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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 × 3
- Why 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.
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Which expression shows the results of applying the Comunitive Property of addition to the expression 6 1 9 7 2?
This question cannot be answered. There is no such word as "Comunitive" and so "the Comunitive Property of addition" does not exist. One possible alternative is the "commutative" property, but that is only of marginal relevance in terms of the given expression. Thus, it is not at all clear what property the question is about and why any such property should be invoked.
What is a communitive property?
Commutative property - 2 reference results Commutativity In mathematics, commutativity is the ability to change the order of something without changing the end result. It is a fundamental property in most branches of mathematics and many proofs depend on it. The commutativity of simple operations was for many years implicitly assumed and the property was not given a name or attributed until the 19th century when mathematicians began to formalize the theory of mathematics. The commutative property (or commutative law) is a property associated with binary operations and functions. Similarly, if the commutative property holds for a pair of elements under a certain binary operation then it is said that the two elements commute under that operation. In group and set theory, many algebraic structures are called commutative when certain operands satisfy the commutative property. In higher branches of math, such as analysis and linear algebra the commutativity of well known operations (such as addition and multiplication on real and complex numbers) is often used (or implicitly assumed) in proofs. The term "commutative" is used in several related senses. 1. A binary operation ∗ on a set S is said to be commutative if: : forall x,y in S: x * y = y * x , : - An operation that does not satisfy the above property is called noncommutative. 2. One says that x commutes with y under ∗ if: : x * y = y * x , 3. A binary function f:A×A → B is said to be commutative if: : forall x,y in A: f (x, y) = f(y, x) , Records of the implicit use of the commutative property go back to ancient times. The Egyptians used the commutative property of multiplication to simplify computing products. Euclid is known to have assumed the commutative property of multiplication in his book Elements. Formal uses of the commutative property arose in the late 18th and early 19th century when mathematicians began to work on a theory of functions. Today the commutative property is a well known and basic property used in most branches of mathematics. Simple versions of the commutative property are usually taught in beginning mathematics courses. The first use of the actual term commutative was in a memoir by Francois Servois in 1814, which used the word commutatives when describing functions that have what is now called the commutative property. The word is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "tending to" so the word literally means "tending to substitute or switch." The term then appeared in English in Philosophical Transactions of the Royal Society in 1844. The associative property is closely related to the commutative property. The associative property states that the order in which operations are performed does not affect the final result. In contrast, the commutative property states that the order of the terms does not affect the final result. Symmetry can be directly linked to commutativity. When a commutative operator is written as a binary function then the resulting function is symmetric across the line y = x. As an example, if we let a function f represent addition (a commutative operation) so that f(x,y) = x + y then f is a symmetric function which can be seen in the image on the right. * Putting your shoes on resembles a commutative operation since it doesn't matter if you put the left or right shoe on first, the end result (having both shoes on), is the same. * When making change we take advantage of the commutativity of addition. It doesn't matter what order we put the change in, it always adds to the same total. Two well-known examples of commutative binary operations are: * The addition of real numbers, which is commutative since : y + z = z + y quad forall y,zin mathbb{R} : For example 4 + 5 = 5 + 4, since both expressions equal 9. * The multiplication of real numbers, which is commutative since : y z = z y quad forall y,zin mathbb{R} : For example, 3 × 5 = 5 × 3, since both expressions equal 15. * Further examples of commutative binary operations include addition and multiplication of complex numbers, addition of vectors, and intersection and union of sets. * Washing and drying your clothes resembles a noncommutative operation, if you dry first and then wash, you get a significantly different result than if you wash first and then dry. * The Rubik's Cube is noncommutative. For example, twisting the front face clockwise, the top face clockwise and the front face counterclockwise (FUF') does not yield the same result as twisting the front face clockwise, then counterclockwise and finally twisting the top clockwise (FF'U). The twists do not commute. This is studied in group theory. Some noncommutative binary operations are: * subtraction is noncommutative since 0-1neq 1-0 * division is noncommutative since 1/2neq 2/1 * matrix multiplication is noncommutative since begin{bmatrix} 0 & 2 0 & 1 end{bmatrix} = begin{bmatrix} 1 & 1 0 & 1 end{bmatrix} cdot begin{bmatrix} 0 & 1 0 & 1 end{bmatrix} neq begin{bmatrix} 0 & 1 0 & 1 end{bmatrix} cdot begin{bmatrix} 1 & 1 0 & 1 end{bmatrix} = begin{bmatrix} 0 & 1 0 & 1 end{bmatrix} * An abelian group is a group whose group operation is commutative. * A commutative ring is a ring whose multiplication is commutative. (Addition in a ring is by definition always commutative.) * In a field both addition and multiplication are commutative.
What does commutative mean in math terms?
It means that the terms can move and the result will be the same. This applies for addition and multiplication. Examples:3 + 5 = 5 + 3 = 86 x 8 = 8 x 6 = 48Think of the word commute (like traveling from home to work) to remember this property. The terms travel around.
Why is 12 less then 3 plus 7 ambiguous?
Because, unless the word "then" in the question is changed to "than", the phrase given means nothing at all. If the word "then" in the question is changed to "than", then the phrase is not ambiguous, even though it can mean, in mathematical terms, either [(-12 + 3) + 7] or [-12 + (3 + 7)], because both of these expressions have a value of -2, illustrating the commutative property of addition.
What does the word identity in addition mean?
Identity of addition means the answer and then add
The key word for commutative property is?
The key word for the commutative property is interchangeable. Addition and multiplication functions are both commutative and many mathematical proofs rely on this property.
What is the key word for the commutative property?
addition
What property of addition states that the order in which two real numbers are added does not affect the sum?
That is the commutative property. Formally, A + B = B + A. The word "commutative" comes from a root meaning "to move around."
What is the communtavie property do multiplication to create an equivalent expression for 4113?
Not sure what a communtavie property is. The nearest word that I can think of is commutative, and the commutative property of multiplication has no relevance for 4113.
Which expression shows the results of applying the Comunitive Property of addition to the expression 6 1 9 7 2?
This question cannot be answered. There is no such word as "Comunitive" and so "the Comunitive Property of addition" does not exist. One possible alternative is the "commutative" property, but that is only of marginal relevance in terms of the given expression. Thus, it is not at all clear what property the question is about and why any such property should be invoked.
What multiplication property is used for 53 X's 6 equals 6 X's 53?
Commutative property. To remember what the commutative property does, think of the word: commute.A person commutes to work each day. He changes his position (he's at home, then he's at work).In the commutative property of multiplication, the terms can move around or change position and the result will be the same.
What is a communitive property?
Commutative property - 2 reference results Commutativity In mathematics, commutativity is the ability to change the order of something without changing the end result. It is a fundamental property in most branches of mathematics and many proofs depend on it. The commutativity of simple operations was for many years implicitly assumed and the property was not given a name or attributed until the 19th century when mathematicians began to formalize the theory of mathematics. The commutative property (or commutative law) is a property associated with binary operations and functions. Similarly, if the commutative property holds for a pair of elements under a certain binary operation then it is said that the two elements commute under that operation. In group and set theory, many algebraic structures are called commutative when certain operands satisfy the commutative property. In higher branches of math, such as analysis and linear algebra the commutativity of well known operations (such as addition and multiplication on real and complex numbers) is often used (or implicitly assumed) in proofs. The term "commutative" is used in several related senses. 1. A binary operation ∗ on a set S is said to be commutative if: : forall x,y in S: x * y = y * x , : - An operation that does not satisfy the above property is called noncommutative. 2. One says that x commutes with y under ∗ if: : x * y = y * x , 3. A binary function f:A×A → B is said to be commutative if: : forall x,y in A: f (x, y) = f(y, x) , Records of the implicit use of the commutative property go back to ancient times. The Egyptians used the commutative property of multiplication to simplify computing products. Euclid is known to have assumed the commutative property of multiplication in his book Elements. Formal uses of the commutative property arose in the late 18th and early 19th century when mathematicians began to work on a theory of functions. Today the commutative property is a well known and basic property used in most branches of mathematics. Simple versions of the commutative property are usually taught in beginning mathematics courses. The first use of the actual term commutative was in a memoir by Francois Servois in 1814, which used the word commutatives when describing functions that have what is now called the commutative property. The word is a combination of the French word commuter meaning "to substitute or switch" and the suffix -ative meaning "tending to" so the word literally means "tending to substitute or switch." The term then appeared in English in Philosophical Transactions of the Royal Society in 1844. The associative property is closely related to the commutative property. The associative property states that the order in which operations are performed does not affect the final result. In contrast, the commutative property states that the order of the terms does not affect the final result. Symmetry can be directly linked to commutativity. When a commutative operator is written as a binary function then the resulting function is symmetric across the line y = x. As an example, if we let a function f represent addition (a commutative operation) so that f(x,y) = x + y then f is a symmetric function which can be seen in the image on the right. * Putting your shoes on resembles a commutative operation since it doesn't matter if you put the left or right shoe on first, the end result (having both shoes on), is the same. * When making change we take advantage of the commutativity of addition. It doesn't matter what order we put the change in, it always adds to the same total. Two well-known examples of commutative binary operations are: * The addition of real numbers, which is commutative since : y + z = z + y quad forall y,zin mathbb{R} : For example 4 + 5 = 5 + 4, since both expressions equal 9. * The multiplication of real numbers, which is commutative since : y z = z y quad forall y,zin mathbb{R} : For example, 3 × 5 = 5 × 3, since both expressions equal 15. * Further examples of commutative binary operations include addition and multiplication of complex numbers, addition of vectors, and intersection and union of sets. * Washing and drying your clothes resembles a noncommutative operation, if you dry first and then wash, you get a significantly different result than if you wash first and then dry. * The Rubik's Cube is noncommutative. For example, twisting the front face clockwise, the top face clockwise and the front face counterclockwise (FUF') does not yield the same result as twisting the front face clockwise, then counterclockwise and finally twisting the top clockwise (FF'U). The twists do not commute. This is studied in group theory. Some noncommutative binary operations are: * subtraction is noncommutative since 0-1neq 1-0 * division is noncommutative since 1/2neq 2/1 * matrix multiplication is noncommutative since begin{bmatrix} 0 & 2 0 & 1 end{bmatrix} = begin{bmatrix} 1 & 1 0 & 1 end{bmatrix} cdot begin{bmatrix} 0 & 1 0 & 1 end{bmatrix} neq begin{bmatrix} 0 & 1 0 & 1 end{bmatrix} cdot begin{bmatrix} 1 & 1 0 & 1 end{bmatrix} = begin{bmatrix} 0 & 1 0 & 1 end{bmatrix} * An abelian group is a group whose group operation is commutative. * A commutative ring is a ring whose multiplication is commutative. (Addition in a ring is by definition always commutative.) * In a field both addition and multiplication are commutative.
What does commutative mean in math terms?
It means that the terms can move and the result will be the same. This applies for addition and multiplication. Examples:3 + 5 = 5 + 3 = 86 x 8 = 8 x 6 = 48Think of the word commute (like traveling from home to work) to remember this property. The terms travel around.
What is the definition of the Commutative Property?
It means that in certain mathematical operations, you can turn around the order of the numbers without changing the result. Examples:3 + 4 = 4 + 3 (addition of real numbers is commutative)4 x 7 = 7 x 4 (multiplication of real numbers is commutative)3 - 1 is not the same as 1 - 3 (subtraction is not commutative)2 / 1 is not the same as 1 / 2 (division is not commutative)For vectors, A x B = - B x A (not commutative; however, the vector cross product is anticommutative).To help remember this property, think of the word commuteor commuter (like when somebody moves from one place to another, like from home to work).
Explain when an binary operation is commutative?
when we add and substract any number * * * * * "substract" is not a word, and in any case, subtraction is not commutative. A binary operation ~, acting on a set, S, is commutative if for any two elements x, and y belonging to S, x ~ y = y ~ x Common binary commutative operations are addition and multiplication (of numbers) but not subtraction nor division.
Why is 12 less then 3 plus 7 ambiguous?
Because, unless the word "then" in the question is changed to "than", the phrase given means nothing at all. If the word "then" in the question is changed to "than", then the phrase is not ambiguous, even though it can mean, in mathematical terms, either [(-12 + 3) + 7] or [-12 + (3 + 7)], because both of these expressions have a value of -2, illustrating the commutative property of addition.
What is the prefix of the word Commutative?
camunity
