The set of whole numbers arose from the need for man to manipulate negative values, related to commercial and financial matters. In this set, each positive integer has its negative representation. In the multiplication of whole numbers, we must follow some conditions according to the sign of the numbers. In these operations, the signal set is used systematically, according to the following signal table:
( + ) * ( + ) = +
( + ) * ( – ) = –
( – ) * ( + ) = –
( – ) * ( – ) = +
The two numbers have the same sign.
Positive number multiplied by positive number
(+ 3) * (+ 7) = + 21
(+ 5) * (+ 9) = +45
(+ 21) * (+ 10) = + 210
(+ 4) * (+ 9) = +36
(+ 8) * (+ 10) = +80
(+ 22) * (+ 5 ) = +110
Negative number multiplied by negative number
(– 9) * (– 5) = + 45
(–12) * (– 4) = + 48
(– 3) * (– 7) = +21
(– 8) * (– 9) = +72
(– 10) * (– 7) = +70
(–12) * (–5) = +60
The two numbers have the different sign
Positive number multiplied by negative and vice versa
(+ 7) * (– 9) = – 63
(– 4) * (+ 7) = – 28
(– 6) * (+ 7) = – 42
(+ 8) * (– 6) = – 48
(+ 6) * (– 5) = –30
(–120) * (+ 3) = – 360
It is noteworthy that the neutral element of multiplication is the number 1 (one). Look:
(+ 1 ) * ( + 96) = + 96
(–1) * (–98) = + 98
(– 14) * (+ 1) = – 14
(–1) * (+ 9) = – 9
(+ 2) * (+ 1) = +2
(–32) * (–1) = +32
We can see that when multiplying whole numbers by multiplying numbers with equal signs, we have to result is a positive number, and when we multiply numbers with different signs, the result is a number. negative.
by Mark Noah
Graduated in Mathematics
Brazil School Team
Numerical sets - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/multiplicacao-numeros-inteiros.htm
