The operation of division is extraneously linked to multiplication. We say that one is the inverse of the other. But do you know how to carry out the division? And what is the relationship of division with multiplication?
Let's do some examples and try to answer that question!
First, we need to know that each element of the division has a name. In the example, we have the calculation of "ten divided by three” (or 10: 3), using the division algorithm:
The terms of division are: dividend, divisor, quotient and the remainder
Let's try to calculate 125: 5. First, we will analyze the elements of the dividend, answering the questions:
1 is greater than 5? No!
12 is greater than 5? Yea!
Since twelve is greater than five, let's look for a number that, multiplied by 5, comes close to 12. Let's look at multiples of 5:
5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
The result 15 is greater than 12, so it doesn't fit us. Let's use the 5 x 2 = 10.
By multiplying 5 by 2, we get 10 as a product. This was the value that came closest to the 12 that is in the dividend
By subtracting 10 from 12, we get the remainder of 2. To continue our division, we must go down to number 5 (that of the dividend) and place it next to the two, forming 25. So let's repeat the process: what is the number that multiplied by five comes close to 25? let's see:
5 x 1 = 5
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20
5 x 5 = 25
The 5x5 is exactly the number we were looking for. Just complete our division:
We multiply 5 by 5 and get the product 25. This value was what we were looking for.
Since the remainder of the division was zero, we say this is an exact division. If we want to check if our division is correct, we can multiply the quotient by the divisor, that is, 25 x 5 = 125. The result must be exactly the dividend, in the case 125. This process is known as the real proof of division.
Let's look at some other divisions. When the remainder of the division is not zero, we say that the division is inexact, or simply that the division is not exact.
133 divided by 13 and 478 divided by 4 are not exact divisions, while 150 divided by 5 is exact.
By Amanda Gonçalves
Graduated in Mathematics
