Addition

Addition - a process of combining 2 or more numbers. Addition is made up of addends & sums.

Addends are the numbers being added

The sum is the result or the final answer we get after the process..

Five properties of addition

They govern the way numbers behave when added together: Clo sure, Commutative, Associative, Identity and Inverse. These properties make addition predictable and reliable, allowing us to solve even complex mathematical problems w/ confidence.

Closure Property of Addition

States that when you add 2 real numbers, the result is always a real number.

Example:

  if you add 4 and 3 (4+3), answer is 7, which is still a real number

This means that the sum of any 2 numbers in a set is still part of the same set.

Commutative Property of Addition

Tells us that the order in which we add numbers doesn't change the sum.,

Example:

   if you have 2 numbers, say 5 and 2, adding 5+2 gives the same results as adding 2+5.

This property makes addition flexible and easy to work with, especially when dealing w/ multiple numbers.

Associative Property of Addition

According to the Associative Property of Addition, when adding three or more numbers, the way the numbers are grouped doesn’t change the sum. So, if you’re adding 3 + (4 + 5), you’ll get the same result

as (3 + 4) + 5. This property allows us to rearrange numbers when adding, which can often make calculations easier.

Additive Identity Property of Addition

The Additive Identity Property of Addition states that if you add zero (0) to any number, the number stays the same. For example, if you add zero to 7 (7 + 0), the result is still 7. The number zero is called the “additive identity” because adding it doesn’t change the identity of the other number.

Additive Inverse of Addition

The Additive Inverse Property of Addition states that every number has an inverse that, when added to the original number, results in zero. For instance, the additive inverse of 6 is -6 because when you add them (6 + -6), the sum is zero. This property is vital in understanding concepts like subtraction and negative numbers.