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rayj00

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Can someone explain to me like I am a 2nd grader, Why, if you have something and want to multiply it by two, you then have 2 somethings. Yet, when you don't want to multiply it by anything, meaning zero, you end up with zero? Why has my "something" disappeared?
 
1*2 means 1+1 =2.
Just like 5*4 means 5+5+5+5. Multiplication is repeated addition.
0*4 means 0+0+0+0 = 0...............................edited

Why has something disappeared? It didn't disappear. You had 0 and you still have 0.
 
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OK, second grade.

Multiplying by 2 means replacing each of the items you have with 2 of them. If I have 3 apples, I replace each of them with 2 apples and end up with 2+2+2 = 6.

Multiplying by 0 means replacing each of the items you have with 0 of them. If I have 3 apples, I replace each of them with 0 apples and end up with 0+0+0 = 0.

Or, you could say that multiplying by 2 means taking your whole set away and replacing it with 2 identical sets. If I have a set of 3 apples, I replace that with 2 sets of 3 apples, so I have 3+3 = 6.

The same way, multiplying by 0 means taking your whole set away and replacing it with 0 identical sets. If I have a set of 3 apples, I replace that with 0 sets of 3 apples, so I have 0.

The key idea that people tend to miss here is replacement. You aren't adding to what you have; you are taking away what you had and replacing them with something new.
 
rayj00 said:
Can someone explain to me like I am a 2nd grader, Why, if you have something and want to multiply it by two, you then have 2 somethings. Yet, when you don't want to multiply it by anything, meaning zero, you end up with zero? Why has my "something" disappeared?
Click to expand...
Now I'll give you a slightly higher level, maybe third grade, maybe tenth:

When you don't multiply a number, that's not multiplying by zero. You're probably thinking of adding zero, which leaves the number unchanged. (We call 0 the additive identity.)

When you leave a number unchanged, you're multiplying by 1. (We call 1 the multiplicative identity.) That's because you're taking away 1 of each object, and replacing it with ... 1 of the object. Nothing changes.

Multiplying by zero does something very different. It doesn't leave things unchanged; it erases them. It replaces them with nothing. (And that's why zero is such a dangerous thing in algebra: When you multiply by zero, there's nothing left, so you can't undo what you did. You can't even tell what there's nothing left of! As a result, you can't divide by zero, because division means undoing multiplication.)

So "multiplying by nothing" is not "not multiplying at all", in the way that "adding nothing" is the same as "not adding anything". Multiplication is far more interesting than addition.
 
Jomo said:
1*2 means 1+1 =2.
Just like 5*4 means 5+5+5+5. Multiplication is repeated addition.
0*4 means 0+0+0+0=4.

Why has something disappeared? It didn't disappear. You had 0 and you still have 0.
Click to expand...
Jomo? Have you had your coffee yet?
 
1*2 means 1+1 =2.
Just like 5*4 means 5+5+5+5. Multiplication is repeated addition.

If 0*4 means 0+0+0+0=0, why doesn't 4*0 = 4+0=4?.
 
rayj00 said:
1*2 means 1+1 =2.
Just like 5*4 means 5+5+5+5. Multiplication is repeated addition.

If 0*4 means 0+0+0+0=0, why doesn't 4*0 = 4+0=4?.
Click to expand...
Why do you think it would mean 4+0???

If 0*4 means the sum of 4 zeros, wouldn't 4*0 means the sum of 0 fours? It certainly wouldn't be the sum of 4 and zero.

If you add together 0 fours, there's nothing to add. You get 0. This corresponds to my statement,

The same way, multiplying by 0 means taking your whole set away and replacing it with 0 identical sets. If I have a set of 3 apples, I replace that with 0 sets of 3 apples, so I have 0.​

But I prefer my first version, 3 sets of 0 apples (which is equivalent to what Jomo showed). You always get the same result either way, just as 2 times 3 = 3 times 2. In this case, you get 0 whether it's zero groups, or groups of zero.
 
rayj00 said:
1*2 means 1+1 =2.
Just like 5*4 means 5+5+5+5. Multiplication is repeated addition.

If 0*4 means 0+0+0+0=0, why doesn't 4*0 = 4+0=4?.
Click to expand...
"If 0*4 means 0+0+0+0=0" then "4*0= 4+0" is a complete non-sequiture! 0*4 was not 0+ 4.

If 0*4 means 0 added to itself 4 times then 4*0 means 4 added to itself 0 times. Any number added to iteself 0 timess is 0.
 
rayj00 said:
1*2 means 1+1 =2.
Just like 5*4 means 5+5+5+5. Multiplication is repeated addition.

If 0*4 means 0+0+0+0=0, why doesn't 4*0 = 4+0=4?.
Click to expand...

I got to this late. With these whole numbers, a consistent interpretation for the
product is that the first factor tells you how many of the second factors you
have (to add).

1*2 ----> one two ----> 2
2*1 ----> two ones ----> 1 + 1

5*4 ----> five fours ----> 4 + 4 + 4 + 4 + 4
4*5 ----> four fives ----> 5 + 5 + 5 + 5

0*4 ----> zero fours (or no fours) ----> ___ ----> 0
4*0 ----> 0 + 0 + 0 + 0
 
If I count to 2, and do it 3 times, I have counted 6. If I count to 4, and I do it 0 times, I have counted 0.

Multiplication is not a progression of additions, but is an adjustment of magnitude. A length of 2, scaled by 3, becomes a length of 6. A length of 4, scaled by 0, becomes a length of 0.
 
Mr. Bland said:
Multiplication is not a progression of additions, but is an adjustment of magnitude.
Click to expand...


Whenever there is the product a*b, a is a whole number, as I already mentioned, the
multiplication is equivalent to the "progression of additions." Multiplication (a product)
in general is not a "progression of additions."
 
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