How many times did you fall asleep in math classes thinking that so many numbers had nothing to do with your life? And the teacher who woke you up all the time. But now we will show you the usefulness of knowing how to apply calculations with the rule of three; so that you think twice before getting bored again in a class.
The truth is that we perform this operation daily without realizing it: when we go to the market, when we pay debts or when you simply organize our room. How can this be? Easy, the rule of three consists of solving problems related to proportionality, between three or more already known values, from an unknown.
Now, you will be thinking that you stayed in the same; but actually solving proportionality problems is more common in everyday life than you might think. For example, a typical case is found in the kitchen; when extra relatives show up at the last minute for dinner and we’ve already bought the bread. So, we ask ourselves the following question: if with two loaves we eat four people, and now two more people have joined, how many loaves should I buy so that we are all comfortable?
Quickly, logically we know the result, thanks to the practice we have in distributing food equally among the diners at our family table on a daily basis. However, what you often ignore is that you are solving a rule of three problem known as simple-direct.
Live and calculate
In other words, there are infinities of calculations that we do every day that involve a mathematical operation to find the proportionality of a fourth term within a linear relationship between three or more values. There are many examples, in this post we will give you some, but the most important thing is to try to solve real life situations aware of the application of this rule.
Generally, in the educational environment, the rule of three is taught from a more abstract than functional perspective; That is why many students get bored in math class. However, formalisms can be learned from a more functionalist application; collaborating with this to guarantee meaningful and useful learning.
What do we mean by this? Well, first of all, mathematics and calculation operations are part of life; and for this reason they must be studied while living. In other words, don’t stay in formalities kid and live that it’s three days. Learning mathematics is not pure pen and paper, we use it the most in the kitchen, at work, putting on makeup, cleaning the house and even in the park, much more than in a notebook.
Instructions for Rule of Three – solve a Rule of 3
There are different types of rules of three: the simple direct, the simple inverse and the compound. Which we are going to explain below so that you can learn to solve a rule of three.
The simple rule of three
In this type of rule of three called simple, you will have to establish a proportional relationship between two values; these must be known and we can formally call them “A” and “B”; thus, knowing a third value called “X”, you will calculate the fourth value called “Y”.
The proportionality relationship can formally occur directly or inversely. You will know that it is a direct relationship when the greater the value of “A” you get the greater the value of “B”. On the other hand, when it is an inverse relationship, you will find that the higher the value of “A” falls, the lower the value of “B”.
The simple-direct rule of three
The direct simple rule of three is based on the proportional relationship between its values. For example, when you are going to organize the relationships between values, the proportionalities must go on the same side. Analyze the following exercise so that you can better visualize what we have explained to you:
If five dogs have 10 bones, and you want to know how many bones you need for 7 dogs; the number of dogs must go on the same side, as follows:
Number of dogs → Number of bones
5 10
7X
So that 5 is directly proportional to10, as X is to 7, where X is equal to the product of 7 times 10, divided by 5; which results in 14.
Let’s look at another everyday example: if you need 8 liters of water to make 2 kilos of pasta, how many liters of water will you need to cook 5 kilos of pasta?
This problem is one of the typical ones that arise in the kitchen; which you can interpret in the following way: the relationship is absolutely direct; since, the greater the number of kilos of pasta, the more liters of water will be needed, and you can represent it like this: (2X 5)/8= 1.25
The simple-inverse rule of three
In this type of rule of three, known as simple-inverse, for the given product to remain constant, the increase in one of its values will imply the decrease in another value; thus the product will remain constant. This relationship specifically can be represented as follows: A is inversely proportional to B, just as X is to Y, with the value of Y equal to the product of the value of A times B, divided by X. A →B, X →Y; where Y=(A x B)/X
To make it clearer, we give you the following example: if 8 masons build a wall in approximately 15 hours, how long will it take 5 masons to build the same wall? Obviously, it is obvious that the more masons working on the site, the fewer hours it will take to build the same wall. Of course, assuming that they all work at a similar or proportional rate.
So, we say that:
Bricklayers Hours
8 15
5 ?
The total hours of work on the site to build the wall would be 120 hours, which can be done by a single bricklayer that takes 120 hours, 2 bricklayers in 60 hours, 3 bricklayers will require 40 hours, and so on. As you can see, always in all cases, the total number of hours remains constant. Therefore, we are dealing with an inversely proportional relationship.
The compound rule of three
In some cases they will get you that the problem posed involves more than three known values, in addition to the unknown. Take a look at this example, which we will present below to give you an idea of how to resolve this issue:
If you need 12 men to lift and carry a 100-kilogram rock, how many men will you need to lift and carry a 75-kilogram rock over a 26-hour period?
If you look closely, you will get two implicit proportionality relationships in the exercise. In addition to this, to make the problem more complex, you will notice an inverse relationship and another that participates as a direct one. So, logic tells us that if you need 12 men to lift and transport a rock weighing 100 kilograms, obviously to transport a rock weighing 75 kilograms (less weight – less effort) you will need fewer men.
Therefore, since the smaller the rock, the less number of men needed: we are talking here about a direct proportional relationship. On the other hand, if you have 15 hours for 12 men to move the rock, of course, having 26 hours will require fewer men. In other words, increasing one value decreases the other; Therefore, in this case it is an inverse proportional relationship.
The problem can be stated as follows: 100 kilos are 15 hours with 12 men, just as 75 kilos are 26 hours with “Y” men.
Do not get involved with the statement, which are only style formalities in the mathematical language. Simply the solution to the problem is based on multiplying 12 x 75 and then by 15; then, you divide the result by the product of 100 x 26. In short, 13,500 / 2,600 yields 5.19 as a result; which, by rounding, equals 6 men, since 5 men would not be enough to perform the required action.
What do you need for Rule of Three – solve a Rule of 3?
- Paper.
- Feather.
- Calculator.
- Relaxed mind.
- Three or more values and one unknown.
- Implicit mathematical operations: division, multiplication and addition.
Tips for Rule of Three – solving a Rule of 3
- It already puts aside the prejudice that mathematics is difficult. Open your mind and your eyes and realize that calculating is in everything you do on a daily basis and without realizing it you constantly apply numerous operations without any complications.
- Before embarking on any mathematical problem, you have to take into account the importance of knowing the theory, so that the processes are carried out properly.
- Writing down a summary of the theory will help you to have the procedure as a cheat sheet, in case you are forgetting a step, you can check there and verify that you are on the right track.
- Generally, we solve problems on a daily basis in our lives by applying the rules of thumb, but we don’t realize it. For this reason, now you will be able to be more aware of these cases and thus you will be able to practice when a situation arises that merits the learned mathematical procedure.
- Remember that to solve compound rule of three problems you must consider each type of implicit rule of three separately, to avoid confusing values.