Math - Number Properties

Number properties refer to rules that you can apply to real numbers in mathematical operations.

Commutative Property

$a+b=b+a$
$a*b=b*a$

The commutative property applies in:

• Addition: Changing the order of the numbers does not affect the sum.
  • Example: $3+5=5+3$
  • Example: $7+1=1+7$
• Multiplication: Changing the order of the numbers does not affect the product.
  • Example: $2*3=3*2$
  • Example: $6*7=7*6$

Associative Property

$(a+b)+c=(a+c)+b$
$(a*b)*c=(a*c)*b$

The associative property applies in:

• Addition: Changing the grouping of addends does not affect the sum.
  • $(8+1)+3=(8+3)+1$
  • $(9+2)+7=(7+9)+2$
• Multiplication: Changing the grouping of factors does not affect the product.
  • $(8*9)*10=(8*10)*9$
  • $(2*7)*5=(5*7)*2$

Distributive Property

$a(b+c)=(a*b)+(a*c)$

The distributive property connects addition/subtraction and multiplication by “distributing” multiplication over terms inside parentheses.

Examples

• $3(2+5)=(3*2)+(3*5)$
• $3(2+5)=(3*2)+(3*5)$