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Ratios represent a relationship between two numbers, showing how many times one value contains or is contained within the other. For example, a ratio of 2:3 indicates that for every 2 units of one quantity, there are 3 units of another. Ratios can be written in various forms like \(2:3\), \(2/3\), or '2 to 3'.
Understanding how to work with ratios is crucial in many areas of math, including proportions.
When comparing ratios, it's often necessary to simplify them, just like with fractions, to see if they are equivalent.

The greatest common divisor (GCD), also known as the greatest common factor (GCF), is the largest number that divides two or more integers without leaving a remainder. For instance, the GCD of 16 and 24 is 8. To find the GCD, you can list the factors of each number and identify the largest factor they share.
Using the GCD allows us to simplify ratios and fractions. In our problem, we simplified \(\frac{16}{24}\) by dividing both the numerator (16) and the denominator (24) by their GCD, which is 8. This gave us the simplified ratio \(\frac{2}{3}\).

Simplifying fractions, or reducing them to their simplest form, means rewriting the fraction so that the numerator and denominator have no common factors other than 1. This process often makes the fraction easier to understand and work with.
To simplify a fraction, identify the greatest common divisor (GCD) of the numerator and the denominator. Divide both parts of the fraction by this GCD.
For example, in the provided exercise, we simplified \(\frac{16}{24}\) by finding the GCD of 16 and 24 (which is 8) and then dividing both the numerator and denominator by 8, resulting in \(\frac{2}{3}\).
This step is crucial when determining if two ratios form a proportion, as it helps to easily see if the ratios are equivalent.