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Ratios are a way to compare two quantities by using division. When you write a ratio, you are essentially stating how many times one quantity contains the other. For example, a ratio of 72 dollars to 220 dollars can tell you how much more, or less, one quantity is in relation to the other.
Ratios can be represented in several ways, such as:

• Fractions (e.g., \( \frac{72}{220} \))
• Colons (e.g., 72:220)
• Words (e.g., 72 to 220)

Understanding ratios is crucial because they appear in numerous real-life situations, from cooking recipes to comparing costs. By mastering ratios, you can make better-informed decisions in everyday life.

Simplifying fractions means reducing them to their lowest terms. This process makes the fraction easier to understand and work with.
To simplify a fraction, follow these steps:
1. Identify the numerator (the top number) and the denominator (the bottom number) of your fraction.
2. Find the greatest common divisor (GCD) of the numerator and denominator.
3. Divide both the numerator and denominator by the GCD.
Let's simplify the fraction \( \frac{72}{220} \). The GCD of 72 and 220 is 4. Divide 72 by 4 to get 18, and divide 220 by 4 to get 55. As a result, \( \frac{72}{220} \) simplifies to \( \frac{18}{55} \).
By simplifying fractions, you make them easier to read, understand, and work with in further calculations or comparisons.

The greatest common divisor (GCD) is the largest integer that can divide both the numerator and the denominator of a fraction without leaving a remainder. Finding the GCD is essential for simplifying fractions.
Here's a simple method to find the GCD:
1. List the factors of each number.
2. Identify the largest factor that appears in both lists.
For example, consider the numbers 72 and 220:

• Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
• Factors of 220: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220

The common factors are 1, 2, and 4, with 4 being the largest. Thus, the GCD of 72 and 220 is 4.
Knowing how to find the GCD can significantly streamline your work when dealing with ratios and fractions, ensuring your answers are always in their simplest, most understandable form.