Cross Multiply Fractions — Simple Steps and Practical Examples

The truth is that fractions are a stumbling block for many. In fact, when most people see them, their heads start to spin, right? Well, that’s all because fractions are too complicated to deal with.

But this complexity takes up a notch when you have to simplify or find the smaller and larger from a group of fractions. So, if you also find yourself in a similar situation, you need to learn the art of cross multiplying fractions. And that’s exactly where this topic will come in handy.

In this blog post, we’ll elaborate on how to cross multiply fractions with the help of the simplest of steps. We’ll start by explaining this concept. But as we move along, we’ll also share its implementation with respect to the other scenarios related to the cross multiplication of fractions. This will help you understand everything completely. So, let’s dive in here without any further delay!

What Is Cross Multiplication?

The term ‘cross multiplication’ refers to a technique in mathematics that revolves around the following problems:

• Solving equations involving fractions.

OR

• Simply comparing two fractions.

As the name of this strategy describes, it involves multiplying two fractions in the cross. This means that the numerator of one fraction will get multiplied by the second fraction’s denominator and vice versa. And whatever the resulting fraction you’ll get, you will have to compare or use it to solve the equation. 

But now, the million-dollar question is why people use this technique. Well, to put it simply, this useful mathematical strategy proves helpful in the following scenarios:

• When your fractions don’t have the same denominator, like this: 3/4 and 2/3.
• When you have to solve fraction equations that involve unknown variables, like this: x/5 = 3/4.

How to Cross Multiply Fractions?

So far, you may have developed a theoretical understanding of cross multiplying fractions. If so, let’s now discuss how to apply this handy mathematical technique. 

So, in order to perform cross multiplication fractions here, you simply need to take the product in the following way:

• The first fraction’s numerator and the second fraction’s denominator.
• The second fraction’s numerator and the first fraction’s denominator.

Let’s understand this better through an example. Consider the following template of two fractions:

a/b and c/d

Now, by applying the two rules above, the equation will become:

a x d  and  c x b

Hence, that’s the simplest way to take the cross-product of any two fractions!

When Do You Cross-Multiply Fractions?

If you are following this blog post from the beginning, you may have learned by now what cross multiplication of fractions is and how to apply it practically. But you need to understand that you can’t apply this mathematical technique wherever you want. Its implementation is only possible in specific scenarios. Here is a list of those situations:

1. During Comparing Two Fractions

There are times when you have to compare two fractions and find the largest or smallest one out of both. In such circumstances, you can cross multiply fractions and reach a conclusion.

2. For Solving Equations Involving Fractions

In mathematics, sometimes, you have to compute two fractions to find the value of the unknown variable. So, cross multiplying fractions is the only way to solve such math puzzles.

3. When Checking for Proportions

Since cross multiplication fractions can help you determine which fraction is smaller or larger, you can use this conclusion when checking for proportions. For instance, if the comparison states that both fractions are equal, it means that they are in proportion.

4. For Solving Various Real-World Problems

You may have dealt with a problem in your daily life that involves ratios. Such a challenge often occurs when:

• Finding probabilities.
• Scaling recipes.
• Solving rate problems.

So, if you want to solve such real-world mathematical queries, you must learn how to take the product of fractions in the cross.

However, cross-multiplication of fractions will only help your cause if you possess basic computation skills. So, in case you don’t or you want to take the product of fractions in a snap, try the assistance of a fraction calculator. With this tool, you don’t have to calculate anything manually. You just need to input the values and choose the multiplication symbol. This utility will use its AI algorithms to accurately find the product of the entered values and give you a step-by-step explanation. So, by using it, you can perform the art of cross multiplying fractions more effectively.

Cross Multiply Fractions to Compare Unlike Fractions

As we’ve briefly discussed above, you can perform the cross multiplication of fractions to compare two fractions. But this is valid only for fractions having different denominators. In fact, that’s one of the reasons for the popularity of this handy mathematical strategy. So, here is a step-by-step explanation of how to do that:

Step 1: Apply the Rule of Cross Multiplying

First of all, you need to cross multiply fractions using the two rules mentioned above. So, let’s say that you want to compare the following two fractions:

7/10 and 5/8, where,

a = 7, b = 10, c = 5, d = 8

In such a situation, the result will be as follows:

7 x 8 = 56 (ad)

5 x 10 = 50 (cb)

Step 2: Compare the Product and Obtain Conclusion

Next, you simply need to compare the results obtained from the product and use the following rules to reach a conclusion:

• If the resultant products of two fractions are equal, this indicates that both fractions are equal.
• Suppose the product of the first fraction’s numerator and the second fraction’s denominator (ad) is greater than that of the second fraction’s numerator and the first fraction’s denominator (cb). In that case, the first fraction (a/b) will be greater than the second fraction (c/d).
• On the other hand, let’s say that the product of the first fraction’s numerator and the second fraction’s denominator (ad) is lesser than that of the second fraction’s numerator and the first fraction’s denominator (cb). In such a situation, the first fraction (a/b) will be smaller than the second fraction (c/d).

So, let’s apply these rules to the result obtained in the previous step and reach a conclusion.

As you can see, ‘ad,’ which is ‘56,’ is bigger than ‘cb,’ which is ‘50.’ This means that the first fraction (7/10) is greater than the second fraction (5/8).

Cross Multiplication to Compare Ratios

As the above-specified scenarios of fractions’ cross multiplication state, you can apply this technique to compare ratios. So, let’s now discuss how to do that step-by-step. To make things easier, we’ll take assistance from this example:

Let’s say that you’ve got a math puzzle where you have to determine if the following ratios are proportional:

2 : 3  and  4: 6

Now, to solve this problem, simply use the following instructions:

Step 1: Write Ratios as Fraction

First, write the given ratios in the form of fractions. So, the above expression will take the following shape:

2/3 and 4/6

Step 2: Apply Cross Multiplication

Then, cross multiply fractions using the above-specified rules. Upon implementing this step to the example taken here, we’ll get the following results:

2 x 6 = 12

4 x 3 = 12

Step 3: Compare the Obtained Products

Using the rules discussed previously, we can quickly reach a conclusion. As you can see, the product of both fractions is equal, which means that the ratios are proportional.

Cross Multiply Fractions With Variables

As we’ve already mentioned above, cross multiplying fractions also assist in finding the value of unknown variables involved in an equation. So, here is how to apply this technique for such a scenario:

Step 1: Identify the Fractions

The first thing you need to do is to identify the fractions according to the following universal template:

a/b and c/d

So, let’s say that you want to conduct cross multiplication fractions for the following equation:

3/4 = x/8

In that case, your fraction’s identification will be as follows:

a = 3, b = 4, c = x, d = 8

Step 2: Use the Cross Multiplication Rule

Next, it’s time to apply the rule of cross multiplying. So, in the case of the sample fraction (3/4 = x/8) taken in the previous step, the result will be as follows:

3 x 8 = 2 x 4

x x 4 = 4x

Step 3: Set Up the Equation

Now, you need to set up the result of the product (ad and cb) in the form of the equation. So, here is the template for doing that:

ad = cb

By replacing this equation with the resultant values of the second step, this is how the whole equation will set up in our case:

24 = 4x

Step 4: Solve for the Unknown

Finally, it’s time to solve the whole equation for the unknown variable, which in our case is ‘x.’ To do that, use the following approach:

• First, separate all the numbers on one side and the unknown variable on the other side.
• Then, compute to find the final value of the unknown variable.

So, in our situation, here’s what this whole scenario will look like:

24/4 = x

6 = x

Hence, the final value of the unknown variable (x) in this case is ‘6.’

When Cross Multiplication Is Not Applicable?

Cross multiplication is not a versatile mathematical strategy. So, you can’t apply it everywhere. And since we’ve already discussed when do you cross multiply, let’s now share when it is not correct or feasible to implement this technique. So, here are a few scenarios related to this:

• You can’t implement this strategy when dealing with fractions that need to be added or subtracted.
• You can’t apply cross multiplication if you intend to reduce a fraction to its lowest form.
• If you’re comparing fractions with the same denominator, you can’t cross multiply them.
• This technique only works for equations involving fractions. So, if you are dealing with a problem that doesn’t include any fractions, it will be impossible to apply this strategy.

Practice Questions (1-4)

By now, you may have completely understood cross multiplication fractions. So, if that’s the case, you can apply your knowledge to the following questions and check where you stand:

1. Check whether the fractions 7/12 and 5/8 are proportional.

2. Compare  3/4 and 9/12 find out which fraction is larger.

3. Find the value of ‘x’ in the following equation: x/5 = 3/7

4. Two recipes require the following ratios of sugar to flour:

Recipe A: 2 :3

Recipe B: 5 :8

Check whether ‘Recipe A’ uses less sugar relative to the amount of flour or the ‘Recipe B.’

Key Takeaways

To summarize this blog post, it won’t be wrong to claim that cross multiplication is a simple yet powerful way of working with various fractions. That’s because it goes well with both comparing values and solving equations. But like with every other thing, mastering this strategy will take you both time and effort. So, practice with different examples, such as the ones discussed above. Doing so will help you gain confidence. And eventually, you’ll see how valuable this skill is in both academics and real-life scenarios.