How to Find Ratios in 6th Grade?

Ratios in 6th grade can be understood as comparisons between two quantities, showing how much of one thing there is compared to another.

Understanding Ratios

Ratios can be expressed in several ways:

Using the word "to": For example, 3 to 5 (3:5).
Using a colon (:): For example, 3:5.
As a fraction: For example, 3/5 (although it's a ratio not a fraction; it indicates a comparison).

Identify the Quantities: Determine the two quantities you are comparing.
Order Matters: The order in which the quantities are written in a ratio is important. For instance, a ratio of 3:5 is different from a ratio of 5:3. As highlighted in the reference video, the order is crucial and must reflect the relationship described by the problem. For example, if a problem says “24 to 15”, but the quantities should be presented as 30 to 48 based on the context, then the ratio 24 to 15 would be incorrect and the correct ratio to analyze would be 30 to 48.
Express the Relationship: Use the chosen method (to, :, or fraction) to show the comparison between the two quantities.
Simplify the Ratio: If possible, simplify the ratio by dividing both numbers by their greatest common factor (GCF). For instance, a ratio of 6:8 can be simplified to 3:4 by dividing both terms by 2.

Example 1: There are 12 apples and 8 oranges. The ratio of apples to oranges is 12:8. This simplifies to 3:2 (dividing both by 4). This means there are 3 apples for every 2 oranges.
Example 2: In the video example, the quantities were 30 and 48. The ratio is 30:48. This can be simplified to 5:8 by dividing both parts of the ratio by their GCF of 6.

Real-Life Applications: Ratios are frequently used in real-life situations, including recipes, maps, scales, and more.
Graphic Organizers: The reference also used a graphic organizer to help find the correct ratio. Visual tools like graphic organizers can help when dealing with more complex ratios.

Simplifying a ratio is similar to simplifying a fraction, and will make it easier to comprehend.

Divide by GCF: Find the greatest common factor of both quantities, and divide each by it to reduce the ratio to its simplest form.

By understanding and practicing these steps, 6th graders can master the concept of ratios and their uses.