Algebraic Properties Example
Identity Property of Addition (Additive Identity)
Any number when added to 0 is itself.
Identity Property of Multiplication (Multiplicative Identity)
Any number multiplied by 1 is itself.
Multiplicative Property of Zero
Any number multiplied by zero is zero.
Commutative Property of Addition
The order in which you add does not change the sum.
Commutative Property of Multiplication
The order in which you multiply does not change the product.
Associative Property of Addition
The order in which you group numbers does not change the sum.
Associative Property of Multiplication
The order in which you group numbers does not change the product.
Symmetric Property
If one number is equal to a second numbers, then the second number is equal to the first.
Substitution Property
If a = b then a can be substituted into an equation for b.
Distributive Property
The product of a number and a sum or difference is the same as the sum or difference of the
products of the number and each element of the sum or difference.
Additive Inverse
The sum of a number and its inverse is zero.
Multiplicative Inverse
The product of a number and its inverse is one.
Addition Property of Equality
Adding the same number to each side of an equation produces an equivalent equation.
Subtraction property of Equality
Subtracting the same number from each side of an equation produces an equivalent equation.
Multiplication Property of Equality
Multiplying each side of the equation by the same number produces equivalent equations.
Division Property of Equality
Dividing each side of the equation by the same number produces equivalent equations.
Exponential Property of Equality
Raising each side of the equation by the same number produces equivalent equations.
Name the property demonstrated by each statement.
1.
2.
3.
Answer:_______________
Answer: __________________
Answer:_____________________
Use the stated property to write an equivalent expression
4. Commutative Property of Addition: 5. Associative Property of
Multiplication:
6. Identity Property of Addition: