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Chapter 1: Problem 22

Use the properties of division to simplify the expression, if possible. \(\frac{0}{3}\)

Short Answer

Expert verified
The simplified form of \(\frac{0}{3}\) is 0.

Step by step solution

01

Identify the Numerator and Denominator

In the fraction \(\frac{0}{3}\), identify the numerator (the top part) and the denominator (the bottom part). Here, the numerator is 0 and the denominator is 3.
02

Apply the Property of Zero in Division

Recall that any number divided by a non-zero number is 0. Using this property, since the numerator is 0, \(\frac{0}{3} = 0\).
03

Simplify the Expression

Given that the numerator is 0, the simplified form of the expression \(\frac{0}{3}\) is simply 0.

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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. It tells you how many parts of the whole you have. In the fraction \(\frac{0}{3}\), the numerator is 0. This means there are 0 parts of the whole.
  • Think of a pizza: if you have 0 slices, that's your numerator!
  • In fractions, the numerator can be any integer (positive, negative, or zero).
Understanding the numerator helps you know the amount in comparison to the whole, defined by the denominator.
Denominator
The denominator is the bottom part of a fraction. It tells you how many equal parts the whole is divided into. In the fraction \(\frac{0}{3}\), the denominator is 3. This means the whole is divided into 3 equal parts.
  • Continuing with the pizza example: if a whole pizza is cut into 3 slices, 3 is your denominator.
  • The denominator helps you understand the size of each part.
Always remember, the denominator cannot be zero. Otherwise, the fraction is undefined.
Zero Property
The zero property of division is simple but very important. It states that any number divided by a non-zero number is 0. This is because you have nothing to share among the parts. In the example \(\frac{0}{3}\), 0 divided by 3 is 0.
  • If there are 0 pizzas to share between 3 friends, each friend gets 0 pizzas.
  • This property only works when the numerator is 0, and the denominator is not zero.
In summary, using the zero property allows us to easily simplify fractions like \(\frac{0}{3}\) to 0.

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