Understanding and Writing Ratios

Video Lessons > Understanding and Writing Ratios

Introduction and Video

Ratios are fundamental tools in math that help us to compare different values and understand their relationships. In this video lesson, you will learn about writing ratios in different ways. We will also discuss the three types of ratios.

Before you work with ratios, it is helpful to know how to write and simplify fractions.

Lesson Notes

Let's look at the details of the lesson including: the definition of ratio, the three types of ratios, and writing ratios in different ways.

What is a Ratio?

A ratio is a comparison of two values, showcasing their relationship in terms of magnitude. There are three primary types of ratios:

1. Total to Total Ratio: This type compares the entire quantity of one item to the entire quantity of another. For example, comparing the total number of stars to the total number of circles.
2. Part to Total Ratio: With a part to total ratio, a part of something is compared to the total quantity of that item. An example could be comparing the number of orange squares to the total number of squares in an image.
3. Part to Part Ratio: Part to part ratios involves comparing a part of something to another part of the same thing. For instance, comparing the number of orange squares to the number of blue squares in an image.

Examples of Ratios

Now that we discussed the three types of ratios, let's look at examples of each one.

Total to Total Ratio: Suppose we have four stars and seven circles. The ratio of stars to circles is represented as 4:7, emphasizing the order specified in the question.

Part to Total Ratio: In a scenario where there are three orange squares out of a total of ten squares, the ratio of orange squares to the total number of squares is represented as 3:10.

Part to Part Ratio: When comparing three orange squares to five blue squares, the ratio is expressed as 3:5, emphasizing the order as instructed in the question.

Writing Ratios

Ratios can be represented in different formats. Here are a few examples:

• Using words: For example, 4 stars to 7 circles or 3 orange squares out of 10 squares.
• Using a colon: For example, 4:7 or 4 stars : 7 circles.
• Using fractions: For example, 4/7 or 4 stars / 7 circles.

It's very important to maintain the order specified in the problem when expressing ratios, as it significantly impacts how the ratio is interpreted. For example, if there are 4 stars and 7 circles, the ratio of stars to circles is 4:7. However the ratio of circles to stars is 7:4.

Summary and Practice

In this lesson, you learned that ratios help us understand relationships by comparing values. The types of ratios include total to total, part to total, and part to part. Ratios can be represented with words (such as "to" or "out of"), with a colon, or numerically using a fraction, decimal or percent. Understanding ratios is foundational for many types of math problems, and mastering this concept opens doors to working with percents, converting units of measurement, and more.

Try this practice activity to see what you learned. Click on the ratios to select them.

Related Standard: Common Core 6.RP.A.1