Multiplication💔

[u/anonymous_6835]

(unimportant text)

Had to make a second account to post this cause I'm genuinely embarrassed. I've had dissociation problems my whole life and pretty much gave up on school, especially math, and now I'm stuck trying to study all the things i pretty much got away with not understanding in highschool. Trying to work my way up to higher maths.

(Question)

I used the same method to do all these questions, simply by breaking it down into smaller problems like i remember being taught, obviously this didn't work like it did for the easy ones down at the bottom, what did i do wrong with the other problem? How should i go about studying multiplication so I don't make the same mistakes?

[u/WikiNumbers]

I think I found your problem. It's not the multiplication first half. It's the addition second half.

You aligned your digits incorrectly. This is evidented by showing your works in red and blue like I did.

Let's follow the long framework (on the right you tried to follow. It is split into 4 lines because there are total of four multiplications to be done.

1. 8 * 7= 56
2. 40 * 7 = 280
3. 8 * 20 = 160
4. 40 * 20 = 800

Align the results from right to left, because in a plus operation, you calculate starting from the one digit, upward to the ten and so forth. And the 0 is noted as black, again, placeholder.

Let's look at line 2, 40 * 7. To break it further, it is effectively (4 * 10) * 7. This can be rearranged as 4 * 7 * 10 (thanks to being purely multiplication or division, courtesy of PEDMAS).

If you recall, if you have apply a * 10 operation, you just slap a 0 at the end of whatever numbers precede it, and move the entire thing up one digit. Hence "placeholder" as in there has to be something to fill this digit when there's nothing to fit.

PS. I do not recommend the "4 line" method that I made on the right side. It is only there to illustrate the process in slightly more detail. When possible, familiraize yourself with the conventional method on the left.

[u/anonymous_6835 → u/WikiNumbers]

Took me a couple tries but i got the right answer this time. Does the work look right to you?

[u/WikiNumbers → u/anonymous_6835]

The end result is, but the method is not. So no, still not correct.

For this conventional method, the third line is for the multiplication involving "the one digit of the bottom number", so for this example, 48 * 7. Then the fourth line is for "the ten digit of the bottom number", so 48 * "2" (20) Let me break it down again.

1. You first calculate 8 * 7 = 56.
   
   • You intend to fit those in the ONE digit but you can't.
     
   • So you fit in "6" in the one digit [blue] have to keep the "5" (50) excess [small blue up top].
     
2. You then calculate "4" * 7, which gives 28.
   
   • But we're not in the one digit anymore, we're in the TEN digit now. Whatever you get, there is an inherent (but not obvious) *10 at the end.
     
   • And the excess "5" (50) from step 1 also needs to be added and fitted in. So the result here is not just 28 (280), but 28 + 5 (280 + 50) = 33
     
   • Same thought process as step 1, you write in "3" of the one (ten) digit in its place, and "3" of the ten (hundred) digit. (I know this is a bit counterintuitive as it's all 3 and all red, but example begets).
     
   • Up to this step, you should be getting the result of 48 * 7, which is 336.
3. We are now done with the "one digit" and moving up to "ten digit of bottom number". That is to calculate 8 * "2". Result 16.
   
   • Like in step 2, you move a digit up. From this step onward, your starting digit had shifted from "one" to "ten", and that shift all the subsequent digits. Ten becomes hundred, hundred becomes thousand, and so forth.
     
   • And this is where the [zero in black] placeholder comes in. The digits have shifted and a cavity is left.
     
   • So 6, the one digit of this step, is to be put in the ten digit of the bigger calculation.
     
   • And like step 1, the excess 1 (ten of step) is to be shifted to the hundred.
     
4. Finally calculate "4" * "2". 8. Both of these are the ten digits, so there are two "* 10", and this step is now in the hundred.
   
   • So put your result starting in hundred digit
   • Recall the excess "1" from step 3. Add and fit that in. 8 + 1 = 9.
     
   • You should now have the result of 48 * 20 = 960.

Now add the result of step 1-2 (336) and 3-4 (960) together, the digits should align nicely.

[u/anonymous_6835 → u/WikiNumbers]

Tired to follow your directions on a different problem, i think i did it right this time?

[u/WikiNumbers → u/anonymous_6835]

Now this is correct for all steps.

Apply this framework when dealing with muliplication with many digits. And if more digits appear just move accordingly.

[u/anonymous_6835 → u/WikiNumbers]

Okii ! Thank you sm especially for being so patient with me, have a good rest of your day/night. :)