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Chapter 5: Problem 16

Write each number as a fraction. $$-21$$

Short Answer

Expert verified
\(-21\) as a fraction is \(-\frac{21}{1}\).

Step by step solution

01

Understand the Concept

When a number is written as a fraction, it is expressed as a ratio of two integers: the numerator and the denominator. For whole numbers like -21, we can express them as fractions by placing them over 1.
02

Express the Number as a Fraction

To write -21 as a fraction, simply use -21 as the numerator and 1 as the denominator. This gives us the fraction: \(-21/1\).
03

Verify the Fraction Form

Double-check if the fraction form \(-\frac{21}{1}\) is correctly expressing the original whole number. Any whole number \(a\) expressed as \(\frac{a}{1}\) remains equivalent to \(a\).

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Key Concepts

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

Numerator
The numerator is a fundamental component of fractions. It's the number placed above the division line in a fraction.
It defines how many parts of a whole are being considered. In our example, the whole number -21 becomes the numerator when expressed as a fraction.When working with fractions, the numerator can be any integer, negative or positive. For example:
  • In \-21/1\, \-21\ is the numerator.
  • In \3/4\, \3\ is the numerator.
  • In \1/5\, \1\ is the numerator.
A negative numerator indicates that the fraction represents a negative quantity.
This is why \(-21\) in our example represents a portion below zero when considered among fractions.
Denominator
The denominator is equally essential in understanding fractions. It's the number found below the division line in a fraction. The denominator tells us into how many equal parts the whole is divided. In the given example, the fraction \-21/1\ uses \1\ as the denominator.Here's why it's so crucial:
  • If you increase the denominator while keeping the numerator constant, the fraction becomes smaller.
  • Conversely, decreasing the denominator makes the fraction larger.
  • In \(-21/1\), \(1\) as the denominator means \(-21\) is not divided into smaller parts but remains whole.
Denominators differ from the numerator, as they cannot be zero. Having zero as a denominator would make a fraction undefined.
Whole Numbers
Whole numbers are the basic, clean-cut numbers without fractions or decimals involved. They include all positive, zero, and negative numbers without any division remainder. Consider numbers like \0, 1, 2,\ and \-21\.When expressing whole numbers as fractions:
  • Every whole number can transform into a fraction by placing it over 1, such as \(5\) becoming \(\frac{5}{1}\).
  • Another example is \(-21\), where you write it as \(-\frac{21}{1}\).
  • This method keeps the value unchanged, revealing a unique relationship between whole numbers and fractions.
Whole numbers keep their integrity even when expressed as fractions. This extends a simple view on the concept of fractions, making them a useful tool for math operations, comparison, and more.

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Most popular questions from this chapter

Write each decimal as a fraction or mixed number in simplest form. $$-0.2$$

Explain how rational numbers are related to other sets of numbers. Illustrate your reasoning with examples of numbers that belong to more than one set and examples of numbers that are only rational.

Find each product. Write in simplest form. $$-2 \frac{4}{5} \cdot \frac{3}{8}$$

Write each decimal as a fraction or mixed number in simplest form. $$0 . \overline{7}$$

Find the distance between each pair of points. Round to the nearest tenth, if necessary. $$M(4,-2), N(-6,-7)$$
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