Identifying Proportional Ratios

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Introduction and Video

In this video lesson, we will explore three different methods for identifying proportional ratios. By understanding these methods, you will be equipped with the necessary tools to analyze and determine the proportionality of ratios in various scenarios.

Lesson Notes for Identifying Proportional Ratios

Let's look at examples of the three methods including common denominator, cross-products, and converting to decimals.

Method 1: Common Denominator

Let's begin with the first method, which involves the use of a common denominator.

Consider the following example: We are given two ratios set up as fractions, 5/8 and 15/24.
To determine if these ratios are proportional, we need to ensure that the fractions have a common denominator.
In this case, the least common multiple of 8 and 24 is 24. By making both fractions have 24 as their denominator, we obtain 15/24 for the first fraction.
When comparing the fractions, we observe that they are equivalent, showing that the ratios are indeed proportional.

Identifying Proportional Ratios. Example of determining whether two fractions are proportional using common denominators.

Method 2: Cross-Products

Let's move on to the second method, known as the cross-products method.

Let's consider another example: We are given two ratios, 2/5 and 7/9.
To determine if these ratios are proportional, we find the cross-products by multiplying the numerator of one fraction by the denominator of the other fraction.
In this case, the cross products are calculated as follows: 2 multiplied by 9 equals 18, and 5 multiplied by 7 equals 35.
Since the cross-products are not equal, we can conclude that the ratios are not proportional.

Identifying Proportional Ratios. Example of determining whether two fractions are proportional by comparing their cross-products.

Method 3: Converting to Decimals

Lastly, let's explore the third method, which involves converting ratios to decimals.

Consider the following example: We are given two ratios, 7/20 and 21/35.
To determine if these ratios are proportional, we convert the fractions to decimals by dividing the numerators by the denominators.
After dividing, we obtain the decimal equivalents of 0.35 and 0.6, respectively. Since these decimal equivalents are not equal to each other, we can infer that the ratios are not proportional.

Identifying Proportional Ratios. Example of determining whether two fractions are proportional by converting them to decimals and comparing.

Summary and Practice

In this video lesson, you have now learned three different methods to determine whether ratios are proportional to each other. These methods, namely the common denominator method, the cross products method, and the conversion to decimals method, provide a comprehensive approach to solving such problems. By applying these methods, you will be able to confidently analyze and identify the proportionality of ratios in various math scenarios.

Video Transcript

Now we're going to learn how to identify whether or not ratios are proportional. So in these problems, we're going to be given two ratios setup as fractions. And our job will be to determine if they are proportional to each other.

For our first example, we have to determine whether five over eight is proportional to 15 over 24. And we're going to look at three different methods for determining whether the ratios are proportional. For our first method, we're going to make the fractions have a common denominator.

So here's our two fractions and we have a question mark over our equal sign because we're not sure if they are equal to each other or not. And remember that's our goal here. Fractions are proportional if they are equivalent.

So let's make these fractions have a common denominator. Well, the least common multiple of eight and 24 is 24. So we can make both of these fractions have 24 as their denominator. And the one on the right already has 24 as its denominator. So for the fraction on the left, we can multiply its denominator by three because three times eight would give us 24. But we also need to multiply the numerator by the same number.

We always have to multiply both parts of the fraction by the same number. And if we do that, this fraction becomes 15 over 24. And now let's see if it is equivalent to our other fraction. And it is. These fractions are equivalent, so that means that our ratios are proportional.

Here's our second example. Determine whether two over five is proportional to seven over nine. And here we're going to find the cross-products to determine whether they're proportional. So if we set up our fractions here, we're going to find what the cross products of them are.

And remember, cross products mean that we're taking the numerator of one fraction and multiplying it by the denominator of the other fraction. So we're looking at the two numbers that are diagonal from each other. So for this cross product we have two times nine, which is 18.

And for the other cross product, we'll look at the numbers on the other diagonal. Five times seven gives us 35. These cross products are not equal to each other, 18 is not equal to 35. So that tells us that the ratios are not proportional.

Here's our last example. Determine whether seven over 20 is proportional to 21 over 35. And our third method for this one will be to convert the fractions to decimals. So here's our two fractions. And remember to convert a fraction to a decimal, we can divide the numerator by the denominator.

So on the fraction on the left, we're going to do seven divided by 20, which gives us 0.35. And for the fraction on the right, we'll do 21 divided by 35 and that gives us 0.6. And we can see that these decimals are not equivalent. So therefore the ratios are not proportional. So you just learned three different methods that you can use to determine whether ratios are proportional to each other.

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

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