1 X 0 equal to zero
Answers
Answer:
ya....its right.....
Answer:
Explanation:
In my answer I am using 'n' as a shorthand for 'any number')
First the commonsense explanation:
Say you are giving away free apples. An infinitely big apple tree has sprouted in your garden (it's hypothetical) and you have decided to give away apples to each person who comes by. You have decided that you'll give 1 apple to each person that comes by. If one person comes by, you have given away one apple. If two people come by, you have given away two apples. If seventy-five people come by you have given away seventy-five apples. This is multiplication by 1. If there are n people that come by, 1*n tells you how many apples you have given away.
Say you are giving away 2 apples per person. If one person comes by, you have given away two apples. If two people come by you have given away four apples. If thirty people come by you have given away sixty apples. This is multiplication by 2. So if 'n' is how many people came by, 2*n tells you how many apples you have given away.
Similarly, if you are giving away 100 apples per person, 100*n tells you how many apples you have given away in total where 'n' is how many people came by to collect their apples (everyone loves apples).
If you are giving away 0 apples per person, then regardless of how many people come by, how many apples would you have given out by the end of the day? Logically? None, of course! Hence, 0*n = 0.
This also works the other way around, because of the commutative law for multiplication. So lets say no people come by, i.e., n = 0. Regardless of how many apples you want to give away, the total number of apples you have given away will always be 0. Cause no one comes by to take the apples! So a*0 = 0 where a is how many apples you give away per person, which doesn't matter.
Now for an explanation hinging slightly more on mathematical notation:
Multiplication is basically addition, done over and over again. Multiplying a number n by 2 means adding n twice --> n + n
Multiplying a number by 7 means adding it seven times --> n + n + n + n + n + n + n
Multiplying a number a gazillion times means n + n + n ... (a gazillion n's)
So what you multiply 'n' by tells you the number of n you have to add together. If you multiply n by 0, then there are no n's in the picture. Since you are not adding anything, you are left with nothing, aka 0. So:
2*n = n + n (two n's on this side)
7*n = n + n + n + n + n + n + n (seven n's on this side)
0*n = (how many n's do you see on this side? That's right--none!)
An example of 'mathematical proof'
I realize you don't want too much mathematics, but I'd like to point out that it is rather trivial to "prove", using only the basic few axioms (up to the distributive law)
I suppose you do not need much convincing that 0 + 0 = 0 (which itself is a consequence of the additive identity n + 0 = a, with a = 0)
Now, as per the distributive law, n * (b+c) = n*b + n*c
(b and c are two other arbitrary numbers. So there are b oranges and c apples in a bag. A bag is (b+c). If you buy 2 bags, then you get twice the number of oranges and twice the number of apples --> 2(b+c) = 2b + 2c.)
And so n*0 = n* (0+0) = n*0 + n*0, (from the previous bit)
So n*0 = n*0 + n*0
Subtract (n*0) from both sides, giving
0 = n*0
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I presume this is for an elementary mathematics class or something like that? The reason I gave such an involved answer is because I've taught elementary mathematics and this sort of commonsense thinking proved to be quite convincing.
Hope it helps you dear!!!