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Chapter 3: Problem 20

Which number cannot be used as the denominator of a fraction? A. 1 B. 0 C. 6 D. 100

Short Answer

Expert verified
0 cannot be used as the denominator of a fraction.

Step by step solution

01

Understanding Fractions

A fraction consists of a numerator and a denominator. The denominator represents the number of equal parts the whole is divided into.
02

Identifying the Restriction for Denominators

The denominator of a fraction cannot be zero. Dividing by zero is undefined in mathematics because it does not result in a finite number.
03

Evaluating the Choices

Review the given options: (A) 1, (B) 0, (C) 6, and (D) 100. Check if any of these numbers are zero. If so, they cannot be used as a denominator.
04

Determine the Answer

Among the options, 0 is the only number that cannot be used as a denominator because it would make the division undefined.

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Key Concepts

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

Understanding the Denominator
In every fraction, the denominator serves a pivotal role. It essentially tells us how many parts the whole is divided into. For instance, in the fraction \( \frac{3}{4} \), the denominator is 4. This indicates that the whole is divided into 4 equal parts. The numerator, in this case 3, tells us how many of those parts we have.When considering fractions, it's crucial to remember that the denominator cannot be zero. This restriction exists because division by zero does not produce a valid mathematical result. It is undefined, meaning it does not fit into the number system. Therefore, when dealing with fractions, always ensure the denominator is a non-zero number.
Dividing by Zero 鈥� Why It鈥檚 Undefined
The concept of dividing by zero can be perplexing, but it's an important one to grasp. In simple terms, division by zero is like attempting to distribute something among nothing, which doesn't make sense mathematically.Here's why dividing by zero is undefined in a practical sense:
  • In any division, we ask "how many times does the divisor fit into the dividend?" But with zero, you can鈥檛 fit something into nothing.
  • Consider \( \frac{5}{1} = 5 \), meaning 5 is divided into 1 part. But \( \frac{5}{0} \) asks us to divide 5 into nonexistent parts, and that's not possible.
So, whenever you are working with fractions, ensure your denominator is never zero. If it is, you're venturing into mathematical territory that doesn't result in a sensible value or answer. Always double-check fractions for this common pitfall before calculating.
The Role of the Numerator
The numerator is a fundamental part of every fraction, sitting atop the fraction line. It indicates the number of equal parts we are considering out of the whole as specified by the denominator.Using the fraction \( \frac{3}{4} \) again as an example:
  • The numerator is 3. It counts the parts we're taking or considering.
  • The denominator is 4, which tells us about the whole being divided into 4 equal parts.
In a fraction, the numerator can be any integer (positive or negative). However, if the numerator is zero, like in \( \frac{0}{4} \), the value of the fraction is zero. This makes sense because it means you have zero parts of the whole. In contrast, if the denominator is zero, the fraction is not defined at all.Understanding both the numerator and the denominator, and their interaction, is key to mastering fractions efficiently.

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Most popular questions from this chapter

Reduce \(\frac{54}{72}\) to lowest terms. A. \(\frac{4}{3}\) B. \(\frac{3}{4}\) c. \(\frac{5}{6}\) D. \(\frac{5}{8}\)

Which of the following is a mixed number? A. \(\frac{3}{5}\) B. \(\frac{8}{5}\) c. \(\frac{6}{2}\) D. \(2 \frac{3}{8}\)

Change \(\frac{11}{4}\) to a mixed number. A. \(2 \frac{3}{4}\) B. \(3 \frac{1}{4}\) c. \(2 \frac{1}{4}\) D. \(5 \frac{1}{2}\)

Which of the following is an improper fraction? A. \(\frac{11}{8}\) B. \(\frac{3}{4}\) C. \(\frac{1}{5}\) D. \(\frac{9}{10}\)

Change \(\frac{1}{8}\) to an equivalent fraction in higher terms. A. \(\frac{12}{16}\) B. \(\frac{54}{64}\) c. \(\frac{21}{24}\) D. \(\frac{29}{32}\)
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