Properties of operations (commutative, associative, distributive) let you rewrite expressions without changing their value. Equalities that hold for every allowed value of the variables are called identities.
An identity is true for every allowed value of the variables
Properties of operations help simplify expressions
Check a transformation: the value must stay the same
Property cards
Read each formula and its explanation.
Commutative property of addition
a+b=b+a
Changing places of addends does not change the sum.
Commutative property of multiplication
a⋅b=b⋅a
Changing places of factors does not change the product.
Associative property of addition
(a+b)+c=a+(b+c)
Different grouping gives the same sum.
Associative property of multiplication
(a⋅b)⋅c=a⋅(b⋅c)
Different grouping gives the same product.
Distributive property
a⋅(b+c)=a⋅b+a⋅c
Multiplication distributes over addition.
Quiz on identities
Decide whether the equality is an identity.
Is this true? (−3)⋅5=5⋅(−3)
Reminder
| Property | Formula |
|---|---|
| Commutative (addition) | a+b=b+a |
| Associative (multiplication) | (ab)c=a(bc) |
| Distributive | a(b+c)=ab+ac |
✅If after a transformation the expression keeps the same value for all values of the variables, that is an identical transformation.