THE multiplication is one of basic math operations. It is a natural evolution of addition, as it is defined so that it represents the sum of a certain number of sets that have the same amount of elements.
For example: it is usual to buy many copies of the same product in supermarkets. If you buy eight products that cost BRL 2.00, the total to be paid will be BRL 16.00, because we add the amount R$ 2.00 eight times. Therefore:
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16
That sum can be represented by the symbol “x” or “·”. In the previous example:
2x8 = 2·8 = 16
Thus, we add eight sets of 2 reais each. In this example, the numbers 2 and 8 are named factors and this operation should be read as follows: two times eight equals sixteen.
In other words, multiplication is a way to make adding equal numbers easier. The following image contains all the results of multiplications involving factors 1 to 10.
Multiplication Algorithm
Knowing the result of multiplications that involve only factors less than or equal to 10, we can define an algorithm that is capable of performing any
multiplication. This algorithm will be described below from the following example: 25x482.First write the numbers from the units' box, aligning them.
482
x 25
the first number to be multiplied it is the home of the units in the second line. It should be multiplied by all the first number starting from the ones square. In this case, 5x2 = 10. In the algorithm above, we will write:
1
482
x 25
0
Note that the value of units is in the result and the value of the tens “goes up”. now it's time to multiply 5x8. Remember of add the ten that "came up" to the result of this multiplication. So, 5x8 = 40 and 40 + 1 = 41. Soon, we will have in the algorithm:
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4 1
482
x 25
10
Finally, we'll multiply 5x4 = 20, which, added to 4, makes 24. As there is nowhere else to "climb", this result will be placed in its entirety in the appropriate place.
4 1
482
x 25
2410
Finished the multiplications referring to the digit 5, we will start the multiplications referring to the digit 2. Note that this number is in the tens place, so the first multiplication it should also be placed in the tens place, just below 2410. Watch:
482
x 25
2410
4
Now multiply 2x8 = 16, leave 6 and “go up” 1.
1
482
x 25
2410
64
Finally multiply 2x4 = 8 and add 1 to the result (8 + 1 = 9). In the algorithm, we will have:
1
482
x 25
2410
964
To finish the calculation, add the two results found:
1
482
x 25
2410
+ 964
12050
Multiplication Properties
there are four multiplication properties and one involving multiplication and addition. Check out:
Commutativity: The order of factors does not change the product, that is, consider the real numbers a and b, we will have:
a·b = b·a
associativity: The order in which three factors are multiplied is irrelevant. In other words, consider a, b and c belonging to the real numbers, we will have:
(a·b)·c = a·(b·c)
Existence of a neutral element: The number 1 does not change the result of a multiplication when it is a factor. Thus:
1·a = a·1 = a
Existence of an inverse multiplicative element: Whatever the real number, there is another real number that, multiplied by it, gives 1. In other words, consider The belonging to the set of real numbers, there is 1/a such that:
a·1/a = 1
Distributivity: The product of a real number by a sum is equal to the sum of the products of the parcels by the real number, that is, consider a, b and c real, we will have:
a (b + c) = a·b + a·c
By Luiz Paulo Moreira
Graduated in Mathematics
Would you like to reference this text in a school or academic work? Look:
SILVA, Luiz Paulo Moreira. "What is multiplication?"; Brazil School. Available in: https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-multiplicacao.htm. Accessed on June 27, 2021.
