But that is a statement about apples, not mathematics. it shows that that particular interpretation of "0 times 100 apples" is "0 apples". It does NOT show "0 * 0= 0".
The author has shown that a*0 + a*0 = a * (0+0) = a*0 = a*0 + 0. In particular:a*0 + a*0 = a * (0+0) = a*0 = a*0 + 0, so that a*0 and 0 are both solutions of the equation x + a*0 = a*0, hence equal, by F3.
(...) he loses me when he states that a*0 and 0 are both solutions of the equation. If they are solutions I can understand that they would be equal by F3.
as a perhaps redundant addition:One possible conceptual way to think about it is to say, multiplying 2 * 100 is like having 2 groups of 100 cookies on the table. Multiplying 1 * 100 is like having 1 group of 100 cookies on the table. Multiplying 0 * 100 is like having no groups of 100 cookies on the table, hence no cookies at all.
However, I agree that this is may not be very intuitive. When dealing with 0, it is sometimes more difficult to match mathematical situations to real life situations. It is probably better to understand 0 * any number = 0 just as a consequence of several properties of numbers that we take for granted.
Hi all.This is far too natural to be confusing. Remember that multiplication is repeated addition. If you add 100, ZERO times, you have ZERO. If you want 100 as result, then you must add 100 ONE time.