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Chapter 1: Problem 65

Evaluate each of the following expressions, if possible. $$\frac{9-5}{5-5}$$

Short Answer

Expert verified
The expression is undefined because the denominator is zero.

Step by step solution

01

Evaluate the Numerator

Evaluate the expression in the numerator. The numerator is given by \(9 - 5\). Calculate this difference: \[9 - 5 = 4\].
02

Evaluate the Denominator

Evaluate the expression in the denominator. The denominator is given by \(5 - 5\). Calculate this difference: \[5 - 5 = 0\].
03

Determine if Division is Possible

Check if the denominator is zero. If the denominator is zero, division by zero is undefined. Since the denominator is zero in this case, \(\frac{4}{0}\) is undefined.

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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 part of a fraction.
In our example, the fraction is given as \(\frac{9-5}{5-5}\).
The numerator here is the expression \(\text{9 - 5}\).
You first need to evaluate this expression to get a simpler value.
After calculating, \(\text{9 - 5}\) simplifies to \(\text{4}\).

This simplification helps in understanding how the fraction behaves.
In any fraction, having a clear numerator is crucial for carrying out division or further simplifying the expression.
Denominator
The denominator is the bottom part of a fraction, located beneath the dividing line.
In the given example \(\frac{9-5}{5-5}\), the denominator is \(\text{5 - 5}\).
Just like with the numerator, you need to simplify this expression first.
When we do the math, \(\text{5 - 5}\) equals \(\text{0}\).
This result tells us something very special about our fraction.
The denominator has a significant role because it determines the possibility of performing the division.
A zero in the denominator will lead to an undefined division, which we will discuss in detail next.
Undefined Division
Undefined division happens when the denominator in a fraction equals zero.
In simpler terms, you can't divide a number by zero.
This is crucial in mathematics because division by zero leads to results that don't make sense or are not allowed.
In our example \(\frac{4}{0}\), the denominator is zero.
This means the fraction is undefined.

Whenever you encounter a zero in the denominator, you should immediately recognize that the division is undefined.
This concept helps to avoid mistakes in calculations and understanding why certain mathematical operations are not possible.

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Most popular questions from this chapter

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