Properties of addition

key notes :

🎇 Properties of Addition

Commutative Property

Definition: Changing the order of the numbers being added does not change the sum.

  • Formula: a+b=b+a
  • Example: 4+9=9+4 → Both equal 13.

Associative Property

Definition: Changing the grouping of numbers being added does not change the sum.

  • Formula: (a+b)+c=a+(b+c)
  • Example: (2+3)+4=2+(3+4) → Both equal 9.

Identity Property (Additive Identity)

Definition: The sum of any number and zero is the number itself.

  • Formula: a+0=a
  • Example: 7+0=7

Distributive Property(Related to Addition and Multiplication)

Definition: Multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products.

  • Formula: a×(b+c)=(a×b)+(a×c)

Example: 3×(2+4)=(3×2)+(3×4) → Both equal 18.

🧨Properties of Subtraction

Non-Commutative Property

Definition: The order of numbers in subtraction matters; changing the order changes the result.

  • Example: 9−5 is not the same as 5−9.
  • Explanation: 9−5=4, but 5−9 would result in −4, which is different.

Non-Associative Property

Definition: Changing the grouping of numbers in subtraction will change the result.

  • Example: (10−5)−2 is not the same as 10−(5−2).
  • Explanation: (10−5)−2=3, while 10−(5−2)=7.

Identity Property of Subtraction

Definition: Subtracting zero from any number leaves the number unchanged.

  • Formula: a−0=a
  • Example: 8−0=8

Subtraction as the Inverse of Addition

Definition: Subtraction is the opposite of addition. If you add a number and then subtract the same number, you return to the original number.

  • Formula: a+b−b=a
  • Example: 15+5−5=15

Commutative property:

 h + j = j + h
You can add numbers in any order and get the same sum.

Ex: 2 + 6 = 6 + 2

Associative property:

(f + g) + h = f + (g + h)
You can group the addends with brackets and get the same sum.

Ex: 6 + (9 + 7) = (6 + 9) + 7

Identity property:

 t = 0 + t
Adding zero does not change a number.

Ex : 2 = 2 + 0

Learn with an example

🎯 Which property of addition is shown?

🎯 3 = 3 + 0

  • associative
  • commutative
  • identity
  • 3 = 3 + 0
  • This equation shows the identity property. Adding zero does not change the sum.

🎯 Which equation shows the associative property of addition?

  • 5 + 7 = 7 + 5
  • 5 + (3 + 7) = (5 + 3) + 7
  • 1 = 0 + 1
  • 3 = 3 + 0
  • 5 + (3 + 7) = (5 + 3) + 7
  • This equation shows the associative property. The grouping of the addends is changed.

🎯 Which property of addition is shown?

🎯 9 + 3 = 3 + 9

  • associative
  • commutative
  • identity
  • 9 + 3 = 3 + 9
  • This equation shows the commutative property. The order of the addends is changed.

Let’s practice!