Page 4 - Matematica_Mathematics - Teorema impartirii cu rest_The Long division theorem

4. The long division theorem (“Teorema împărțirii cu rest”)

The theorem is a sentence whose truth we establish by a demonstration.

Suppose you told your colleagues or
friends that you can do something special,
such as guessing a playing card from a stack
or spinning the ball on a finger. If they showed
signs of doubt, you told them, “I can prove it to
you!” and you showed them that you can do that.
Much the same thing happens when you want
to make a mathematical demonstration, only
this time you will use a series of calculations,
reasoning to show the truth of a statement.

In fact, you did such demonstrations in the primary classes, let’s say - when you learned the division.
First you learned that division is a repeated subtraction of equal terms.
Let’s take an example: 12 : 4

We calculate in the following way:
12 – 4 = 8
8 – 4 = 4

4 – 4 = 0

We see that we dropped 3 times 4 until we reached 0, so 12 : 4 = 3
But it’s a bit complicated and takes a lot of time to solve, so you’ve been looking for a easier solution,
starting from the fact that division is the reverse operation to multiplication. Therefore, if 9 × 3 = 27, then

27 : 9 = 3 and 27 : 3 = 9.

Practice
1. Find out the product of numbers 15 and 7, then make the verification using division.

Taking a practical situation, if you have 12 candies
and you want to split them equally to 4 friends, each of
them will get 3 candies.
If you want to give 4 candies to each one, you would
have to have 16, because 4 × 4 = 16.