How to Do Ratios in 6th Grade?

Ratios in 6th grade are all about comparing two quantities! Here's a breakdown of how to understand and work with them:

Understanding Ratios

What is a Ratio? A ratio shows the relative sizes of two or more values. It tells you how much of one thing there is compared to another thing.
Ways to Write Ratios: You can write a ratio in three main ways:
- Using the word "to": For example, "3 to 5"
- Using a colon (:): For example, "3:5"
- As a fraction: For example, "3/5"
All three mean the same thing: for every 3 of the first quantity, there are 5 of the second quantity.

Identifying the Quantities: First, you need to identify what two things are being compared. For example, you might be comparing the number of boys to the number of girls in a class, or the number of apples to the number of oranges in a basket.
Writing the Ratio: Once you know what you're comparing, write the ratio in the correct order. The order matters! If you are comparing boys to girls, the number of boys should come first in the ratio. For example, if there are 10 boys and 12 girls, the ratio of boys to girls is 10:12.
Simplifying Ratios: Just like fractions, ratios can often be simplified. To simplify a ratio, find the greatest common factor (GCF) of the two numbers and divide both parts of the ratio by the GCF.
- Example: The ratio 10:12 can be simplified. The GCF of 10 and 12 is 2. Divide both sides by 2: 10/2 : 12/2 = 5:6. So the simplified ratio is 5:6.
Equivalent Ratios: Equivalent ratios are ratios that represent the same comparison. You can find equivalent ratios by multiplying or dividing both parts of a ratio by the same number.
- Example: The ratio 1:2 is equivalent to 2:4, 3:6, 4:8, and so on. You get these by multiplying both 1 and 2 by the same number (2, 3, 4, respectively). As the YouTube video referenced suggests (from 3:30 in the video): Checking for equivalent ratios means to find a common number for both values of the ratio. 30 to 48 can be simplified by dividing both by 6 and the ratio is the same as 5 to 8.

Example 1: In a class, there are 15 students who like pizza and 10 students who like tacos. What is the ratio of students who like pizza to students who like tacos?
- Ratio: 15:10
- Simplified Ratio: 3:2 (Divide both by 5)
Example 2: A recipe calls for 2 cups of flour and 1 cup of sugar. What is the ratio of flour to sugar?
- Ratio: 2:1

Read Carefully: Pay close attention to the order in which the quantities are presented in the problem.
Simplify: Always simplify your ratios to their simplest form.
Practice: The more you practice, the better you'll become at understanding and working with ratios.