There are a few basic properties of numbers - the three properties of numbers are:
1: The Associative Property
2: The Commutative Property
3: The Distributive Property
Here I will discuss the Distributive Property of numbers and why it is important to math tricks.
Let’s begin with a general formula which demonstrates the distributive property of numbers:
a(b + c) = ab + bc
The way to memorize this property is to think of the number outside of the parentheses as “distributing itself” among the values being added in the parentheses.
So how does this relate to math tricks? Let me give you an example of why understanding this property is useful for doing fast multiplication in your head. Let’s say we want to multiply 8 x 1249. Sure, it looks daunting, but remember that we can break down the number 1249 to:
1000 + 200 + 40 + 9
Now we can do the multiplication in this fashion:
8(1000 + 200 + 40 + 9)
From the distributive property, we know that:
8(1000 + 200 + 40 + 9) = (8 x 1000) + (8 x 200) + (8 x 40) + (8 x 9)
Now the problem is structured such that we can easily solve mentally by first multiplying left to right:
8000 + 1600 + 320 + 72
And then doing the simple addition step to arrive at the answer, 9992.
Subscribe to:
Posts (Atom)