Multiplying two 3 digit numbers on paper - How quickly can you do it?

In My Humble Opinion
1

Seems like a trivial exercise and it is, but I’m 57 and sometimes you wonder just how rusty your basic mental skills are so I wanted to know how quickly I could do this. I chose two random 3 digit numbers and put them down on paper to multiply by hand.

I can usually add together up two and three digits numbers in my head so on the first try I wanted a good time speedwise so I just multiplied the numbers in each row )1’s, 10’s & 100’s) put down the totals and added them together mentally. It was incorrect. So I tried again with a different set of numbers being a little more careful this time and screwed it up again. Finally I went back to basics for a third set of three digit numbers and drew little lines to keep the numbers aligned the right rows/powers sequence and doubled checked my calculations. I took longer to be so careful but I finally got the right answer.

My lazy adult quick addition habits were screwing up my ability to be precise. Interesting and a bit humbling. I’ve gotten it down to 3 minutes to calculate 2 random 3 digit numbers accurately after several tries but I’m still screwing up about one out of 5 due to not keeping the powers aligned and (embarrassingly) a few simple single digit multiplication mistakes. It’s a very basic exercise but actually working through it manually makes you realize how rusty some skills have become.

If you don’t want to choose randomly here are some of the number pairs I used

373x695
576x852
567x793
473x829
693x974
726x838

2

I like to do math problems in my head. It is fun.

But, multiplying 2 three digits numbers, I look to the calculator.

3

I tried them on pencil and paper. I’m a little rusty. I had to relearn my multiplication rules for the first answer and got it wrong, but as it came back to me, I got the remaining four out of five right. I screwed up the alignment on 473x829 and got that one wrong. It wasn’t easy. It took a bit of mental effort. Fortunately, I usually have my phone close at hand so I can use the calculator.

4

Pencil and paper: about 1:45 each.

(And that was a really boring hour and forty-five minutes!) :wink:

5

Just for fun, I unsheathed my trusty slide-rule (you’ve got yours handy, right?) and worked them out

373 x 695 Answer= 259,235 Slide Rule= 259,500 Error= 0.10%
576 x 852 Answer= 490,752 Slide Rule= 490,100 Error= -0.13%
567 x 793 Answer= 449,631 Slide Rule= 448,500 Error= -0.25%
473 x 829 Answer= 392,117 Slide Rule= 392,200 Error= 0.02%
693 x 974 Answer= 674,982 Slide Rule= 675,000 Error= 0.00%
726 x 838 Answer= 608,388 Slide Rule= 608,000 Error= -0.06%

Not bad. I guess I still do pretty well. All less than 0.5%, most within 0.1%. And that was with my bad eyes.

6

I used to be able to do them in my head, easily and quickly. Now I can barely do them with a calculator.

7

Just did the last one on your list. 34 seconds.

8

I did it three times with a stopwatch, and didn’t count the time to generate the random numbers or write them down. I got the right answer in each case. My times were 31.50 seconds, 30.63 seconds, and 33.00 seconds.

9

37 seconds for me for the last one. Took a couple seconds to come up with 7x8 :smack: However, went much quicker the next time. :smiley:

10

I tried your first three examples, and did them each in 30-40 seconds. But, I made a dumb little error and got the wrong answer for the third. I was trying to see how fast I could do them; if accuracy had been important, I would have worked more slowly and carefully.

For the record, I can’t remember when I’ve last tried to multiply multi-digit numbers without a calculator. But the foundational skills—multiplying single-digit numbers and addiing multi-digit numbers—I use quite frequently. I would expect a randomly-selected person to take much longer, if they could do it at all—I’ve seen people who couldn’t multiply by 1 without a calculator.

11

I just tried a few having not done any pencil&paper multiplication in years. All attempts fell within 40-70 seconds.

12

To some degree the answer will depend on the numbers; for instance.

100 x 100 I can do almost instantly in my head.

222 x 222 took about 5-6 seconds in my head.

426 x 838 (one of you examples) about 10-15 seconds. I’d imagine most three digit number combos would come in at about that time.

13

I did the first four on the list and took 30-40 seconds for each.

Nice little exercise, interesting way to start the day.