In multiplication we will have to express the increase in quantities, we will perform multiplication in order to reduce the operation of addition (addition), so multiplication is a mathematical tool that makes it possible to reduce numerical calculations of addition. Now we will see how it can happen.
3+3+3+3+3=15
3×5=15
Notice my dear student in addition the number three was repeated five times, while in multiplication, the numerical term three was multiplied by five, which is the number of repetitions that the number three had in the sum. It is possible to notice that the answer obtained is the same, both in the addition operation and in the multiplication.
Property of Multiplication
Commutative property
The commutative property defines that it doesn’t matter what order of the values you’re multiplying. You can swap the order and the result is the same.
5 x 6 = 30 and 6 x 5 = 30
Since a and b are any real numbers, the commutative guarantees that
a x b = b x a
Distributive property
The distributive property is used when a number is multiplying an addition or subtraction. Just multiply each term separately and add or subtract the result.
3 x (7 + 4) = 3 x 7 + 3 x 4
We distribute the multiplication from 3, to 7, and to 4.
With letters it’s the same thing
A x (B + C) = A x B + A x C
Associative Ownership
The associative property tells us that if you’re multiplying three or more numbers, you can associate the factors in different and more convenient ways.
(7 x 4) x 5 = 7 x (4 x 5)
Neutral element
The number 1 is called the neutral element of multiplication, not for nothing. See the following examples:
51 x 1 = 51
In a multiplication, the number 1 does not change the result, it is neutral.
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