Problem 55 - Basic College Mathematics

Question

Simplify. $$ \frac{3}{3} $$

Step-by-Step Solution

Answer

1

Step 1: Understand the Fraction

A fraction \( \frac{a}{a} \) where the numerator is equal to the denominator simplifies to 1.

Step 2: Apply the Simplification

Since the numerator (3) and the denominator (3) are the same, you can simplify \( \frac{3}{3} \) to 1.

Key Concepts

fraction simplification

Simplifying fractions is one of the first steps in mastering basic arithmetic. When you simplify a fraction, you reduce it to its simplest form by ensuring that the numerator and the denominator no longer have any common factors other than 1. This makes the fraction easier to understand and work with.
In the given exercise, the fraction is \[ \frac{3}{3} \]. Here, both the numerator and the denominator are the same. When you notice this, you should know that \[ \frac{a}{a} = 1 \], irrespective of any value for 'a' as long as it is not zero.
This is because any number divided by itself is equal to 1. Understanding why is crucial: let's break it down further.

numerator and denominator

In any fraction, like \[ \frac{3}{3} \], the number on top is called the numerator and the number at the bottom is known as the denominator. The numerator represents the parts you have, while the denominator represents the total number of parts something is divided into.
In the case of \[ \frac{3}{3} \], you have 3 parts out of a total of 3, which intuitively also means you have '1' whole. Calculating it shows the same: 3 divided by 3 equals 1. Let's visualize: Imagine cutting a pizza into 3 equal slices. If you have all 3 slices, you practically have 1 whole pizza.
Remember, if the numerator is equal to the denominator, the fraction always simplifies to 1.

basic arithmetic

Basic arithmetic involves addition, subtraction, multiplication, and division. Simplifying fractions falls under division because you essentially divide the numerator by the denominator. In our example, \[ \frac{3}{3} \], we divide 3 by 3, which equals 1.
Understanding this concept is critical as it lays the foundation for solving more complex equations and fractions later on. Let’s delve deeper into dividing fractions: when you divide a number by itself, the result is always 1 because the number contains exactly one unit of itself.
This approach applies to any fraction where the numerator equals the denominator, and it's a fundamental rule in arithmetic you will use frequently.