Understanding Proportional Ratios

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Introduction and Video

In this video lesson, we're going to explore different ratios and learn what it means for ratios to be considered proportional. Understanding proportional ratios is crucial in mathematics as it allows us to effectively analyze and compare quantities in various scenarios.

Lesson Notes for Understanding Proportional Ratios

Let's look at the details of the lesson including the definition of proportional ratios and a few examples.

Definition of Proportional Ratios

Ratios are deemed proportional if they are equivalent. This means that even when the quantities of the items being compared change, the ratio remains the same. Let's take a closer look at this concept with some examples.

Example 1: Total-to-Total Proportional Ratios

To illustrate the idea of proportional ratios, let's consider a scenario where we have a certain number of stars and circles.

Understanding proportional ratios as equivalent fractions. Example shown as 4 stars to 7 circles being proportional to 8 stars to 14 circles.

Initially, the ratio of stars to circles is 4:7, which can be represented as the fraction 4/7.
Note that this is a total-to-total ratio because it represents the total number of stars to the total number of circles.
Now, let's double the number of stars and circles. As a result, we have a new ratio of 8:14, which can be expressed as the fraction 8/14.
Despite the change in quantity, the two fractions are equivalent, indicating that the proportional relationship between stars and circles remains unchanged.

Example 2: Part-to-Total Proportional Ratios

Now, let's explore another example to solidify our understanding of proportional ratios. Imagine a rectangle filled with various boxes.

Understanding proportional ratios as equivalent fractions. Example shown as 3 out of 10 being equivalent to 9 out of 30.

In this scenario, the initial ratio is 3 orange squares to 10 total squares, which can be represented as the fraction 3/10.
Note that this is a part-to-total ratio because it represents a partial group of the squares (3 orange) to the total number of squares (10).
Let's triple the number of squares and see what happens. As a result, we now have 9 orange squares and 30 total squares, which can be expressed as the fraction 9/30.
Similar to the previous example, despite the increase in quantity, the two fractions are equivalent, signifying a proportional relationship between the number of orange squares and the total number of squares.

Summary and Practice

In summary, proportional ratios are ratios that remain equivalent even when the quantities being compared change. When represented as fractions, proportional ratios should demonstrate two fractions that are equal to each other. By understanding and applying the concept of proportional ratios, we can effectively analyze and compare quantities in various mathematical scenarios, enabling us to gain deeper insights into the relationships between different quantities.

Try this practice activity to see what you learned. Click on the correct answer.

Video Transcript

In this lesson, we're going to learn about proportional ratios. So what does it mean for ratios to be proportional? Well, ratios are proportional if they are equivalent.

If we have these stars and circles, we could say that their relationship shows that there are four stars to seven circles. And if we want to represent this ratio as a fraction, we could write four over seven.

And say if we wanted to double the number of stars and circles that we have, we could say that we have eight stars to 14 circles, and as a fraction, that would be eight over 14. Well, if you'll notice, these two fractions are equivalent.

Equivalent fractions mean that even though they have different numbers, they still represent the same value. So even when we double the number stars and circles, it still represents that there are four stars for every seven circles. So these ratios are proportional.

Let's look at another example. Here we have a rectangle that's filled with these different boxes. One relationship that we can describe here is that there are three orange squares out of ten total squares. And if we write that ratio as a fraction, it would be three over ten.

And let's say that we wanted to increase the number of squares that we have by tripling the number. So here we have nine orange squares out of 30 total squares as a fraction, that will be nine over 30. And these fractions are equivalent.

So even though we have three times as many squares, the ratio still shows that there are three orange squares out of every ten squares, even when there's nine out of 30. So these ratios are proportional.

So just remember that proportional ratios are equivalent. So when we represent them as fractions, they should show two fractions that are equal to each other.

Related Standard: Common Core 7.RP.A.2

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