Problem 4 - Fundamentals of Mathematics

Question

(Section 4.2) Write, in words, \(\frac{4}{5}\).

Step-by-Step Solution

Answer

The fraction \( \frac{4}{5} \) is written as 'four-fifths'.

Step 1: Understand the Fraction

A fraction consists of two parts: the numerator and the denominator. The numerator is the top number, and the denominator is the bottom number.

Step 2: Identify the Numerator and Denominator

In the fraction \( \frac{4}{5} \), the numerator is 4, and the denominator is 5.

Step 3: Convert the Numerator to Words

The numerator 4 is written in words as 'four'.

Step 4: Convert the Denominator to Words

The denominator 5 is written in words as 'five'.

Step 5: Combine the Parts in Words

Combine the words for the numerator and the denominator to express the fraction. \( \frac{4}{5} \) is written as 'four-fifths' in words.

Key Concepts

Numerator

In fractions, the numerator serves as the top number. It shows how many parts of a whole you have. To visualize this, imagine a pizza cut into equal slices. If you eat four out of five slices, the number '4' becomes your numerator. The numerator is crucial because it differentiates the fraction and gives it its specific value.

• Represents parts you have
• The top number in a fraction
• Essential in indicating the portion of the whole

Understanding the numerator helps when converting fractions into words. For instance, the numeral 4 in the fraction \( \frac{4}{5} \) translates to the word 'four.' Recognizing numerators is the first step toward comprehending fractions.

Denominator

The denominator is the bottom number in a fraction. It tells you the total number of equal parts the whole is divided into. Going back to the pizza example, if the entire pizza is divided into five equal slices, the number '5' would be the denominator. It ensures that each fraction part has proportional equalness.

• Denotes total number of equal parts
• Represents the bottom number in a fraction
• Essential for understanding the division of the whole

When reading fractions in words, the denominator signifies the number of divisions. In \( \frac{4}{5} \), the denominator 5 is expressed as 'fifths,' hence describing the fraction accurately in words is reliant on this element.

Writing Fractions in Words

Converting fractions into words is simple once you understand the main principles. The fraction \( \frac{4}{5} \) is read as 'four-fifths.' Consider each part separately first: 'four' for the numerator and 'fifths' for the denominator.
To convert:

• Identify the numerator and say it in words.
• Identify the denominator and determine the right suffix (e.g., 'half,' 'third,' 'quarter,' 'fifth').
• Combine them to form a descriptive term.

When learning to express fractions as words, remember:

• Numerators above the number 1 simply use the number (e.g., 'four').
• Denominator words often end in '-ths' (e.g., 'fifths').
• Special denominators like 2, 3, and 4 become 'halves,' 'thirds,' and 'quarters.'

By mastering these steps, you can accurately convert any fraction you come across into its verbal form.