=y+x
commutative:
z(x+y)=(z+x)+y | | | |
| Q. | Do the commutative and associative properties hold for subtraction and division? | Related Search:
Mathematics | | | My teacher got pissed off at one student because she had no idea what the difference between associative and commutative now my teacher wants me and everyone else in the class to write about it. I understand this question but have no idea how to explain it in more than a sentence what sucks is I need it in 1 paragraph.
| | A. | You are in Luck. I am taught this for 33 years. So listen up.
The commutative property of addition is a+b=b+a You can "commute" the two numbers around the + sign and still have the same answer.
4+2=2+4 The commutative property of multiplication is ab=ba meaning you can "commute" the numbers and still have the same answer. 5(6)=6(5) 30=30
There is no commutative property of subtraction or division. I will show you two counterexamples. 6-2=4 but 2-6= (-4) 4 does not equal (-4).
12 divided by 6= 2 but 6 divided by 12= 1/2
To remember this property, the word commute means to go back and forth from one place to another. Like commuting to work from home and back. It is the same distance coming and going. Also, the Commutative has C O as the first two letters. C could stand for Change and O stand for Order. Change order of the terms or numbers.6+2 the order changes to 2=6.
Now, the associative property of addition and multiplication is changing the grouping symbols and leaving the numbers fixed.
For example: a + (b+c)= (a+b) +c Notice the three numbers are in the same order, but the grouping is changed. 5+ ( 6+2)= (5 +6) +2
5 +8= 11+2 13+13
a(bc)=(ab)c 4x(2x6)=(4x2)x6 4x 12= 8x6 48=48
To associate with friends means to talk to them. Think of this example.
Mary You Bill are standing in a row. First you talk to Mary.
That would be (mary + You) + Bill Bill is still there but he is not in the conversation. Next, You turn to Bill and talk to him. That would be Mary + ( You + Bill). The three people or numbers are still there -only the grouping or the association would change.
There is not associative property of subtraction or division:
10- ( 8 -2 ) does not equal ( 10 - 8 ) -2
10- ( 6)= 4 2 -2=0 4 does not equal 0.
Good Luck. Try to summarize this. Do not use word for word in your explanation. Your teacher will know that you didn't write it. | | | |
| Q. | Determine whether or not the composition of functions is associative? | Related Search:
Mathematics | | | If F(x)= x+2 and G(x)= x/2, how do I determine if the composition of functions is associative?
| | A. | F(G(x))=F(x/2) = x/2+2
G(F(x))=G(x+2) = (x+2)/2
Did you mean commutative? If so, the answer is no.
We need three functions to test associativity. | | | |
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