Ratios and Proportions Explained
Understanding Ratios
Comparing with Ratios
Imagine you're making a simple salad dressing. The recipe calls for 3 parts oil and 1 part vinegar. This relationship between the oil and the vinegar is a ratio. It doesn't tell you the exact amount of oil or vinegar to use, like tablespoons or cups. Instead, it tells you how much oil you need for every part of vinegar.
A ratio is simply a way to compare two or more quantities.
If you use 3 tablespoons of oil, you'll use 1 tablespoon of vinegar. If you decide to make a bigger batch with 3 cups of oil, you'll need 1 cup of vinegar. The ratio stays the same, keeping the taste consistent.
Ratio
noun
The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
How to Write a Ratio
Ratios can be written in a few different ways, but they all mean the same thing. Let's say we have a fruit bowl with 5 apples and 4 oranges.
If we want to express the ratio of apples to oranges, we can write it in three common ways:
| Notation | Example | How to Read It |
|---|---|---|
| Using a colon | 5:4 | "five to four" |
| Using the word "to" | 5 to 4 | "five to four" |
| As a fraction | 5/4 | "five to four" |
Notice that even when written like a fraction, we still often read it aloud as "five to four" when we're talking about it as a ratio. All three forms represent the same comparison: for every 5 apples, there are 4 oranges.
Order Matters
When you write a ratio, the order of the numbers is crucial. The ratio of apples to oranges (5:4) is different from the ratio of oranges to apples.
To find the ratio of oranges to apples, you just flip the numbers. It would be 4:5, or 4 to 5. This means for every 4 oranges, there are 5 apples. It's the same group of fruit, but the comparison is being made from a different perspective.
Always make sure the numbers in your ratio are in the same order as the items you are comparing.
You see ratios everywhere. On a map, the scale might be 1:100,000, meaning 1 inch on the map represents 100,000 inches in the real world. When you're mixing concrete, the ratio of cement to sand to gravel is critical for strength. In sports, a team's win-loss ratio compares how many games they've won to how many they've lost.
Ratios are a fundamental tool for comparing the world around us.
A fruit basket contains 8 bananas and 6 pears. What is the ratio of pears to bananas?
Which of the following is NOT a correct way to write a ratio of 3 wins to 4 losses?