Know the most common mistakes made when using rule of three

Rule of three is a mathematical method used to determine unknown values ​​in problems with quantities. It's one of the contents that always falls into competition and college entrance exams and that, although it seems easy, many people tend to make mistakes in its use.

Therefore, be aware of most mistakes made when using rule of three and see examples of how to use the rule of three correctly.

Mistake 1 — Not interpreting the problem

Problems involving the use of the rule of three are problems in everyday situations. They involve numbers that express time, distances, length, prices, quantities of things, objects, people, among others.

The first thing to do to solve a rule of three problem is to read the statement carefully. attention and understand what the problem is asking for, that is, understand what result you need to arrive.

Next, you should check what information is available, that is, what data you have and how it can help you solve the problem. Often,

in a statement, there is information that will not even be used.

Not interpreting a math problem and following what was said above is a big mistake made by mathematicians. students, who often go out calculating a lot of things without need because they don't know where they really want to arrive.

Mistake 2 — Not mounting the problem correctly

Many students also get confused when setting up the rule of three problem. This happens due to lack of clarity about the method or even lack of attention and wanting to solve problems automatically.

It is necessary to know that rule of three is a procedure used to find a value in a proportion, which is nothing more than an equality between two reasons.

But what are reasons? Ratios are divisions between two numbers, represented as a fraction. They are used to compare values ​​of a quantity.

Thus, in a rule of three problem, we must assemble the ratios and equate them, obtaining a proportion. However, this is not done randomly, this assembly depends on the interpretation of the problem and the way in which the data are related.

Example 1: In an orange cake recipe, you call for 3 eggs for every 2 cups of flour. Renata decides to increase the recipe and use 6 cups of wheat flour. How many eggs should Renata use?

• What do we need to determine? x amount of eggs.
• What do we know? That the amount of eggs is related to the amount of wheat flour, and the more flour, the more eggs.

Information table:

flour cups	egg units
2	3
6

Fitting Aspect Ratio:

Attention! This is the correct way to set up this problem, if we change order 2 and 6, or 3 and x, the final result will be wrong.

Cross-multiplying, we get the value of x:

Therefore, Renata should use 9 eggs for 6 cups of wheat flour.

Error 3 — Not checking if the magnitudes are directly or inversely proportional

Rule of three problems involve at least two quantities. These quantities can be related in two possible ways, we can have directly or inversely proportional quantities.

In each of these cases, the use of the rule of three is different. So, we must understand the difference between these types of magnitudes.

When an increase in the value of one quantity leads to an increase in the value of the other quantity, they are directly proportional quantities. However, when an increase in the value of one quantity leads to a decrease in the value of the other quantity, or vice versa, they are inversely proportional quantities.

In the example of the orange cake, the amount of flour and the amount of eggs are directly proportional, because by increasing the amount of flour, we increase the amount of eggs.

Now, let's see an example of using the rule of three with inversely proportional quantities, in which we must invert the order of one of the quantities before cross-multiplying.

Example 2: In a store, the average waiting time for service is 5 minutes when there are 8 agents working. What will be the average wait time if the number of agents is reduced to 6.

• What do we need to determine? Waiting time x.
• What do we know? That the number of attendants is related to the waiting time, and the fewer attendants, the longer the waiting time.

Information table:

Number of attendants	Waiting time
8	5
6

The magnitudes are inversely proportional, so when setting up the proportion we must invert the order of the number of attendants or invert the order of the waiting time.

Fitting Aspect Ratio:

Cross multiplying:

Therefore, if the number of attendants is reduced to 6, the average waiting time will be approximately 7 minutes.

Error 4 — Not checking if the result obtained is consistent

Whenever we use a rule of three, we must know what the value found means and check whether it is consistent or not.

In example 1, the orange cake, an x ​​value less than 3 would already indicate that the rule of three was not used correctly. For, you see, if 2 cups of flour require 3 eggs, then 6 cups of flour require much more than 3.

In example 2, of service time, an x ​​value less than 5 would indicate something wrong. Just observe that if with 8 attendants the waiting time is 5 minutes, then with 6 attendants the time must increase and not decrease, it must be greater than 5 minutes.

In addition, we can always substitute the value found in the proportion and check if the product of the extreme terms is equal to the product of the middle terms. If so, the rule of three is correct.

You may also be interested:

• List of Rule of Three Exercises
• Exercises on the rule of three compound
• Mathematics tips and tricks for the Enem