Basic Arithmetic

Basic Arithmetic covers fundamental mathematical operations including addition, subtraction, multiplication, and division.

AdditionSubtractionMultiplicationDivision
Order of OperationsWord ProblemsProperties of OperationsInverse Operations
Shopping and Making ChangeCooking and MeasuringPlanning and Time Management
Estimation and Mental MathShowing Your Work and Double-CheckingBreaking Down Problems
AdditionSubtractionMultiplicationDivisionOrder of OperationsWord ProblemsProperties of Operat...Inverse OperationsShopping and Making ...Cooking and Measurin...Planning and Time Ma...Estimation and Menta...Showing Your Work an...Breaking Down Proble...
Advanced Topics

Properties of Operations

What Are Properties of Operations?

There are special rules in math that make calculations easier and faster! These are called properties.

Commutative Property

  • You can switch the numbers around when adding or multiplying, and the answer stays the same.
    • \( a + b = b + a \)
    • \( a \times b = b \times a \)

Associative Property

  • The way you group numbers doesn’t change the answer.
    • \( (a + b) + c = a + (b + c) \)
    • \( (a \times b) \times c = a \times (b \times c) \)

Identity Property

  • Adding zero or multiplying by one keeps the number the same.
    • \( a + 0 = a \)
    • \( a \times 1 = a \)

Why Properties Help

These rules make math easier and let you solve problems faster!

Examples

  • 4 + 5 = 5 + 4 (commutative property)

  • (2 × 3) × 4 = 2 × (3 × 4) (associative property)

In a Nutshell

Properties are rules that help you add and multiply numbers in any order or group.

Key Terms

Commutative
Changing the order of numbers doesn’t change the result.
Associative
Changing the grouping of numbers doesn’t change the result.
Identity
Adding zero or multiplying by one keeps the number the same.
Next
Inverse Operations