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Addition is one of the basic operations in mathematics that involves combining two or more numbers to get a total sum. It's like putting things together. For example, if you have 4 apples and you add 3 more, you end up with 7 apples. Addition is written using the plus sign "+".
When you perform addition, it doesn't matter how you group the numbers if you are adding more than two numbers together. This principle is called the associative property of addition.
Here are some simple properties of addition:

• Commutative Property: You can change the order: 2 + 3 = 3 + 2.
• Associative Property: You can change the grouping: (2 + 3) + 4 = 2 + (3 + 4).
• Identity Property: Adding zero doesn't change the number: 5 + 0 = 5.

Prealgebra is an essential foundation for understanding more advanced math concepts. It includes basic arithmetic operations like addition, subtraction, multiplication, and division. But it also introduces variables and expressions, opening the world to algebra.
In prealgebra, you often deal with simple expressions involving numbers and variables like \(4 + n\). The goal is to understand how these expressions can be manipulated using various mathematical properties, such as the associative property.
The purpose of prealgebra is to prepare students for algebra, encouraging logical thinking and problem-solving abilities. Even when dealing with simple expressions, it teaches students how to approach mathematics in a structured way. This stage is crucial as it builds confidence in dealing with numbers in any form.

Mathematical expressions are combinations of numbers, variables, and operators like addition, subtraction, multiplication, and division, all put together to represent a value or concept. They are fundamental in both prealgebra and algebra.
Expressions can be simple, like 4 + 5, or more complex, involving multiple terms and variables such as \((4 + n) + 1\). Understanding how to manipulate these expressions is key to solving problems.
Using properties such as the associative property of addition allows us to rearrange and group parts of expressions differently without changing their value. This flexibility is particularly useful when simplifying expressions or making computations easier to handle.
Studying expressions helps students understand and communicate mathematical ideas effectively, laying the groundwork for more complex mathematical concepts in higher-level math.