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Chapter 1: Problem 63

Evaluate each of the following expressions, if possible. $$\frac{8(-6)-2}{-3-2}$$

Short Answer

Expert verified
The value of the expression is 10.

Step by step solution

01

Simplify the numerator

First, calculate the expression in the numerator: \(8(-6) - 2\). Multiply 8 by -6 to get -48. Then subtract 2: \(-48 - 2 = -50\). So the numerator simplifies to \(-50\).
02

Simplify the denominator

Next, calculate the expression in the denominator: \(-3 - 2\). Subtract 2 from -3: \(-3 - 2 = -5\). So the denominator simplifies to \(-5\).
03

Divide the simplified numerator by the simplified denominator

Now divide the simplified numerator by the simplified denominator: \( \frac{-50}{-5} = 10 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Numerator Simplification
When we evaluate expressions, one of the key steps is simplifying the numerator. The numerator is the top part of a fraction. Let's start by looking at the expression in the numerator: \(8(-6) - 2\).

Begin by addressing the multiplication first: Multiply 8 by -6, which results in -48. Next, we subtract 2 from -48.
This gives us: \(-48 - 2 = -50\).

The numerator is now simpler and has been reduced to \(-50\). Breaking the expression into smaller, manageable steps like this helps to avoid errors and makes the problem easier to solve.
Denominator Simplification
Next, simplify the denominator. The denominator is the bottom part of a fraction. For our problem, the denominator is \(-3 - 2\).

To simplify, perform the subtraction: Subtract 2 from -3. This results in \(-3 - 2 = -5\).

Now, the denominator is reduced to \(-5\). Always perform operations in an orderly manner and remember the rules for dealing with negative numbers. Making sure the denominator is simplified accurately is crucial for the final division step.
Integer Division
After both the numerator and the denominator are simplified, the next step is integer division. In our example, we have the fraction \(\frac{-50}{-5}\).

Integer division means dividing one integer by another. Here, we divide -50 by -5. When you divide two negative numbers, the result is positive: \(\frac{-50}{-5} = 10\).

It's essential to understand how to handle signs when dividing. Remember:
  • A positive divided by a positive equals a positive.
  • A negative divided by a negative equals a positive.
  • A positive divided by a negative (or vice versa) equals a negative.
Putting it all together, our simplified expression evaluates to 10.

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