Problem 99 - Prealgebra and Introductory Algebra

Question

Evaluate the expression for the given values of the variables. $$-a \div b, \text { for } a=-36 \text { and } b=-4$$

Step-by-Step Solution

Answer

The result of evaluating the given expression with the given values of variables is -9.

Step 1 Identify variables

In the presented expression, \(-a\div b\), the given variables are \(a = -36\) and \(b = -4\).

Step 2 Substitute values

Substitute the given values into the expression. This implies that -a will be --36 which results to 36 and b will be -4.

Step 3 Evaluate expression

The operation in the expression is division. We divide 36 by -4 to find -9.

Key Concepts

Understanding Negative Numbers

Negative numbers can sometimes be tricky, but they're just numbers with a minus sign. They represent values less than zero. For example,

• Think of temperatures: below zero degrees are negative.
• A bank overdraft means negative balance.

When we have two negative numbers and multiply or divide them, we get a positive number. This happens because the negatives cancel each other out.
For instance,

• Multiplying i.e., a negative by a negative gives us a positive result: (-5) × (-3) = 15.
• Dividing i.e., negative by negative also yields a positive result.

You can think of the negative sign as a direction change. Changing direction twice brings you back to the original direction. Being aware of these rules makes working with negative numbers much easier and less confusing.

Substituting Values into Expressions

Substituting values means replacing variables with their actual numbers. It's like a recipe that needs a specific ingredient. In algebra, when we put in the given numbers for variables, we create something we can calculate.
For the expression a = -36 and b = -4, we substitute these into -a and b. Notice that -a means the opposite of a.

• Therefore, -a becomes --36, which simplifies to 36, since double negatives make a positive.
• b keeps its negative sign as -4.

Substituting helps simplify expressions and prepare them for the next step: evaluation. Understanding this step ensures clarity and prevents errors.

Evaluating Expressions

Evaluating is all about computation. It's taking substituted numbers and performing the operations. With our example: -36 divided by -4 becomes 36 divided by -4 due to substitution.

• Simply divide 36 by 4.
• Remember, dividing by a negative flips the sign to negative.

The result here is -9. This step is essential in solving algebraic expressions and finding exact values. It's crucial to follow the order of operations and pay attention to signs. Practice makes evaluating expressions straightforward and less intimidating.