Problem 9 - Fundamentals of Mathematics

Question

Write the following fractions using whole numbers. eight hundred seven-thousandths

Step-by-Step Solution

Answer

The fraction eight hundred seven-thousandths simplifies to \(\frac{4}{5}\), which cannot be a whole number.

Step 1: Understand the fraction

The fraction given is "eight hundred seven-thousandths." This is a way to express a simple fraction with words where "eight hundred" is the numerator and "thousandths" indicates the denominator is 1000.

Step 2: Write the fraction in numerical form

Write the fraction represented by the words. In this case, "eight hundred seven-thousandths" means \(\frac{800}{1000}\).

Step 3: Simplify the fraction

To simplify \(\frac{800}{1000}\), identify the greatest common divisor (GCD) of 800 and 1000. Both numbers are divisible by 200. Hence, divide the numerator and the denominator by 200: \(\frac{800}{200} = 4\) and \(\frac{1000}{200} = 5\). Thus, the simplified fraction is \(\frac{4}{5}\).

Step 4: Express as a whole number (if applicable)

Since \(\frac{4}{5}\) cannot be expressed as a whole number without a remainder, it remains as a fraction. A whole number representation isn't possible for this fraction.

Key Concepts

Understanding the Numerator

In a fraction, the top number is referred to as the numerator. It represents how many parts of the whole you have. For example, consider the fraction \(\frac{800}{1000}\). The numerator here is 800. This indicates that there are 800 parts being considered out of a total of 1000.

When interpreting a fraction, the numerator is crucial because it directly affects the value of the fraction. If you change the numerator while keeping the denominator the same, the fraction's value changes.

• If the numerator increases, the value of the fraction increases, assuming the denominator remains constant.
• If the numerator decreases, the fraction's value decreases under the same conditions.

Having a clear understanding of the numerator helps in performing operations such as addition, subtraction, or simplification of fractions.

Grasping the Denominator

The bottom number in a fraction is known as the denominator. It tells you into how many equal parts the whole is divided. In the example for \(\frac{800}{1000}\), the denominator is 1000. This means the whole is split into 1000 equal parts, and the fraction describes 800 out of these parts.

The denominator plays a key role in determining the size of each part of the whole, or unit. Changes to the denominator affect the size of these parts:

• If the denominator increases and the numerator stays the same, each part becomes smaller, and the fraction's value decreases.
• If the denominator decreases with a constant numerator, each part becomes larger, resulting in an increased fraction value.

Understanding the denominator helps in tasks such as finding equivalent fractions and performing arithmetic operations involving fractions.

Simplifying Fractions

Simplifying fractions is the process of making a fraction as simple as possible while keeping its value the same. This involves reducing the numerator and the denominator to their smallest possible whole numbers, without changing the actual value of the fraction.

For example, to simplify \(\frac{800}{1000}\), you must find the greatest common divisor (GCD) of these two numbers. The GCD is the largest number that divides both the numerator and the denominator evenly.

• For \(\frac{800}{1000}\), the GCD is 200.
• By dividing both the numerator and the denominator by 200, you get \(\frac{4}{5}\), which is the simplified form.

Simplifying fractions helps make calculations easier and often provides clearer insight into the fraction's value in relation to the whole.