tell me about expressing ratios, particularly: "I can identify the two parts and the whole of a divided quantity. I can express a division as a part:part ratio. I can express a division as a part:whole ratio."

I'd love to help you master how to break down and express these different kinds of ratios.

To make sure we use examples and practice problems that are the most interesting and useful to you, could you let me know if you are working on a specific grade level, or if you would prefer to use real-world scenarios (like cooking, video games, or sports) to practice?

I'm working on school math (6th/7th grade)

It is great to have you here! Since you are working on 6th and 7th-grade math, we will focus on making these concepts super clear with visual examples that show up a lot in school.

What are Parts and Wholes

Before we write any ratios, let's make sure we are comfortable finding the and the in a group of items. Imagine you have a backpack containing 3 blue notebooks and 2 red notebooks. Each individual color group makes up a part of your collection. So, we have two parts here: 3 blue notebooks is one part, and 2 red notebooks is the other part. The whole is simply the total number of items when you combine all the parts together. To find the whole, we just add the parts together:

\text{Whole} = 3\text{ blue} + 2\text{ red} = 5\text{ notebooks in total}

A three-part visual showing three blue notebooks and two red notebooks combining into five total notebooks inside a backpack.

To make sure this makes sense before we start writing ratios, let's try a quick check.

Let's do a practice question to find parts and wholes

Let's test our skills with a quick challenge using a lunchbox scenario. We need to find the parts and the whole before we write any ratios.

Suppose a lunchbox contains 4 apple slices and 5 carrot sticks.

What are the two individual parts, and what is the whole?