- Understanding ratios and their notation

What Are Ratios?

A ratio is a way to compare two or more quantities, showing how many times one value contains or is contained within the other. Ratios are commonly used in mathematics, science, and everyday life to express relationships between numbers or amounts.

Basic Ratio Notation

Ratios can be written in several ways, but the most common notations are:

• Colon notation: a : b (read as "a to b")
• Fraction notation: a/b (read as "a divided by b")
• Word notation: "a to b"

For example, if there are 2 apples and 3 oranges, the ratio of apples to oranges can be written as 2:3, 2/3, or "2 to 3".

Interpreting Ratios

Ratios show the relative size of two quantities. In the example above, for every 2 apples, there are 3 oranges. This relationship stays the same even if the actual numbers increase or decrease, as long as the proportion is maintained (e.g., 4 apples to 6 oranges is also a 2:3 ratio).

Simplifying Ratios

Just like fractions, ratios can be simplified by dividing both terms by their greatest common factor. For example:

• The ratio 6:9 can be simplified to 2:3 by dividing both numbers by 3.

Common Uses of Ratios

• Comparing quantities (e.g., ingredients in a recipe)
• Scaling up or down (e.g., maps, models)
• Expressing probability and odds

Tip: Always write ratios in the order specified by the question. The ratio of apples to oranges is not the same as the ratio of oranges to apples.