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Simplifying expressions involves making an algebraic expression easier to work with by combining like terms and applying properties of operations. Here, we focus on using the distributive property.
In our example, we start with \( \frac{1}{3}(u+9) \). Using the distributive property, we multiply \( \frac{1}{3} \) with both the terms inside the parentheses. This means:
\[ \frac{1}{3} \times u + \frac{1}{3} \times 9 \]
This step by step method helps break down the problem into simpler parts. Once each multiplication is done, we combine the results, giving us:
\[ \frac{1}{3}u + 3 \]
Remember, the main goal in simplifying expressions is to make them more manageable, which can be very useful in solving equations or in further mathematical operations.

Prealgebra is the foundation of all algebra concepts. It includes basic arithmetic operations and introduces variables and simple equations. This prepares students for more advanced topics.
In prealgebra, one of the early skills learned is how to handle expressions like \( \frac{1}{3}(u+9) \). Here, we use a basic but crucial math principle—the distributive property. By understanding and applying this property, students build a solid base for tackling more complex algebraic expressions later.
Before diving into algebra, mastering prealgebra ensures students are comfortable with numbers, operations, and basic properties like distributivity. This comfort is crucial for their success as they progress in mathematics.

Mathematical operations, such as addition, subtraction, multiplication, and division, are fundamental actions we perform on numbers. In algebra, we extend these operations to variables.
Let's focus on multiplication in this exercise. The distributive property states that multiplying a single term and a sum inside parentheses works like this:
\[ a(b + c) = ab + ac \]
In our example, we have:
\[ \frac{1}{3}(u+9) \]
This means we multiply \( \frac{1}{3} \) with both \( u \) and \( 9 \), illustrated as:
\[ \frac{1}{3} \times u + \frac{1}{3} \times 9 \]
Understanding these operations and properties is essential because they form the building blocks of more complicated maths.