What Does multiple Mean
From the Latin multiplus , multiple is an adjective that is used in mathematics and grammar . In mathematics, it is about the number or quantity that contains another or another several times exactly .
An integer r is a multiple of an integer s when there is another natural number that, multiplied by s , gives us the result r . For example: 12 is a multiple of 3 since 3 x 4 = 12 . We then see that if we multiply 3 by 4 , we have as a result 12 , which means that 12 is a multiple of 3 .
If we want to know if one number is a multiple of another, we must perform a division operation between the two. When the quotient is a whole number (and, therefore, the rest of the operation is 0 ), we are dealing with a multiple number of the other. Going back to our previous example, 12/3 = 4 .
The set of multiples of a natural number is infinite . In other words, there are as many multiples of a number as there are natural numbers. The multiples of 3 are {3, 6, 9, 12, 15. 18, 21…} . Let's see the properties of multiples below:
* all integers are multiples of 1, since any number can be obtained by multiplying by 1 (18 x 1 = 18, 134 x 1 = 134);
* if a number a is a multiple of b , it is also given that b is a divisor of a (since 33 is a multiple of 11, 11 is a divisor of 33, since 33/3 = 11);
* 0 (zero) is a multiple of any number, that is, multiplying it by any value gives 0;
* when adding different multiples of a given number, another multiple of it is obtained;
* Similar to the previous point, the difference of two multiples of any number results in a third multiple;
* if a is a multiple of b and this is a multiple of c , then a is a multiple of c ;
* if a is a multiple of b , all multiples of a are also a multiple of b .
Submultiple
A submultiple is any number that another number contains exactly (with a remainder of zero) a certain number of times. For example, 3 is a submultiple of 27, since it contains it 9 times (3 x 9 = 27). Seen from another perspective, for this condition to occur it is also necessary that the second number be a multiple of the first (27 is, in effect, a multiple of 3).
In the real world, in practice, multiples and submultiples have various applications , the most common being the conversion of measurement units to facilitate the understanding of the information; For example, to talk about the length of a road, we usually speak in kilometers, while to express the thickness of a mobile phone, we use millimeters.
Let's look at some of the submultiples of the most used units of measure:
* gram : decigram, centigram and milligram;
* liter : deciliter, centiliter and milliliter;
* meter : decimeter, centimeter and millimeter.
On the other hand, let's analyze the properties of submultiples:
* 1 is a submultiple of any given number, since dividing a number by itself always gives 1;
* all numbers are submultiples of themselves, since they are obtained as a result of their division by 1;
* all numbers are submultiples of 0.
Other meanings
In the field of grammar, an adjective or multiple numeral noun is one whose meaning is generated from the multiplication of a quantity . Double , triple , quadruple and quintuple are examples of multiples: “My room is twice as big as yours” , “The musician was subjected to a triple bypass” .