In today’s post we are going to work on **proportions**. This time we will look at a way of solving direct and inverse proportions: **the rule of 3**.

#### What is the rule of 3?

The **rule of 3** is an operation that helps us quickly solve both direct and inverse** proportion** word problems.

In order to use the rule of 3, we need **three values; **two that are proportional to one another, and a third. From there, we will **figure out the fourth value**.

#### Direct rule of 3

We will begin by looking at how to apply it **in the case of direct proportions**.

We will place the **3 values** (which we will call **“a”**, **“b”**, and **“c”**) and the unknown value that we want to figure out (**“x”**) in a table. Next, we will apply the following formula:

We are going to solve the following problem as an example:

*Upon arriving at the hotel, the staff gave us a map displaying the places of interest in the city, and told us that 5 centimeters on the map represented 600 meters in reality. Today we want to go to a park that is located 8 centimeters from the hotel on the map. How far from the hotel is the park?*

Let’s **make a table** with the 3 values and the unknown value (“x”), and we will find “x” **with the formula** that we have just learned.

__Centimeters on the map__ __Meters in reality__

** **

Answer: **The park is located 960 meters from the hotel**

#### Inverse Rule of 3

Now we will look at how to apply the rule of 3 **in the case of inverse proportions**.

We will place the 3 values and the unknown value in the *table, just as we did** in the previous case, b*ut **we will apply a different formula:**

*Let’s look an example:*

*Yesterday, 2 trucks transported goods from the port to the warehouse. Today, 3 trucks, the same size as yesterday, will have to make 6 trips to transport the same amount of goods from the warehouse to the mall. How many trips did the trucks make yesterday?*

We place **the values** in a table and **apply the formula **for the **inverse rule of 3**:

** Trucks Trips Necessary**

* *

Answer: **Yesterday, 2 trucks made 9 trips each**

What did you think of this post? Isn’t it easy to apply the rule of 3 to proportion word problems!

You can learn more about direct and inverse proportion with this previous post on our blog: Rule of three problems

Remember that you will be able to practice **exercises, proportion word problems** and **much more with Smartick!**

### Learn More:

- Direct and Inverse Rule of Three Problems
- How to Solve Problems With Distance Conversions
- How to Apply The Associative Property in a Problem
- Proportionality Problems: Learn How to Solve them
- Adding With an Unknown Quantity

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This example doesn’t show why it works or how to differentiate one formula versus the other. Understanding the relationship between the numbers is key, and this doesn’t even touch in that.

Hi Cindy,

Thanks for your comment! We previously published a blog post on direct and inverse proportions with some problems, which describes how to identify and differentiate them in more detail. We’ve edited the Rule of Three post to include a link to it, you can read it by clicking here: https://www.smartickmethod.com/blog/index.php/rule-of-three-problems/