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Chapter 2: Problem 98

Perform the indicated operation. $$\frac{0}{-5}$$

Short Answer

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Step by step solution

01

Understanding the Numerator and Denominator

Recognize the components of the fraction. The numerator of the fraction is 0 and the denominator is -5.
02

Recognize the Special Case

Recall that any number divided by a non-zero number is 0. Therefore, 0 divided by -5 is 0.
03

Simplify the Expression

Apply the rule from the previous step: \( \frac{0}{-5} = 0 \).

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Key Concepts

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

Numerator and Denominator
In dealing with fractions, understanding the numerator and denominator is essential. The numerator is the top number in a fraction. It tells us how many parts of a whole we have.
The denominator, on the other hand, is the bottom number. It tells us into how many parts the whole is divided.

For example, in the fraction \(\frac{0}{-5}\), the numerator is **0** and the denominator is **-5**. This fraction signifies zero parts out of five possible parts.
Recognizing these components is crucial for accurately performing operations on fractions.
Special Case in Division
There are special rules in math for dividing by zero and dividing zero by any number. One such rule is: Any number divided by another non-zero number is zero. This means if our numerator is 0 and the denominator is any non-zero number, the result is always 0.
For example, \(\frac{0}{-5}\) translates to zero divided by negative five. Since -5 is not zero, according to the rule, this fraction evaluates to 0.

This is why \(\frac{0}{-5} = 0\). Understanding and applying these special cases help avoid mistakes in fraction operations.
Simplification of Fractions
Simplifying fractions means reducing them to their simplest form. This involves dividing both the numerator and denominator by their greatest common divisor.
However, for fractions where the numerator is 0, simplification is straightforward. As long as the denominator is not zero, the fraction simplifies directly to 0.

In our example, \(\frac{0}{-5}\) does not need any further steps because \(\frac{0}{-5} = 0\). Simplifying fractions correctly is a fundamental skill for mastering fraction operations.

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Most popular questions from this chapter

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