Problem 12 - Fundamentals of Mathematics

Question

Write each fraction using words. $$\frac{21}{38}$$

Step-by-Step Solution

Answer

Twenty-one thirty-eighths.

Step 1: Identify the Numerator

The numerator of the fraction \( \frac{21}{38} \) is 21. This is the number above the line in a fraction and represents the part of the whole that is being considered. In words, the numerator 21 is written as "twenty-one."

Step 2: Identify the Denominator

The denominator of the fraction \( \frac{21}{38} \) is 38. This is the number below the line in a fraction and represents the total number of equal parts into which the whole is divided. In words, the denominator 38 is written as "thirty-eight."

Step 3: Write the Fraction Using Words

Combine the numerator and the denominator to express the entire fraction in words. The fraction \( \frac{21}{38} \) is written as "twenty-one thirty-eighths." This shows that the fraction is composed of 21 parts out of 38 equal parts.

Key Concepts

Understanding the Numerator

The numerator is a fundamental part of a fraction. It is the top number, situated above the fraction line, known as the vinculum. The role of the numerator is to indicate how many parts of a whole we are considering.It tells us the count of particular portions we are dealing with. For instance, in the fraction \(\frac{21}{38}\), the numerator is 21. This means we have 21 parts out of a possible total represented by the denominator.

• The numerator is always on top in fraction notation.
• It tells how many parts of a whole we have.

Writing the numerator in words can make fractions easier to understand, especially in communication. Here, \(21\) becomes "twenty-one," giving a verbal representation of the part of the whole we have.

Demystifying the Denominator

The denominator, found below the fraction line, holds the key to understanding what the "whole" consists of in a fraction. This number reveals into how many equal sections the whole is divided.For the fraction \(\frac{21}{38}\), our denominator is \(38\). This denotes that the entire entity is split into 38 equal parts. Out of these, the numerator specifies how many are being considered.

• The denominator is the base number of equal parts.
• It helps in determining the size of each individual portion.

By translating the denominator into words, "thirty-eight" in this case, we support comprehension by illustrating the total number of segments.

Decoding Fraction Notation

Fraction notation is a mathematical way of representing parts of a whole. It’s laid out with two numbers and a horizontal line between them. This setup is surprisingly informative but can be misunderstood without a proper breakdown.Fraction notation consists of:

• A numerator above the line which represents the number of parts taken.
• A denominator below the line to show how many parts make up the complete whole.

For the notation \(\frac{21}{38}\), when written in words, it turns into "twenty-one thirty-eighths." This conveys that out of 38 equal divisions of something, 21 are in use or being referred to.Understanding and writing fractions like this enhances clarity in conveying amounts, particularly when delving into more complex mathematical concepts.