How To Use Cross Products To See If Each Pair Of Ratios In 2023

Introduction

When working with ratios, it’s important to ensure that they are in proportion. One way to check whether two ratios are in proportion is by using cross products. In this article, we will discuss what cross products are and how to use them to check ratios.

What Are Cross Products?

Cross products are the products of the numerator of one ratio and the denominator of the other ratio. For example, if we have two ratios: 2/3 and 4/6, the cross products would be 2 x 6 and 4 x 3, which are both equal to 12.

Why Use Cross Products?

Cross products are used to check whether two ratios are in proportion. If the cross products are equal, then the ratios are in proportion. If the cross products are not equal, then the ratios are not in proportion.

How to Use Cross Products

Using cross products is a straightforward process. Let’s consider the following example:

John has 12 apples and 16 oranges. His friend, Jane, has 18 apples and 24 oranges. Are the ratios of the number of apples to oranges the same for both John and Jane?

Step 1: Write the Ratios

First, we need to write the ratios for John and Jane. John’s ratio is 12/16, and Jane’s ratio is 18/24.

Step 2: Cross Multiply

Next, we cross multiply the ratios. For John, the cross product is 12 x 24, which equals 288. For Jane, the cross product is 18 x 16, which equals 288. Since both cross products are equal, the ratios are in proportion.

Step 3: Interpret the Results

Since the cross products are equal, we can conclude that the ratios of the number of apples to oranges are the same for both John and Jane.

When to Use Cross Products

Cross products are useful when comparing two sets of numbers or ratios. For example, cross products can be used to compare the price of items in two different stores or to compare the speed of two different cars. In both cases, we can use cross products to determine whether the ratios are in proportion.

Conclusion

Cross products are a handy tool for checking whether two ratios are in proportion. By following the steps outlined in this article, you can use cross products to compare ratios in various situations. Remember, if the cross products are equal, the ratios are in proportion!