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:

rule of 3

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

rule of 3

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

 rule of 3

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, but we will apply a different formula:

rule of 3

Let’s look an example:

rule of 3Yesterday, 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

 rule of 3

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!

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