Problem 36 - Fundamentals of Mathematics

Question

For the following 10 problems, write the fractions using whole numbers. ninety-two one-millionths

Step-by-Step Solution

Answer

\( \frac{92}{1,000,000} \)

Step 1: Understand the Problem

The task is to write the given fraction, "ninety-two one-millionths," using whole numbers.

Step 2: Recall the Fraction Concept

The term "one-millionth" implies a fraction where 1 is the numerator and 1,000,000 is the denominator. Thus, one one-millionth is \( \frac{1}{1,000,000} \).

Step 3: Multiply by the Numerator

"Ninety-two one-millionths" means we take 92 of these one-millionths. Therefore, we multiply 92 by \( \frac{1}{1,000,000} \) to obtain the fraction form: \( \frac{92}{1,000,000} \).

Step 4: Write the Fraction Using Whole Numbers

The fraction \( \frac{92}{1,000,000} \) is already written using whole numbers, with 92 as the numerator and 1,000,000 as the denominator.

Key Concepts

Whole Numbers

Whole numbers are the basic building blocks of arithmetic that most of us start learning in early math classes. Simply put, whole numbers include all of the positive numbers starting from zero. For example, 0, 1, 2, 3, and so on are all whole numbers.
These numbers are easy to understand because they do not have any fractional or decimal parts - they're entire and complete. When working with fractions, whole numbers often represent either the numerator or the denominator, or can be used to express multiple parts of a fraction.

They are crucial in various mathematical operations and provide a foundational understanding when dealing with more complex concepts such as fractions, ratios, and proportions. In our example exercise, 92 and 1,000,000 are both whole numbers used in the fraction representation.

Numerator and Denominator

In fractions, two important parts are the numerator and the denominator. Understanding these terms is vital to grasp how fractions work.

• The **numerator** is the number on top of the fraction's horizontal line. It tells you how many parts of the whole you have.
• The **denominator** is the number below the line. This indicates the total number of equal parts the whole is divided into.

For instance, in the fraction \( \frac{92}{1,000,000} \), 92 is the numerator and it represents how many one-millionths we have. Meanwhile, 1,000,000 is the denominator, showing into how many parts the whole is divided.
This setup allows us to convey precise quantities using fractions, which is especially useful in complex problems where exact division of parts is needed. By breaking it down this way, understanding and working with fractions becomes more intuitive.

Fraction Multiplication

Fraction multiplication involves multiplying the numerators together and the denominators together, using the basic arithmetic of multiplication. This means if you were multiplying two fractions, you'd multiply their respective numerators and denominators to get the new fraction in a single step.
For example, when figuring out "ninety-two one-millionths," you start with the fraction \( \frac{1}{1,000,000} \). Multiplication is applied by taking 92 of these parts, effectively multiplying 92 by \( \frac{1}{1,000,000} \).

The multiplication of a whole number by a fraction is similar: multiply the whole number by the numerator, then keep the denominator the same. This results in your multiplied fraction retaining the original fraction's structure while expanding its parts. Hence, in our problem, it calculates to \( \frac{92}{1,000,000} \) through simple multiplication of whole numbers with the fractional base.