Basic Operations
Learn order of operations and number properties
Start with the basics and progress through 9 lessons. Each lesson builds on the previous one.
0 of 9 lessons done
Test Your Knowledge
10 questions, new mix each time (from 145)
In This Topic (9 lessons)
Order of Operations (PEMDAS)
Learn the correct order to solve math problems with multiple operations using PEMDAS.
Mental Math: Subtraction Strategies
Learn powerful mental strategies to subtract numbers quickly and accurately without a calculator.
Properties of Numbers
Learn the fundamental rules that govern how numbers behave in arithmetic operations.
Mental Math: Addition Strategies
Learn powerful mental math strategies to add numbers quickly in your head without a calculator.
Long Division
Master the step-by-step process of dividing large numbers using the long division method.
Mental Math: Multiplication Strategies
Master powerful mental math techniques to multiply numbers quickly without a calculator.
Estimation Strategies
Learn how to estimate answers quickly using rounding, front-end estimation, and compatible numbers.
Compatible Numbers
Learn how to use compatible numbers to make mental math faster and easier.
Rounding Whole Numbers
Learn how to round whole numbers to the nearest ten, hundred, or thousand.
The four basic operations—addition, subtraction, multiplication, and division—are the foundation of all mathematics. These operations are used in every area of math and daily life, from calculating totals to splitting bills to measuring ingredients. Mastering these operations with confidence is essential for mathematical success.
In this topic, you will build fluency with all four operations across whole numbers. You will learn the properties that make calculations easier: commutative, associative, and distributive properties. Order of operations (PEMDAS/BODMAS) ensures everyone gets the same answer for complex expressions.
Our lessons emphasize both mental math strategies and written procedures. You will develop number sense that helps you estimate answers, check reasonableness, and solve problems efficiently. These foundational skills support all future mathematics learning.
What You'll Learn
- Add and subtract multi-digit numbers fluently
- Multiply multi-digit numbers using standard algorithm
- Divide with single and multi-digit divisors
- Apply order of operations correctly (PEMDAS)
- Use properties of operations to simplify calculations
- Estimate answers using rounding and mental math
- Solve real-world problems using all four operations
Frequently Asked Questions
Why is order of operations important?
Without agreed-upon rules, the same expression could give different answers. PEMDAS ensures everyone evaluates 2 + 3 × 4 as 14, not 20. It is a universal mathematical convention.
What are the properties of operations?
Commutative (order does not matter for addition/multiplication), Associative (grouping does not matter), and Distributive (multiplication distributes over addition). These properties help simplify calculations.
How can I check if my answer is reasonable?
Estimate first using rounded numbers. If your exact answer is far from your estimate, check your work. For division, multiply to verify: if 144 ÷ 12 = 12, then 12 × 12 should equal 144.