| Math Mojo - Making Math Meaningful |
In a nutshell: x ( a + b) = xa + xb
Right, but what does that mean? It means that when you multiply any group of monomials by any constant or variable, each monomial ends up multiplied by that number or variable.
Right, but what does THAT mean? In English this time:
It means that, because multiplication is "more powerful"* than addition or subtraction, you have to "distribute" the number you are multiplying to all the numbers that are being added and/or subtracted in the parenthesis.
For example, if you see 8 (4 + 7), you have to "distribute" that multiplication by 8 to all the numbers in the parenthesis.
That would give you 8(4) + 8(7) which is 32 + 56. You can do the rest.If you were given an example with variables, like 2 (3a + 4b) you would get 2(3a) + 2(4b). You know that 2(3a) is the same as 2*3*a, and that is the same as 6a. And 2(4b) is the same as 2*4*b.
Of course, if x ( a + b) = xa + xb, then the reverse is also true:
xa + xb = x ( a + b).Let's take and example of how that might work. Let's say x = 50, a = 6 and b = 7.
That would give us (50 x 6) + (50 x 7).
According to the reverse of the distributive law (actually, either way it is know as the distributive law), (50 x 6) + (50 x 7) = 50 (7+6). That is a lot easier to do. It simplifies to 50 x 13.
*By "more powerful" I mean that it comes earlier in the order of operations.
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