Properties of Addition: Definition, Examples

Properties of Addition

Identity Property

Identity Property: The sum of zero and any other number is the number itself.

For example,

5 + 0 = 5

Example:1

There are 5 kids on a team. No other kid joined the team till the end of the game. How many kids were in the game?

As no one joined the game, this meant there was no change in the number of kids.

5 kids + 0 kids = 5 kids

Example: 2

A flock of 12 birds sat over the branch of a tree. No more birds joined them. How many birds are sitting on the branch of the tree?

As no bird joined the flock, the number of birds remains the same, i.e., 12.

This can be written in a mathematical expression as:

12 birds + 0 birds = 12 birds

Commutative Property:

When two numbers are added together, the order of addends does not affect the sum or result. For example, 8 + 4 = 4 + 8.

Example:

Exercise:

1. Prove that a + b = b + a, if a = 10 and b = 9.
2. Complete the addition

(i) 365 + 0 =?

(ii) 0 + 1350 =?

(iii) 1578 +? = 1578

(iv) ? + 1478 = 1478

3. Match the following

Column A	Column B
1. Commutative property	a. (a × b) × c = a × (b × c)
2. Associative Property	b. a (b + c) = ab + ac
3. Identity for multiplication	c. a + b = b + a
4. Distributive Property	d. a × 1 = a

4. What is the additive identity of x?

5. If a + 0 = -11, then what is the value of a?

6. Name the property indicated in the following

 5+0=0+5=5

7. A flower is hidden behind an integer which is at a position 7 less than the spot where the butterfly is placed. Can you find the integer?

8. Add the following

a)17 + 5 + 3 = (17 + 3) + 5

b) 7 + (3 + 4) = (7 + 3) + 4

9. What is the missing number?

5745 + (3856 + 7464) = (                 + 3856) + 7464

10. Fill in the blanks

(i) 64 + 53 = ? + 64

(ii) 365 + 427 = ? + 365

(iii)? + 261 = 261 + 170

(iv) 765 +? = 188 + 765

What We Have Learned:

• Understanding the Addition
• Addition properties
• Associative property
• Commutative property
• Additive identity

Concept Map: