91Ó°ÊÓ

The substitution method is a mathematical technique where we replace a variable with a given number or expression. This method helps us simplify expressions or solve equations. In prealgebra, substitution is a fundamental concept. It allows us to verify or solve expressions for specific variable values.
In our exercise, we begin with the expression \(-5a\). Here, \(a\) is a placeholder for a number. When we're given a specific value, like \(a = -4\), we use substitution to replace \(a\) in the expression. This process is straightforward:

• Identify the variable in the expression
• Replace the variable with the provided number

Substituting in our given expression \(-5a\) with \(a = -4\), changes the expression to \(-5(-4)\). This shift is the key first step before any further mathematical operations.

Multiplication is a basic operation where we take a number and repeatedly add it to itself. When multiplying integers, the process involves a few specific rules, especially concerning positive and negative numbers.
In this case, let's explore integer multiplication:

• When two positive numbers are multiplied, the result is positive.
• When two negative numbers are multiplied, the result is also positive.
• However, if one number is negative and the other is positive, the result is negative.

In our exercise, after substituting \(a = -4\) into \(-5a\), we need to calculate \(-5 \times -4\). Both numbers are negative, so following our rules, the result becomes positive, which is \(20\). Understanding these multiplication rules is crucial for avoiding mistakes and correctly interpreting results.

Negative numbers are values less than zero and are represented with a minus sign (\(-\)). They describe quantities that are below zero, which is essential in many real-world contexts, such as temperatures or debts.
When working with negative numbers in math, it's important to remember:

• Adding a negative is like subtracting a positive.
• Subtracting a negative is the same as adding a positive.
• Multiplying or dividing two negatives results in a positive outcome.

In our exercise, understanding negative numbers helped us evaluate \(-5a\) with \(a = -4\). Knowing that multiplying two negative integers results in a positive value was key to realizing that \(-5 \times -4 = 20\). Grasping these concepts makes working with negative numbers much easier, especially when they appear in multiplication or division operations.