Review the Different Properties of Multiplication
Sometimes multiplying can be complicated but, knowing the tables and the properties of multiplication, we can make this task much easier … Lets go see it!
There are three properties of multiplication: commutative, associative and distributive.
It states that the order of the factors does not change the product, that is, it does not matter if you multiplied 7 × 5 or 5 × 7, the result will always be the same, 35.
Thus, it may be that the multiplication table that was so hard for us to memorize is no longer so difficult, because we can change the order of the factors and, 7 × 5, it is not as difficult, because the table of five is easier: 5 × 7 = 35.
This property and the previous one are two properties of multiplication linked to each other. Thus, this property states that, in a series of consecutive multiplications, the order in which their factors are multiplied makes no difference. So, to multiply 7x5x3, I be the same to solve (7×5) x3 as 7x (5×3), it will always give me 105.
Knowing this property of multiplication, we can easily solve some operations that seem complicated by dividing the factors into products of smaller numbers; For example 7 × 15 can be difficult, but we can express 15 as 5 × 3 and get 7x5x3, which can be solved in several ways according to its associative property:
(7 * 5) * 3
Or as it was at first 7x (5 × 3)
Which multiplication is easier for you?
This is the last of the multiplication properties and states that multiplying a number by a sum (or subtraction) is the same as multiplying that number by adding (or subtracting) and adding (or minuend or subtracting) those results. That is, 7 x (5 + 10) is the same as 7 × 5 + 7 × 10, in both cases the result will be 105.
Therefore, when we encounter a multiplication that seems difficult to us, we can express one of its numbers as a sum and apply the distributive property, like this:
7 × 15 = 7x (5 + 10) = 7 × 5 + 7 × 10 = 35 + 70 = 105
Do you not find the multiplication of 7×5 and 7×10 easier than 7×15?
We end the post with the algebraic expressions that represent the properties of multiplication:
- Commutative: axb = bxa
- Associative: axbxc = ax (bxc) = (axb) xc
- Distributive: ax (b + c) = axb + axc
If you have found these properties curious and useful, you can continue to discover more about them at Smartick.