/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 101 In your own words, explain why \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 101

In your own words, explain why \(\frac{0}{10}=0\) and \(\frac{10}{0}\) is undefined.

Short Answer

Expert verified
\(\frac{0}{10} = 0\) is valid because it gives zero to each share, \(\frac{10}{0}\) is undefined as division by zero is impossible.

Step by step solution

01

Understanding Division by a Non-Zero Number

The fraction \(\frac{0}{10}\) represents 0 items divided among 10 people. Since there are no items to distribute, each person gets 0. Therefore, \(\frac{0}{10} = 0\). Division by a non-zero number is possible and straightforward as long as the numerator is 0.
02

Exploring Division by Zero

When you try to divide 10 by 0, as in \(\frac{10}{0}\), you're trying to divide 10 items among zero people, which doesn鈥檛 make sense. Division requires at least one person or a unit to share the amount with. Thus, \(\frac{10}{0}\) is undefined because it breaks the conceptual and mathematical rules of division.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Division by Zero
When we discuss division, we naturally think about sharing things evenly. However, when dividing by zero, this idea falls apart. Let's break it down. Imagine you're trying to share 10 candies among zero friends. How can you distribute candies if there are no recipients?

In mathematics, division by zero is undefined. This means it's impossible because it doesn't make logical or practical sense. This situation defies the basic principles of division. Any number divided by zero doesn't produce a tangible result, making it undefined.
  • It conflicts with the idea of dividing something into parts.
  • Breaking a number into zero parts can't be executed, conceptually or mathematically.
  • It doesn't conform to any rule in arithmetic or algebra.
Fraction Understanding
Fractions are a way of expressing division. They're made up of two parts: the numerator and the denominator, often written as a division of two numbers. Understanding these is crucial for mastering fractions.

Here鈥檚 how they work:
  • The numerator is the top part, showing how many parts you have.
  • The denominator is the bottom part, showing into how many parts the whole is divided.
Each fraction basically tells a story: how something is divided and how much of it we have.

For example, \(\frac{0}{10}\) illustrates having zero portions out of ten possible parts, where ultimately, it remains zero. Such visualization helps make sense of why some fractions yield zero results while others don't.
Undefined Division
Sometimes, division doesn't result in a number you can point to. This often happens when dividing by zero, as seen earlier with \(\frac{10}{0}\).

This kind of division is labeled as "undefined," a term which highlights the disconnect between expectations and outcomes.
  • Undefined division lacks any meaningful outcome.
  • It signals impossible operations that mathematics can't support.
  • In simpler terms, it reflects an error, a misplacement of numbers that defy normal rules.
Understanding this helps to apply mathematical operations sensibly, ensuring division only takes place in viable situations.
Numerator and Denominator Concepts
Understanding numerators and denominators is crucial for grasping the essence of fractions. These two components define every fraction and dictate how division operates.

  • Numerator: The top number in a fraction, indicating parts of a whole.
  • Denominator: The bottom number, representing the total number of equal parts.
Reduction of fractions, such as simplifying \(\frac{4}{8}\) to \(\frac{1}{2}\), relies on these components. They explain why fractions are fractions!

Always remember, if the numerator is zero, as in \(\frac{0}{10}\), it means you have nothing out of something鈥攚hich naturally equals zero. Conversely, if the denominator zero, as in \(\frac{10}{0}\), the fraction becomes undefined since division by zero isn't possible.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Perform the indicated operations. $$ 17 \frac{5}{9}+\left(-14 \frac{2}{3}\right) $$

Each expression contains one addition, one subtraction, one multiplication, and one division. Write the operations in the order that they should be performed. Do not actually simplify. $$[30-4(3+2)] \div \frac{5}{2}$$

Simplify. See Section 1.7. $$5^{3}$$

Write each improper fraction as a mixed number or a whole number. See Example 21. $$\frac{47}{15}$$

Perform the indicated operations. $$ -3 \frac{5}{6} \div\left(-3 \frac{2}{3}\right) $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.