Basic Operations

• Addition: The process of combining two or more numbers to find their total.
• Subtraction: The process of taking one number away from another.
• Multiplication: The process of repeated addition or combining equal groups.
• Division: The process of splitting a number into equal parts or groups.

Properties of Operations

• Commutative Property: Changing the order of the numbers does not change the result (e.g., a + b = b + a).
• Associative Property: Changing the grouping of the numbers does not change the result (e.g., (a + b) + c = a + (b + c)).
• Identity Property: The sum of any number and zero is the number itself (e.g., a + 0 = a).
• Distributive Property: Multiplying a number by the sum of two other numbers is the same as multiplying the number by each of the other numbers and then adding the results together (e.g., a * (b + c) = a * b + a * c).

Order of Operations

The order of operations is a set of rules that defines the sequence in which calculations should be performed. The acronym PEMDAS is often used to remember the order:

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Word Problems

Arithmetic is often used to solve real-world problems involving quantities, distances, times, and more. Word problems require you to translate the given information into mathematical expressions and equations, and then solve for the unknown quantity.

Practice

To master arithmetic, it's important to practice regularly. Use flashcards, online quizzes, and worksheets to work on your addition, subtraction, multiplication, and division skills. As you build confidence, challenge yourself with more complex problems and word exercises.