Operational Properties

Question 1

Commutative Property

Answer 1

An operation is commutative if changing the order of the values involved does not change the outcome.

Example:
2 + 3 + 7 = 3 + 7 + 2
2 × 3 = 3 × 2

Question 2

Associative Property

Answer 2

If the values in an expression can be regrouped, but will yield the same outcome as with the original grouping, it is said to be associative.

Example:
(2 + 3) + 7 equals 2 + (3 + 7)
(3 × 5) × 4 equals 3 × (5 × 4)

Question 3

Distributive Property

Answer 3

creates the option to multiply a factor by a sum by multiplying the factor with each term of that sum separately, and then finding the sum afterward.

Example:
4 × 12
= 4 × (10+2)
= (4×10) + (4×2)
= 40 + 8
= 48

Question 4

Commutative property hint

Answer 4

Order doesn’t matter.

a + b + c = a + c + b

“they can commute around”

Question 5

associative property hint

Answer 5

Grouping symbols don’t matter.

(a + b) + c = a + (b + c)

“they can associate with whomever they choose”

Question 6

Distributive Property hint

Answer 6

Multiplying a factor by the terms inside a quantity.

a(b + c) = ab + ac

“they can distribute themselves”