# What are the Properties of Addition and Multiplication?

## Properties Of Addition and Multiplication

There are several properties that work in both multiplication and addition. They vary slightly i how they work but the main concepts remain the same. These properties help us understand number sense and how numbers work.

## Commutative Property

## Commutative Property

The Commutative Property states that the order which numbers or terms are added or multiplied does not affect the outcome or answer

key word **ORDER**

Commutative means Order

This property is true for both addition and multiplication. The order in which you multiply doesn't change the answer and the order in which you add does not change the answer.

You can add numbers in any order and still arrive at the same answer. Why do we have this property? It makes adding multiple numbers easier. If I had to add 9 + 7 + 1 +3, I would think 9+1 is 10 and 7+ 3 is 10 so the answer is twenty. I could quickly do this problem in my head versus the slower method of adding them in order. It is all about making your brain work quicker and easier.

## Associative Property

## Associative Property

The Associative Property of addition and multiplication states that the grouping of numbers or terms does not affect the outcome or answer

key word **GROUPINGS**

Associative Property means grouping

When we are thinking about the word grouping picture in our head parenthesis or brackets. These two items group things together.

## Identity Property

## Identity Property

The identity property varies slightly for multiplication and addition.

The identity property want to find the same number that you started with.

**Addition**

In addition the only way to end up with the exact same number is to add zero

So any number plus zero equals itself.

**Multiplication**

The identity property of multiplication is just as it sounds.

Identity equals self.

Any number times 1 equals itself, so therefore the property states that any number multiplied by 1 is it's identity.

## Zero Property

## Zero Property of Mulitplication

The zero property of multiplication states that any number multiplied by zero equals zero.

## How to Remember those Tricky Laws of Arithmetic

Commutative = Order

Associative = Groupings

Identity = how does the answer equal itself

Remember none of these properties work for division or subtraction. These two operations order does matter and it does affect the answer.

## Which Property Quiz

For each question, choose the best answer. The answer key is below.

**1 x 2 = 2**- Commutative
- Associative
- Identity
- Zero

**3 x (2 x 4) = (3 x 2) x 4**- Commutative
- Associative
- Identity
- Zero

**3 x 0 = 0**- Commutative
- Associative
- Identity
- Zero

**3 + 5 = 5+ 2**- Commutative
- Associative
- Identity
- Zero

**4 + (2 + 3) = 4 + (3+ 2)**- Commutative
- Associative
- Identity
- Zero

### Answer Key

- Identity
- Associative
- Zero
- Commutative
- Commutative

## Why do these properies exist?

These properties exist to makes math easier in some respects but also because they apply to algebra and when we get to algebra these rules are going to help us simplify and solve equations. So a little know how now will take us a long way when we get to more difficult math problems. My students often ask me why they have to learn such "simple" concepts at times, I always tell them because it will get harder and if we don't learn the correct way now then we will be lost in the future.

**© 2012 kthix10**

## Comments

**aj** on December 01, 2016:

whats it called when 1 x n = n. what property is it

**Marderius** from Alabama on January 18, 2013:

Excellent information and easily put