Math · Addition

Properties of Addition
Commutative, Associative & Identity with Examples

Learn the 5 properties of addition with examples: commutative, associative, identity, inverse and distributive. For elementary and middle school with exercises.

⚡ RESPUESTA RÁPIDA

The 5 properties of addition: 1) Commutative: a+b=b+a. 2) Associative: (a+b)+c=a+(b+c). 3) Identity: a+0=a. 4) Inverse: a+(-a)=0. 5) Distributive: a×(b+c)=ab+ac.

The 5 Properties — With Examples

Commutative Property: a + b = b + a

Order doesn't matter. 3+5 = 5+3 = 8. Useful for mental math.

Associative Property: (a+b)+c = a+(b+c)

Grouping doesn't matter. (2+8)+5 = 2+(8+5) = 15. Group numbers that make 10.

Identity Property: a + 0 = a

Adding zero doesn't change the number. 7+0=7. Zero is the additive identity.

Inverse Property: a + (-a) = 0

Every number plus its opposite equals zero. 5+(-5)=0.

Distributive Property: a×(b+c) = ab+ac

3×(4+5) = 3×4+3×5 = 27. Connects addition and multiplication.

Identify the Property — 8 Exercises

7+3=3+7
Commutative
(2+8)+5=2+(8+5)
Associative
15+0=15
Identity
(-8)+8=0
Inverse
4×(3+7)=12+28
Distributive
a+b=b+a
Commutative
(x+y)+z=x+(y+z)
Associative
n+0=n
Identity

These properties also apply in algebra. Visit propiedades de la suma for the Spanish version.

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