Problem 16 - Prealgebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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: \(-21/1\).

Step 3: 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 \(a\).

Key Concepts

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.