Problem 32 - Fundamentals of Mathematics

Question

For the following 10 problems, write the fractions using whole numbers. ninety-one one hundred sevenths

Step-by-Step Solution

Answer

The fraction is \( \frac{91}{107} \).

Step 1: Understand the Problem

We need to convert the given words 'ninety-one one hundred sevenths' into a fraction using whole numbers.

Step 2: Identify the Components

The phrase 'ninety-one one hundred sevenths' indicates a fraction where the rest combines the words 'one hundred sevenths.' This phrase refers to the fraction \( \frac{1}{107} \), and when attached to ninety-one, it results in \( \frac{91}{107} \) as a fraction.

Step 3: Construct the Fraction

Using the components identified, write the fraction as \( \frac{91}{107} \). Here, 'ninety-one' serves as the numerator, and 'one hundred sevenths' implies the denominator is 107.

Key Concepts

Understanding Numerators

A numerator is an essential part of a fraction. It is the number that sits above the fraction line. The numerator tells us how many parts we have out of a whole. For example, in the fraction \( \frac{91}{107} \), the numerator is 91. This indicates that we have 91 parts of a whole that has been divided into 107 parts.
The numerator can be any whole number, and it represents how many shares or portions you are considering. If you think of a pizza sliced into 107 pieces, the numerator lets you know how many pieces you are talking about out of those 107. In simple terms:

• The numerator is on top.
• It shows the number of considered parts.

Learning to identify the numerator is crucial as it helps in understanding how fractions represent quantities.

The Significance of the Denominator

The denominator is just as important as the numerator in a fraction. It is the number below the fraction line and signifies the total number of equal parts the whole is divided into. In the fraction \( \frac{91}{107} \), the denominator is 107.
This number tells us that whatever we are referring to is divided into 107 equal parts. Using our pizza analogy again, if a pizza is divided into 107 equal slices, the denominator lets us know the pizza's total parts. Here are some key points about the denominator:

• The denominator is on the bottom.
• It shows the total number of equal parts in a whole.
• It can never be zero because you can't divide something into zero parts.

Understanding the denominator is vital for grasping the concept of fractions as it defines the scale or extent of division.

Mastering Fraction Conversion

Fraction conversion is the process of transforming words or complex phrases into a numerical fraction form. When you encounter a phrase such as 'ninety-one one hundred sevenths,' knowing how to break it down into numbers is crucial.
In this phrase, 'ninety-one' refers to the numerator, while 'one hundred sevenths' translates to the denominator \( \frac{1}{107} \). Combining these gives \( \frac{91}{107} \). Understanding conversion techniques can help in:

• Simplifying calculations.
• Comparing different quantities or proportions.
• Solving real-world problems with ease.

Practicing fraction conversions hones your mathematical literacy, making it easier to navigate various math-related tasks.