Lesson 3: properties of numbers
Words to Know
Multiplicative Property of Zero: a x 0 = 0.
Reflexive Property: a = a.
Symmetric Property: if a = b, then b = a. Example: if 9 = 4 + 5, then 4 + 5 = 9.
Transitive Property: if a = b and b = c, then a = c. Example: If 6 + 9 = 3 + 12 and 3 + 12 = 15,
then 6 + 9 = 15.
Substitution Property: if a = b, then a can be replaced for b. Example: If x = 6, then 4x = 24.
More Properties:
Reflexive Property: a = a.
Symmetric Property: if a = b, then b = a. Example: if 9 = 4 + 5, then 4 + 5 = 9.
Transitive Property: if a = b and b = c, then a = c. Example: If 6 + 9 = 3 + 12 and 3 + 12 = 15,
then 6 + 9 = 15.
Substitution Property: if a = b, then a can be replaced for b. Example: If x = 6, then 4x = 24.
More Properties:
Examples
1. Evaluate using Properties
a) Name the property used in EACH step:
2 x 3 + (4 x 2 - 8)
= 2 x 3 + (8 - 8)
= 2 x 3 + 0
= 6 + 0
= 6
a) Name the property used in EACH step:
2 x 3 + (4 x 2 - 8)
= 2 x 3 + (8 - 8)
= 2 x 3 + 0
= 6 + 0
= 6
b) Name the property used in each step:
7 x 1/7 + 6(15 ÷ 3 - 5)
= 7 x 1/7 + 6(0)
= 1 + 6(0)
= 1 + 0
= 1
7 x 1/7 + 6(15 ÷ 3 - 5)
= 7 x 1/7 + 6(0)
= 1 + 6(0)
= 1 + 0
= 1
2. Apply Properties of Numbers
a) Rafael is buying furniture for his first apartment. He buys a couch for $300, lamps for $30.50, a rug for $25.50, and a table for $50. Find the total cost of these items and name the properties used in each step.
a) Rafael is buying furniture for his first apartment. He buys a couch for $300, lamps for $30.50, a rug for $25.50, and a table for $50. Find the total cost of these items and name the properties used in each step.
3. Use Multiplication Properties
Evaluate and name the property used in each step:
a) 2.9 x 4 x 10
Evaluate and name the property used in each step:
a) 2.9 x 4 x 10
b) 5/3 x 25 x 3 x 2
Tips
Look for pairs of numbers when using the commutative and associative properties to make your calculations easier.
Think of a word that helps you remember each property - you already know how to use them!!
Think of a word that helps you remember each property - you already know how to use them!!
Extra Examples
Click here for additional examples and self check quizzes