Problem 49 - Basic College Mathematics

Question

Simplify. $$ \frac{45}{45} $$

Step-by-Step Solution

Answer

1

Step 1: Identify the numerator and the denominator

The given fraction is \( \frac{45}{45} \). Here, the numerator is 45 and the denominator is 45.

Step 2: Divide the numerator by the denominator

When the numerator and the denominator are the same, dividing them gives 1. Therefore, \( \frac{45}{45} = 1 \).

Key Concepts

Understanding Numerator and Denominator

Every fraction has two parts: the numerator and the denominator. The numerator is the top number of the fraction, and the denominator is the bottom number. In the fraction \(\frac{45}{45}\), both the numerator and denominator are 45. Understanding these parts is crucial because it helps us know how to manipulate and simplify fractions. Think of the numerator as representing how many parts we have, and the denominator as showing how many total parts there are in one whole.

Basic Arithmetic

Basic arithmetic involves simple operations like addition, subtraction, multiplication, and division. For simplifying fractions, division is often used. In this exercise, we used division to simplify \(\frac{45}{45}\). By dividing the numerator (45) by the denominator (45), we get 1. Basic arithmetic helps us perform this division with ease and shows us that \(\frac{45}{45} = 1\). This process is straightforward because any number divided by itself equals 1.

Equivalent Fractions

Equivalent fractions are different fractions that represent the same value. For example, \(\frac{2}{4}\) and \(\frac{1}{2}\) are equivalent because they both equal 0.5 when divided. To determine if two fractions are equivalent, you can cross-multiply and compare the products. Simplifying fractions helps us find equivalent fractions. In our example, simplifying \(\frac{45}{45}\) gives us 1, which means \(\frac{45}{45}\) is equivalent to \(\frac{1}{1}\). This illustrates how simplification can show the core value of a fraction.