Problem 62 - Basic College Mathematics

Question

Simplify. $$ \frac{8-8}{1247} $$

Step-by-Step Solution

Answer

0

Step 1: Identify the Numerator

First, focus on the numerator of the fraction, which is given as \(8 - 8\).

Step 2: Simplify the Numerator

Calculate the result of the expression in the numerator: \(8 - 8 = 0\). Therefore, the numerator simplifies to 0.

Step 3: Simplify the Entire Fraction

Now, rewrite the fraction with the simplified numerator: \(\frac{0}{1247}\). Any fraction with a numerator of 0 is equal to 0, regardless of the value in the denominator.

Key Concepts

Numerator and Denominator

Understanding the terms numerator and denominator is essential to simplifying fractions.
The numerator is the top part of the fraction and represents the number of parts we have.
The denominator is the bottom part of the fraction and tells us into how many parts the whole is divided.
For example, in the fraction \(\frac{3}{4}\), 3 is the numerator, and 4 is the denominator. These two components help define the fraction.

In the given exercise, the numerator is the expression \(8 - 8\). So, we focus first on simplifying that.

Basic Arithmetic Operations

Basic arithmetic operations help us perform calculations. They include addition, subtraction, multiplication, and division.
In the exercise provided, we used subtraction to simplify the numerator.

Subtraction involves taking one quantity away from another. For instance, subtracting 8 from 8 can be written in a math equation as \(8 - 8 = 0\).

Once we've simplified the numerator using arithmetic operations, we can then simplify the fraction further by rewriting the fraction with the simplified numerator, making the rest of the process much easier.

Zero Property of Fractions

The zero property of fractions states that any fraction with a numerator of zero is equal to zero, regardless of the value of the denominator, as long as the denominator is not zero.

For example, fractions like \(\frac{0}{5}\), \(\frac{0}{100}\), and \(\frac{0}{1247}\) all equal zero.
This property is critical to understanding fractions and helps in simplifying them.

In our exercise, after simplifying our numerator to 0, the fraction \(\frac{8-8}{1247}\) became \(\frac{0}{1247}\), and using the zero property of fractions, we know that equals 0.