There are few moments in which we reflect on the mechanisms we have in mathematics to carry out our tests. Therefore, we must pay attention to the meaning of all the numbers that are involved in these mathematical procedures.
One of the elements that deserves due attention is the rest of the division, which is often overlooked and misinterpreted. Because of this, we will see situations in which the rest must be analyzed and interpreted according to the situation in which the division is used.
See the calculations that two students performed for the same problem.
“ABCDEFGH school will take its 895 students on a trip and for that it will rent several buses. Each bus holds a maximum of 50 people, how many buses will the school rent?”
Note that the two students split equally and got the same result, but they got different answers, check Peter's answer:
“Since I got a quotient of 17, the school should only rent 17 buses.”
Lucas replied:
"I don't think so, Pedro, by my calculations the school should rent 18 buses."
Stop and reflect on the conclusion of these two students, which one do you believe is correct?
The two friends continued talking about this problem, with this Lucas asked his friend Pedro: "Pedro, how many people can go on 17 buses?"
Pedro replied: “Hmmmm, each bus fits 50 people, the 17 buses fit 17x50 which is equal to 850. So in 17 buses fit 850 people!”.
With that Lucas questioned his friend again: “And how many people will go on this trip? Are you sure that only 17 buses will be able to take everyone?”.
With that, Pedro admitted that he had been wrong in his calculations.
Let's see what Peter forgot to analyze in his division. For this, we must understand what each number of this division represents:
The number 895 (dividend) represents the total number of students, while the number 50 (dividend) represents the number of students on each bus. When we multiply 50 by 17 we get 850 which is the maximum number of students on 17 buses. Subtracting 895 by 850, we get 45, which in our division is the remainder.
This number 45 deserves special attention, as it is not just a number. It represents something, but what is this thing? Note that “45” came from the subtraction of two numbers that represent people! Therefore, ignoring this rest is the same as saying that 45 people will not be on the tour, as 17 buses hold only 850 students. That's why Pedro said that 18 buses were needed for this tour, so that the other 45 students wouldn't be without traveling.
Therefore, it is important to know the meaning of each number in our division, so that we can understand what the number obtained in the rest actually means in the calculation.
By Gabriel Alessandro de Oliveira
Graduated in Mathematics
SchoolKids Team
