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.

Real-World Applications

Commutative — Grocery Shopping

Adding $12 + $8 or $8 + $12 gives the same total of $20. Order of purchase doesn't change the total.

Associative — Mental Math Trick

47+38+62: regroup as (47+53)+38=100+38=138 instead of 47+38+62 in order.

Identity — Bank Balance

Depositing $0 to a $500 account: $500+$0=$500. Balance unchanged.

15 Practice Exercises

8+5=5+?
8 (comm.)
(3+7)+4=3+(7+?)
4 (assoc.)
15+0
15 (identity)
(-9)+9
0 (inverse)
a+b=b+?
a
(x+y)+z=x+(y+?)
z
n+0
n
(-15)+15
0
47+53+28=100+?
28=128
25+87+75=(25+75)+?
87=187
a+0=?
a
n+(-n)=?
0
b+c=c+?
b
0+x
x
(1+2)+3=1+(2+?)
3

Preguntas Frecuentes

Do these properties work with decimals and fractions?

Yes, all properties of addition apply to any real number including decimals, fractions and negative numbers.

Is subtraction commutative?

No. 10−3=7 but 3−10=−7. Subtraction is NOT commutative. Only addition and multiplication have the commutative property.

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