Ratio Notation and Relationships

Ratios can be shown in different ways: tables, double number lines, and graphs. Each way helps you see how two amounts are connected. Let's look at a paint mix using the ratio 2:3, which means 2 cups of blue paint for every 3 cups of red paint. In a table, each row shows an amount that matches this same ratio. For example, 2 cups of blue would go with 3 cups of red, 4 cups of blue would go with 6 cups of red, and so on. Every row keeps the same relationship between blue and red, even though the actual numbers get bigger.

This section is about ratios and proportions. By the end, you should be able to write a ratio comparing two amounts, use proportions to solve problems, and find a missing amount when two ratios are equal. A ratio compares two quantities, like how many people use one app compared to another. Once you can write and simplify ratios, you can use them to answer real questions, like which app is more popular or how ingredients in a recipe compare to each other.

A recipe calls for 2 cups of whole wheat flour for every 6 cups of white flour. We can write this as the ratio 2:6. If we divide both numbers by 2, we get 1:3. That means for every 1 cup of whole wheat flour, you need 3 cups of white flour. You can also flip it around: for every 1 cup of white flour, you only need 1/3 of a cup of whole wheat flour. Dividing both sides of a ratio by the same number keeps the relationship the same, it just makes the numbers smaller and easier to compare.

A ratio compares two amounts. If a recipe uses 3 cups of orange juice for every 2 cups of pineapple juice, the ratio is 3:2. In a ratio table, you can add the same amounts each time to make a longer list of matching pairs. Starting at 3 and 2, adding 3 more cups of orange juice and 2 more cups of pineapple juice each time gives you 6 and 4, then 9 and 6. Even though the numbers change, 3:2, 6:4, and 9:6 all describe the exact same relationship between orange and pineapple juice.