Key Points

✓A ratio compares two or more quantities.
✓Ratios can be written using a colon (:) or as a fraction.
✓The order of the numbers in a ratio matters.
✓Ratios can be simplified like fractions.
✓Ratios can be used to solve problems involving scaling.

A ratio is a way to compare two or more quantities. It shows how much of one thing there is compared to another. For example, if you have 3 apples and 2 oranges, the ratio of apples to oranges is 3 to 2. This can be written as 3:2 or 3/2. Ratios can be used to solve problems where you need to scale up or down. If you know the ratio of ingredients in a recipe, you can use it to make a larger or smaller batch. Understanding ratios is important for many real-world situations, like cooking, measuring, and understanding maps.

Worked Example

A recipe for cookies calls for 2 cups of flour and 1 cup of sugar. What is the ratio of flour to sugar?

Step 1: Identify the quantities being compared: flour and sugar.
Step 2: Write the ratio in the correct order: flour to sugar is 2 to 1.
Step 3: Express the ratio using a colon: 2:1.

Answer: The ratio of flour to sugar is 2:1.

Try It Yourself

1. There are 5 cats and 3 dogs. What is the ratio of cats to dogs?

2. A class has 12 boys and 18 girls. What is the simplified ratio of boys to girls?

3. A map has a scale of 1 inch = 25 miles. If two cities are 4 inches apart on the map, what is the actual distance between them?

Watch Out For These Mistakes

Writing the ratio in the wrong order (e.g., writing dogs:cats instead of cats:dogs).
Not simplifying the ratio to its simplest form.
Forgetting to include all the quantities being compared in the ratio.