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Why doesn't the commutative property work for other operations?
Wiki User
∙ 8y ago
Try it out.
3 + 9 = 9 + 3
That works.
3 x 9 = 9 x 3
That works.
3 - 9 = 9 - 3
That doesn't work.
3/9 = 9/3
That doesn't work.
The numbers came first. The commutative law was only devised because of the relationship of the numbers. It isn't that the commutative property doesn't work for other operations, it's that the other operations aren't commutative.
Wiki User
∙ 8y ago
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What is an explaination of commutative property?
The commutative property of addition and/or multiplication states that the result will be the same no matter the order. a + b = b + a a x b = b x a Think of commuters going one way and then the other.
What is the distributive property the commutative property the associate property and the identity property?
The COMMUTATIVE property states that the order of the arguments of an operation does not matter. In symbolic terms, for elements a and b and for the operation ~, a ~ b = b ~ a The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, for elements a, b and c, (a ~ b) ~ c = a ~ (b ~ c) and so, without ambiguity, either can be written as a ~ b ~ c. The DISTRIBUTIVE property is a property of two operations, for example, of multiplication over addition. It is not the property of a single operation. For operations ~ and # and elements a, b and c, symbolically, this means that a ~ (b # c) = a ~ b # a ~ c. The existence of an IDENTITY is a property of the set over which the operation ~ is defined; not a property of operation itself. Symbolically, if the identity exists, it is a unique element, denoted by i, such that a ~ i = a = i ~ a for all a in the set. For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned. I have deliberately chosen ~ and # to represent the operations rather than addition or multiplication because there are circumstances in which these properties do not apply to multiplication (for example for matrices), and there are many other operations that they can apply to.
Are Commutative property of multiplication and multiplication Array the same?
No. They are not at all the same thing. A multiplication array is something that you usually use when you're learning multiplication. For example: there are 5 rows of 7. Its a picture that shows something like that. On the other hand, a commutative property is 2 numbers that you can multiply very easily in your head. The numbers are between 0 and 9. If they are double digits, they're not commutative property.
Is division commutative?
No, division is not commutative, because a/b does not necessarily equal b/a. A simple proof by counter-example: Assuming a = 10 and b = 5, we test the property of commutativity with: 10/5 = 2 5/10 = 0.5. This is an example of division failing to be commutative. In general, for a/b to equal b/a, a must equal b. For all other pairs (a,b) the property fails.
What is the property called commutative property of addition?
Here is a bit more information than you asked for:The commutative property is stated as: a+b=b+a, or ab = ba. Notice that the numbers (a and b) move back and forth. Think of a commuter, who travels back and forth to work each day.The associative property is stated as: (a+b)+c=a+(b+c) or (ab)c = a(bc). In this case the parentheses move back and forth, so you might want to call it the commutative property too! But there's something else going on here. Parentheses are grouping symbols, and a you group is the people you hang out with or associate with.So remember: If the grouping symbols move, it's the associative property. If it's the other one where things move, it's the commutative property.
What is the other property besides identity commutative or associative?
distributive
What is an explaination of commutative property?
The commutative property of addition and/or multiplication states that the result will be the same no matter the order. a + b = b + a a x b = b x a Think of commuters going one way and then the other.
What is the distributive property the commutative property the associate property and the identity property?
The COMMUTATIVE property states that the order of the arguments of an operation does not matter. In symbolic terms, for elements a and b and for the operation ~, a ~ b = b ~ a The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, for elements a, b and c, (a ~ b) ~ c = a ~ (b ~ c) and so, without ambiguity, either can be written as a ~ b ~ c. The DISTRIBUTIVE property is a property of two operations, for example, of multiplication over addition. It is not the property of a single operation. For operations ~ and # and elements a, b and c, symbolically, this means that a ~ (b # c) = a ~ b # a ~ c. The existence of an IDENTITY is a property of the set over which the operation ~ is defined; not a property of operation itself. Symbolically, if the identity exists, it is a unique element, denoted by i, such that a ~ i = a = i ~ a for all a in the set. For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned. I have deliberately chosen ~ and # to represent the operations rather than addition or multiplication because there are circumstances in which these properties do not apply to multiplication (for example for matrices), and there are many other operations that they can apply to.
What operation are not associative?
Of the five common operations addition, subtraction, multiplication, division, and power, both addition and multiplication are commutative, as well as associative. The other operations are neither.
Are Commutative property of multiplication and multiplication Array the same?
No. They are not at all the same thing. A multiplication array is something that you usually use when you're learning multiplication. For example: there are 5 rows of 7. Its a picture that shows something like that. On the other hand, a commutative property is 2 numbers that you can multiply very easily in your head. The numbers are between 0 and 9. If they are double digits, they're not commutative property.
Is division commutative?
No, division is not commutative, because a/b does not necessarily equal b/a. A simple proof by counter-example: Assuming a = 10 and b = 5, we test the property of commutativity with: 10/5 = 2 5/10 = 0.5. This is an example of division failing to be commutative. In general, for a/b to equal b/a, a must equal b. For all other pairs (a,b) the property fails.
What is the property called commutative property of addition?
Here is a bit more information than you asked for:The commutative property is stated as: a+b=b+a, or ab = ba. Notice that the numbers (a and b) move back and forth. Think of a commuter, who travels back and forth to work each day.The associative property is stated as: (a+b)+c=a+(b+c) or (ab)c = a(bc). In this case the parentheses move back and forth, so you might want to call it the commutative property too! But there's something else going on here. Parentheses are grouping symbols, and a you group is the people you hang out with or associate with.So remember: If the grouping symbols move, it's the associative property. If it's the other one where things move, it's the commutative property.
What does community property mean in math terms?
I believe you may be thinking of the commutative property. If so, it's a property of a binary operator (one that takes 2 arguments, like addition) that means changing the order of the arguments doesn't change the outcome. For example, addition is commutative: 1 + 3 = 4 and 3 + 1 = 4. This works regardless of the arguments. Subtraction, on the other hand, is NOT commutative: 1 - 3 = -2 and 3 - 1 = 2. In some cases (when the arguments are both the same) changing the order wouldn't matter, but the commutative property means that it works for any arguments, so subtraction doesn't have it.
What is the diffence about commutative property and associative property?
Good question. Many people find it hard to understand which is which. Each of them has an addition version and a multiplication version.The commutative property is stated as: a+b=b+a, or ab = ba. Notice that the numbers (a and b) move back and forth. Think of a commuter, who travels back and forth to work each day.The associative property is stated as: (a+b)+c=a+(b+c) or (ab)c = a(bc). In this case the parentheses move back and forth, so you might want to call it the commutative property too! But there's something else going on here. Parentheses are grouping symbols, and a you group is the people you hang out with or associate with.So remember: If the grouping symbols move, it's the associative property. If it's the other one where things move, it's the commutative property.
How can you use the commutative order of property of multiplication to find the product of eight multiplied by seven?
The commutative property of multiplication states that for numbers x and y, x*y = y*x It is hard to see how this can help in answering 7*8 unless you know the seven times table and not the eight times table or the other way around.
What does a commutative property have to do with combining like terms?
When you have an expression consisting of several terms added together, and they are not all like terms, and there are like terms separated by unlike terms, you use the commutative law of addition to rearrange the terms so that the like terms are next to each other.
What does the word commutative property of addition mean?
The word "commutative" comes from "commute" or "move around", so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is "a + b = b + a"; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is "ab = ba"; in numbers, this means 2×3 = 3×2. Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property.Use the Commutative Property to restate "3×4×x" in at least two ways.They want you to move stuff around, not simplify. In other words, the answer is not "12x"; the answer is any two of the following:4 × 3 × x, 4 × x × 3, 3 × x × 4, x × 3 × 4, and x × 4 × 3Why is it true that 3(4x) = (4x)(3)?Since all they did was move stuff around (they didn't regroup), this is true by the Commutative Property.http://www.purplemath.com/modules/numbprop.htm
