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Chapter 4: Problem 23

Simplify if possible. $$\frac{0}{-3}$$

Short Answer

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Step by step solution

01

Identify the Numerator and Denominator

The given expression is \(\frac{0}{-3}\). Here, the numerator is 0 and the denominator is -3.
02

Understand the Property of Zero in Division

According to mathematical principles, any number divided by a non-zero number equals zero.
03

Perform the Simplification

Using the property from the previous step, simplify \(\frac{0}{-3}\) to 0.

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Key Concepts

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

Division
Division is a fundamental mathematical operation. It involves splitting a number (the dividend) into equal parts. The number you divide by is called the divisor. Division can be expressed using a fraction where the numerator is the dividend, and the denominator is the divisor. For example, in the fraction \(\frac{a}{b}\), \(\text{a}\) is divided by \(\text{b}\). When simplifying fractions, it's essential to understand both components and ensure the divisor is not zero, as division by zero is undefined.
Numerator
The numerator is the top part of a fraction. It tells us how many parts we are considering out of the whole, which is represented by the denominator. In the fraction \(\frac{0}{-3}\), the numerator is 0. When a numerator is zero, it simplifies calculations because dividing zero by any non-zero number will always result in zero. This property stems from the basic principles of division.
Denominator
The denominator is the bottom part of a fraction. It indicates into how many equal parts the whole is divided. In our example \(\frac{0}{-3}\), the denominator is \(-3\). An important rule is that the denominator should never be zero, as it would make the fraction undefined. In this case, \(-3\) is non-zero, which is valid. The denominator plays a crucial role in determining the value of a fraction.
Zero Properties
Zero has unique properties in mathematics, especially in division. One key property is that any number divided by a non-zero number equals zero. This principle is used in our problem to simplify \(\frac{0}{-3}\) to 0. Another property is that multiplying any number by zero results in zero. However, dividing by zero is not possible. Understanding these properties is essential for solving mathematics accurately.

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Most popular questions from this chapter

Plot the fraction on the number line. $$\frac{1}{2}$$

Divide. Write the quotient as a mixed number. $$921 \div 4$$

For Exercises 85鈥�94, plot the fraction on the number line. $$\frac{3}{4}$$

For a recent year, the population of the United States was reported to be \(296,000,000\). During the same year, the population of California was \(36,458,000\). a. Round the U.S. population to the nearest hundred million. b. Round the population of California to the nearest million. c. Using the results from parts (a) and (b), write a simplified fraction showing the portion of the U.S. population represented by California.

Convert the improper fraction to a mixed number. $$\frac{13}{7}$$
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