# What is the Number of Properties? What are the different types of number properties?

There are four main types of number properties. These only apply when we’re adding and multiplying them together:

• Commutative
• Associative
• Distributive
• Identity

Each of these refers to a different rule for dealing with numbers. So let’s look at these words and how they can help us solve maths problems.

What is a Commutative Property?

When we talk about number properties being commutative within addition, this means that no matter which way around you add the numbers, the answer will always be the same. For example, 4+9 is the same as 9+4. Both will give you the solution of 13.

In multiplication, the same rule applies. So whether you do 5×4 or 4×5, you will always get 20 as the answer.

To describe this to your class, you could provide a real-life example of some activities you might do during the day. For example, if you complete some science homework and then watch TV, this will have the same outcome as watching TV and doing science homework. Both tasks will still be completed!

What is an Associative Property?

When we discuss associative properties in addition and multiplication, we’re talking about joining or combining numbers. This means that numbers can be grouped (or ‘associated’) in any order to get the same answer.

For example, if we have the problem of 6+5+8, that’ll give us an answer of 19. We could reach this by adding together 6+5 first to provide us with 11 and then adding 8. We could do 5+8 first to get 13 and then add 6. So no matter how we choose to do it, we’ll always reach 19.

When it comes to multiplication, you can do the same! For example, if you have a problem of (6×2)×3, this will give you 12×3=36. If you instead choose to solve it as (3×6)×2, you’ll get 18×2=36. No matter how you combine the numbers, you’ll always come to the same answer.

Associative law is beneficial when it comes to breaking up more complicated multiplication problems. For example:

16×8

2×8(×8) or 8×8(×2)

64×2=128

What is a Distributive Property?

Distributive properties in numbers involve multiplying a number by adding a group of numbers. Doing this, it’s equal to multiplying the number by every individual number within the group.

For example, you could have three boxes of eggs and three bags of apples, with eggs weighing 150 grams and apples weighing 500 grams.

If you wanted to find out the total weight, you could work out 3×150=450 and 3×500=1500 to give you an answer of 1950 grams. However, you could also calculate this as 3×(150+500) or 3×650=1950. Either method will provide you with the same solution.

Summarised, 3(150)+3(500) is equivalent to 3(150+500).

Learning these number properties will be particularly useful later in a child’s learning journey when introduced to algebra in secondary education.

What is an Identity Property?

This part of number properties will be the easiest for learners to grasp as it’s self-explanatory. In addition, this means that when we add zero to a number, it remains the same. For example, 7+0=7. It’s as simple as that!

In multiplication, it’s slightly different. With this property, when we multiply a number by one, we know that it will remain the same. An example of this is 5×1=5. In essence, when we only have one portion of a particular number, it is the same as that number.