Problem 16 - Fundamentals of Mathematics

Question

In the following 2 problems, state the numerator and denominator, and write each fraction in words. The number \(\frac{5}{9}\) is used in converting from Fahrenheit to Celsius.

Step-by-Step Solution

Answer

The fraction \( \frac{5}{9} \) is read as 'five-ninths.'

Step 1: Identify the Fraction

The given number is \( \frac{5}{9} \). This is a numerical fraction with a top part (numerator) and a bottom part (denominator).

Step 2: State the Numerator

In the fraction \( \frac{5}{9} \), the number above the fraction line is the numerator. The numerator is 5.

Step 3: State the Denominator

In the fraction \( \frac{5}{9} \), the number below the fraction line is the denominator. The denominator is 9.

Step 4: Convert the Fraction to Words

To write the fraction \( \frac{5}{9} \) in words, we say 'five-ninths' because the numerator, 5, is written as "five," and the denominator, 9, is written as "ninths."

Key Concepts

Numerator

Let's begin with understanding what a numerator is. When you look at a fraction like \( \frac{5}{9} \), you see two numbers separated by a line called the fraction bar. The number on top, which in this case is \( 5 \), is the numerator. The numerator is very significant as it indicates how many parts of the whole are being considered. For example:

• In the fraction \( \frac{5}{9} \), the \( 5 \) signifies five parts.
• The numerator can be any integer, positive or negative.
• When dealing with fractions, think of the numerator as the "counter" of parts.

By having a clear understanding of the numerator, you can better comprehend how much of something you have. This becomes particularly useful when you're measuring ingredients for a recipe or converting temperatures, like in our exercise!

Denominator

Moving on to the denominator, let's see what role it plays in a fraction. In \( \frac{5}{9} \), the number below the fraction bar, which is \( 9 \), is the denominator.The denominator tells you into how many equal parts the whole is divided. Here are some key points:

• In \( \frac{5}{9} \), the \( 9 \) indicates that the whole consists of nine equal parts.
• The denominator is always a positive integer.
• It is essential for setting the scale or size of each part represented by the numerator.

Understanding the denominator helps you to see the fraction as a division. For instance, if you have a cake and it's split into nine slices, the denominator shows that your data set is made up of those nine slices. It anchors the numerator to the whole and provides context for the entire fraction.

Fraction in Words

Reading fractions as words can be surprisingly simple once you know the basic terms. Let's translate \( \frac{5}{9} \) to words.To write a fraction in words, you need to know how to express both the numerator and the denominator verbally:

• The numerator \( 5 \) becomes "five," which is straightforward.
• The denominator \( 9 \) is transformed into the word "ninths," because when the denominator is greater than one, you typically add "-ths" to the word describing the number.

So, \( \frac{5}{9} \) is spoken as "five-ninths." When expressing fractions in words, you form a single term that provides a clear picture of the fraction's meaning. Saying it aloud makes it easier to communicate the value of the fraction without needing to see the numbers visually. This skill can be particularly practical in daily activities, such as cooking or financial transactions, where verbal clarity is crucial.