## Why does the commutative property of multiplication work?

The commutative property of multiplication states that when two numbers are being multiplied, their order can be changed without affecting the product.

For example, has the same product as .

These properties apply to all real numbers.

Let’s take a look at a few addition examples..

## What is commutative property of whole numbers?

Commutative Property When we add two or more whole numbers, their sum is the same regardless of the order of the addends. The sum of both 2 + 4 and 4 + 2 is 6. That means, we can add whole numbers in any order.

## What is associative and commutative property of addition?

In math, the associative and commutative properties are laws applied to addition and multiplication that always exist. The associative property states that you can re-group numbers and you will get the same answer and the commutative property states that you can move numbers around and still arrive at the same answer.

## What is an example of distributive property?

The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2. … According to this property, you can add the numbers and then multiply by 3. 3(10 + 2) = 3(12) = 36.

## What do you mean by commutative property?

The commutative property is a math rule that says that the order in which we multiply numbers does not change the product.

## What is the difference between closure property and commutative property?

In summary, the Closure Property simply states that if we add or multiply any two real numbers together, we will get only one unique answer and that answer will also be a real number. The Commutative Property states that for addition or multiplication of real numbers, the order of the numbers does not matter.

## What are the three properties?

There are four basic properties of numbers: commutative, associative, distributive, and identity. You should be familiar with each of these. It is especially important to understand these properties once you reach advanced math such as algebra and calculus.

## What are the 3 properties of multiplication?

There are three properties of multiplication: commutative, associative, and distributive.Commutative Property.Associative Property.Distributive Property.

## What is commutative and distributive property?

When you rewrite an expression by a commutative property, you change the order of the numbers being added or multiplied. … The distributive property can be used to rewrite expressions for a variety of purposes. When you are multiplying a number by a sum, you can add and then multiply.

## How do you explain the commutative property of addition?

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.

Commutative Property The commutative property of addition says that when the order of the addends is changed, the answer still stays the same. Tip: The word commutative is kind of like the word commute, which means to move around.

## What’s the associative property of addition?

Basically the Associative Law of Addition means that the order that the numbers are added does not matter.

## What is the distributive property of addition?

According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

## What is the commutative law of addition?

Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba. … From these laws it follows that any finite sum or product is unaltered by reordering its terms or factors.

## What do you mean by commutative?

Mathematics. (of a binary operation) having the property that one term operating on a second is equal to the second operating on the first, as a × b = b × a. having reference to this property: commutative law for multiplication.

## What is the difference between associative and commutative property?

For that reason, it is important to understand the difference between the two. The commutative property concerns the order of certain mathematical operations. … The associative property, on the other hand, concerns the grouping of elements in an operation. This can be shown by the equation (a + b) + c = a + (b + c).

## What is an example of commutative property of multiplication?

Commutative property of multiplication: Changing the order of factors does not change the product. For example, 4 × 3 = 3 × 4 4 \times 3 = 3 \times 4 4×3=3×44, times, 3, equals, 3, times, 4.

## Why is the commutative property of addition important?

The Commutative Property is a great strategy to use when adding multi-digit numbers. When I taught first grade, I taught counting up as an addition and subtraction strategy. But if students know that they can switch the order of the addends and start adding with the greater number FIRST, it makes counting up easier.

## What is an example of commutative property?

Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4. Associative property of addition: Changing the grouping of addends does not change the sum.