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Chapter 1: Problem 59

Evaluate. If an expression is undefined, say so. $$\frac{-3-5}{6-(-2)}$$

Short Answer

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Step by step solution

01

Identify the Numerator and Denominator

The given expression is \(\frac{-3-5}{6-(-2)}\). Identify the numerator as \(-3-5\) and the denominator as \(6-(-2)\).
02

Simplify the Numerator

Calculate the value of the numerator: \(-3-5 = -8\). So, the numerator simplifies to \(-8\).
03

Simplify the Denominator

Simplify the denominator: \(6-(-2)\) is the same as \(6+2\), which equals \(8\).
04

Combine Results and Simplify

Combine the simplified numerator and denominator: \(\frac{-8}{8}\). This simplifies to \(-1\).

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Key Concepts

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

Numerator
The numerator is the top number in a fraction. It represents how many parts we have out of the whole indicated by the denominator.
In the given exercise, the numerator is the expression \(-3-5\). When simplifying, we calculate it as follows:
\( -3-5 = -8 \)
So, our numerator simplifies to \(-8\).
Denominator
The denominator is the bottom number of a fraction. It shows the total number of equal parts into which the whole is divided.
In the given problem, the denominator is \(6-(-2)\). One common error is misinterpreting the subtraction of negative numbers. Instead of \(6-(-2)\), we can rewrite it as: \(6 + 2 \), which simplifies to \(8\).
Negative Numbers
Negative numbers are values less than zero. They have a minus sign in front of them.
When performing operations involving negative numbers, especially with addition and subtraction, it is crucial to apply the correct rules:
  • Subtracting a negative number is the same as adding its positive counterpart: \(a - (-b) = a + b\)
  • Adding two negative numbers gives a more negative number: \((-a) + (-b) = -(a + b)\)

For our numerator calculation: \(-3-5 = -8\)
Addition and Subtraction
Addition and subtraction are basic arithmetic operations. They are related in handling positive and negative values.
Here are some key points to remember:
  • Addition of two positive numbers or two negative numbers increases their magnitude
  • Subtraction means adding the opposite value

In our exercise, we handled two main operations:
  • Subtraction in numerator: \(-3-5 = -8\)
  • Addition in denominator: \(6-(-2) = 6 + 2 = 8\)

Finally, combining both simplified numerator and denominator to get: \(\frac{-8}{8} = -1 \)

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