Problem 22 - Introductory Algebra for College Students

Question

Express each rational number as a decimal. $$\frac{5}{5}$$

Step-by-Step Solution

Answer

The decimal form of the fraction \(\frac{5}{5}\) is 1.0.

Step 1: Understand the Fraction

The given fraction is \(\frac{5}{5}\). In a fraction, the number above the line is called the numerator and the number below the line is called the denominator

Step 2: Division

The fraction can be interpreted as a division operation. So, by dividing the numbers, the numerator 5 is divided by the denominator 5, which equals 1.

Step 3: Express the Result in Decimal Form

In this case, the result of the division is 1. It can be expressed as a decimal, hence 1 can be written as 1.0

Key Concepts

Understanding Fractions

Fractions are a mathematical way to express parts of a whole. They consist of two key parts: the numerator and the denominator. The numerator is the top number and represents how many parts of the whole we are considering. The denominator is the bottom number and tells us into how many parts the whole is divided.
For example, in the fraction \(\frac{5}{5}\), the 5 on the top is the numerator, and the 5 on the bottom is the denominator. The fraction \(\frac{5}{5}\) essentially means that we have 5 parts out of a whole that is divided into 5 parts, or simply put, we have the entire whole.

• Numerator indicates the portion of the whole.
• Denominator defines how many equal parts the whole is divided into.

Fractions can always provide a clear picture of how parts relate to the whole in mathematical terms.

Numerator and Denominator

The numerator and denominator are fundamental concepts when working with fractions. They help us understand the size of each part of the fraction, how many parts exist, and how these parts fit together into a whole.

The **numerator** is the top number in a fraction. It indicates the number of pieces considered from the whole set. Meanwhile, the **denominator** is the bottom number, showing the total number of equal parts into which the whole is divided.
For our fraction \(\frac{5}{5}\):

• The numerator is 5, meaning 5 parts are taken.
• The denominator is also 5, so the whole is divided into 5 parts.

This means the fraction represents the entire set or the whole. When the numerator and denominator are the same, they effectively cancel out to equal 1, indicating completeness.

The Division Process

When converting a fraction into a decimal, we perform a division. This is because a fraction like \(\frac{5}{5}\) can be seen as a division of the numerator by the denominator.
In our example, we have 5 divided by 5, represented mathematically as 5 ÷ 5. By performing this operation, we find that the answer is 1.
This process can be broken down into simple steps:

• Take the numerator, which is 5.
• Divide it by the denominator, also 5.
• Record the result of the division as a decimal.

So, after dividing 5 by 5, we conclude that \(\frac{5}{5} = 1\), or in decimal form, it is written as 1.0. This clear outcome demonstrates how fractions and the division process are intrinsically linked in mathematics.