Stuck? Start here. Read the steps, try the problem, then check your answer.
I can…
I can use the commutative, associative, and identity properties to rewrite expressions.
Key words
Properties of Operations — Rules that let you reorder or regroup numbers without changing an expression's value.
Commutative Property — You can change the order and get the same answer.
Associative Property — You can change the grouping and get the same answer.
Identity Property — Adding 0 or multiplying by 1 keeps the same value.
Property — A rule that is always true in math.
Distributive Property — Multiplying a number by everything inside the parentheses: a(b + c) = ab + ac.
Equivalent expressions — Expressions that have the same value for every value of the variable.
Expand — Multiply out an expression to remove the parentheses.
Factor an expression — Pull a shared factor outside parentheses.
Steps
I have 3 guitarists, 5 drummers, and 2 keyboard players.
I can add them as 3 + 5 + 2, which gives 10.
The Commutative Property says order does not matter: 5 + 3 + 2 also gives 10.
The Associative Property says grouping does not matter: (3 + 5) + 2 = 3 + (5 + 2), both equal 10.
Try it
At the store you put 4 apples, 6 pears, and 3 bananas in a bag. You count them two ways: (4 + 6) + 3 = 4 + (6 + 3). Which property is shown?
Check your answer
Associative Property
The grouping (parentheses) changed but the numbers stayed in the same order, so this is the Associative Property of Addition. Both ways give 13 pieces of fruit.
Sentence starter
I know ___ because ___.
Goal: I can explain my reasoning using the words commutative property, associative property, and identity property.