Multiplication is repeated addition. It says if I add a number (let’s say 3) together some number of times (say 6), what does that give me? 3 x 6 = 18
Division is basically repeated subtraction. If I have some number (let’s say 18), how many times can I subtract this other number (like 6) from it. 18 ÷ 6 = 3
How many times can you subtract 0 from 18? Infinity times. Since infinity is not a number, but an idea you cannot divide by 0.
You can have zero groups of something.
What you can’t do is work out how many groups of zero objects you would need to total another number than zero.
Ten million groups of zero objects won’t even get you to 1 object in total, nor will 20 million groups, or 12, or 500 billion.
And though zero is an exception, that doesn’t help either. Zero groups of zero objects will total zero. But so will 1, 2, 3, 50 quintillion. So what’s the ‘answer’ when you divide by zero? Either no answer at all, or every single possible answer imaginable.
Multiplying is easy. Dividing by zero is impossible and gives only nonsense answers.
Let’s say you had a box of 10 tomatoes.
Multiplication says: if you take many of these boxes, how many tomatoes will you have?
Division says: How many of these boxes do you need to get a 100 tomatoes?
Now say you had a box of 0 tomatoes.
Multiplication says: if you take many of these boxes, you will have no tomatoes.
Division says: How many of these boxes do you need to get a 100 tomatoes?
…
…
Uhh. You have the crashing realization that you can’t get a 100 tomatoes no matter how many boxes you take. And moments after, the computer simulating all of us explodes in a puff of 1s and.. you guessed it, 0s.
If you have any number of things in a row it is n x 1 = n. Now you have any number of things with no row which is n x 0 = 0.
If multiplication is repeated addition then division is repeated subtraction. When you divide by 0 you are subtracting 0 from another number infinitely and you never get anywhere.
Just like multiplication is repeated additions, division is repeated subtractions.
You have 12 apples and want to divide them among 4 people. So the question is, how many times can you take 4 from 12?
1. 12 – 4 = 8
2. 8 – 4 = 4
3. 4 – 4 = 0
3 times.
Now then. You have 10 apples and want to divide them among 0 people. So the question is, how many times can you take 0 from 10?
1. 10 – 0 = 10
2. 10 – 0 = 10.
Uh-oh.
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