do u know examples of the math properties?

Question

im having a hard time with properties like associative and communitive stuff.. do u know examples of the math properties? t....thanx tons if u answer☺☺♥

Answer 1

Distributive Property



The Distributive Property is easy to remember, if you recall that "multiplication distributes over addition". Formally, they write this property as "a(b + c) = ab + ac". In numbers, this means, that 2(3 + 4) = 2×3 + 2×4. Any time they refer in a problem to using the Distributive Property, they want you to take something through the parentheses (or factor something out); any time a computation depends on multiplying through a parentheses (or factoring something out), they want you to say that the computation used the Distributive Property.

Why is the following true? 2(x + y) = 2x + 2y

Since they distributed through the parentheses, this is true by the Distributive Property.



Use the Distributive Property to rearrange: 4x – 8

The Distributive Property either takes something through a parentheses or else factors something out. Since there aren't any parentheses to go into, you must need to factor out of. Then the answer is "By the Distributive Property, 4x – 8 = 4(x – 2)"



"But wait!" you say. "The Distributive Property says multiplication distributes over addition, not subtraction! What gives?" You make a good point. This is one of those times when it's best to be flexible. You can either view the contents of the parentheses as the subtraction of a positive number ("x – 2") or else as the addition of a negative number ("x + (–2)"). In the latter case, it's easy to see that the Distributive Property applies, because you're still adding; you're just adding a negative.



The other two properties come in two versions each: one for addition and the other for multiplication. (Note that the Distributive Property refers to both addition and multiplication, too, but to both within just one rule.)



Associative Property



The word "associative" comes from "associate" or "group";the Associative Property is the rule that refers to grouping. For addition, the rule is "a + (b + c) = (a + b) + c"; in numbers, this means

2 + (3 + 4) = (2 + 3) + 4. For multiplication, the rule is "a(bc) = (ab)c"; in numbers, this means 2(3×4) = (2×3)4. Any time they refer to the Associative Property, they want you to regroup things; any time a computation depends on things being regrouped, they want you to say that the computation uses the Associative Property. Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved

Rearrange, using the Associative Property: 2(3x)

They want you to regroup things, not simplify things. In other words, they do not want you to say "6x". They want to see the following regrouping: (2×3)x



Simplify 2(3x), and justify your steps.

In this case, they do want you to simplify, but you have to tell why it's okay to do... just exactly what you've always done. Here's how this works:



2(3x) original (given) statement

(2×3)x by the Associative Property

6x simplification (2×3 = 6)

Why is it true that 2(3x) = (2×3)x?

Since all they did was regroup things, this is true by the Associative Property.



Commutative Property



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.

Answer 2

As generally used in math class, the distributive property is the ability of one operation to "distribute" over another operation contained inside a set of parenthesis. Most commonly, this refers to the property of multiplication distributing over addition or subtraction, such that x(a+b) = xa + xb.



When we say that multiplication distributes over addition, it means we can distribute the factor outside the set of parenthesis to each item inside, and then add the results. For example, 4(3+7) is equivalent to 4*3 + 4*7 because the multiplication by four was distributed across the addition inside the parenthesis.



Not every operation is distributive. For example, division is not distributive over addition. If we are given 20/(3+7) the true result is 2, but distributing would give you 20/3 + 20/7, which is around 10 and very incorrect!



The distributive property is actually a very simple concept to learn and apply. It will allow you to simplify something like 3(6x + 4), where you have a number being multiplied by a set of parenthesis. Let's start with a simple problem:



6(4 + 2)



Based on the order of operations, you know that anything inside parenthesis should be done first. Adding 4 + 2 is simple enough, resulting in this:



6(6)



When you see a number next to parenthesis like this, it means multiplication, so what we really have here is this (remember that * means multiplication):



6 * 6 = 36



That was easy enough, but we can also solve this problem and get the same answer using the distributive property of multiplication over addition.



6(4 + 2)



Now distribute the 6 across the parenthesis to the two terms inside:



(6 * 4) + (6 * 2) = 24 + 12 = 36 (same as before!)



Now try simplifying this expression:



-2(4y - 8)



This is no more difficult to simplify than the last one. Just distribute the -2 to the terms inside, which are the 4y and the -8:



(-2 * 4y) + (-2 * -8)

-8y + 16

16 - 8y



And that's all there is to it. Once you get the hang of things it will be second-nature to you. You simply have to remember that only certain operations are distributive: multiplication distributes over addition and subtraction, but division does not! You are welcome to continue browsing our site now, or you can read another lesson on the distributive property from AlgebraHelp or this lesson from Dr. Math. .........Property Management Bendigo

Answer 3

For the commutative property, I think of commuting. Four friends go for a ride in the same car and return in the same car, but not in the same seats.



Think of the positions within the parentheses as the seats in a car.



(a + b + c + d) = (b + a + c + d)



For associativity, I think of 3 friends, two walking with arms linked and one walking behind, then a different one walking behind while the other two walk with arms linked.



Think of the two in the parentheses as walking with arms linked.



a + (b + c) = (a + b) + c





For the distributive property, think of dealing (distributing) cards. Each player gets a card. If you skip someone, you're doing it wrong.



The players are inside the parentheses and whatever is multiplying it is what they all get.



- (x + y - 3) = - x - y - - 3

Answer 4

comm. upload: 5+4=4+5 comm. mult: 5x4=4x5 asso. upload: (5+4)+6=5+(4+6) asso. mult: (4x5)x6=4x(5x6) iden. upload: 5+0.5 (theres not probable identity components for addition) iden. mult: 5x1=5 4x1=4

Answer 5

this might help: http://tangent.utc.edu/math-help/properties%20of%20mult%20and%20add.pdf