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Chapter 1: Problem 591

Simplify. $$\frac{0}{9}$$

Short Answer

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Step by step solution

01

Identify the Numerator and Denominator

The given fraction is \(\frac{0}{9}\). Here, the numerator (the top part) is 0, and the denominator (the bottom part) is 9.
02

Understand the Property of Zero

Any fraction where the numerator is zero and the denominator is non-zero simplifies to zero. This is because zero divided by any non-zero number is zero.
03

Simplify the Fraction

Using the property identified, simplify \(\frac{0}{9}\) to 0.

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Key Concepts

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

Understanding the Numerator
A fraction is made up of two parts: the numerator and the denominator. In the fraction \(\frac{0}{9}\), the numerator is the top number, which is 0. The numerator represents how many parts of a whole you have.
For example, if you have \(\frac{3}{4}\) of a pizza, the numerator is 3, meaning you have 3 out of 4 parts of the pizza.
In our case, the numerator is 0, indicating that we have zero parts of something, no matter the denominator.
This sets the stage for the concept we'll discuss next: the property of zero.
Understanding the Denominator
The denominator in a fraction is the bottom number. In the fraction \(\frac{0}{9}\), the denominator is 9. The denominator shows into how many equal parts the whole is divided.
For example, if you have \(\frac{3}{4}\) of a pizza, the denominator is 4, meaning the pizza is divided into 4 pieces.
However, it's important to note that the denominator cannot be zero. If the denominator is zero, the fraction becomes undefined because division by zero is not possible.
In our example, the denominator is non-zero (9), which allows us to simplify the fraction using the property of zero.
Exploring the Property of Zero
The property of zero is a key concept in simplifying fractions. This property states that any fraction where the numerator is zero and the denominator is non-zero simplifies to zero.
Mathematically, this can be understood by noting that zero divided by any non-zero number is zero. So, \(\frac{0}{a} = 0\) for any non-zero number \a\.
In our case, since the numerator is 0 and the denominator is 9, we apply this property to conclude that \(\frac{0}{9}\) simplifies to 0.
Remembering this property makes simplifying certain fractions much easier, especially those with a zero numerator.

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