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The substitution method is a crucial technique in mathematics that helps simplify expressions or solve equations by substituting variables with specific values. For instance, if you encounter an expression like \( \frac{8yz}{15} \), the first step is to identify and replace the variables with the given values. Here, we're given \( y = 5 \) and \( z = 3 \). So, the expression becomes \( \frac{8 \times 5 \times 3}{15} \).

This method is like changing letters in a recipe with their corresponding ingredients. It makes the expressions easier to tackle and compute. Always remember to check the values you are substituting to avoid errors. By systematically replacing each variable with its designated number, complex expressions become a sequence of easier calculations.

Simplifying expressions means rewriting them in a simpler or more manageable form without changing their value. In our example, once substitution is done, the next step is simplifying the expression \( \frac{8 \times 5 \times 3}{15} \). This involves multiplying the terms in the numerator first.

Start with the multiplication:

• Calculate \( 8 \times 5 = 40 \).
• Then, multiply \( 40 \times 3 = 120 \).

So, the expression simplifies to \( \frac{120}{15} \).

Simplification doesn't stop at multiplication; it ensures that the expression is reduced to its simplest form. Think of it as tidying up a room; you're organizing everything to make it look neat and easy to understand. Finally, division will complete the simplification, making our calculated value straightforward to read.

Basic arithmetic operations form the foundation of all math problems. They include addition, subtraction, multiplication, and division. In this exercise, all operations but addition and subtraction are featured.

We already multiplied to simplify the expression, resulting in \( \frac{120}{15} \). Now, it's time for division.

• To divide, simply calculate \( 120 \div 15 \), which results in \( 8 \).

This arithmetic operation provides the final answer. Division, just like multiplication, is essential not only in simplifying expressions but also in giving the results in their simplest form.

These basic operations are the building blocks of math, allowing you to break down problems of any size or complexity into smaller, manageable parts. Mastering these is crucial for tackling math exercises confidently.