Multiplying 3-digit by 2-digit numbers: Error analysis
About this video
The video checks someone's work for 586 x 43 with the standard algorithm. Step one, 586 x 3 = 1,758, is correct. In step two the 4 is really 40, and 586 x 40 should give 23,440 (4 x 5 = 20 plus the regrouped 3 is 23), but the person made a mistake there, so step three's total is also wrong.
You'll be able to
- follow the standard algorithm for 3-digit by 2-digit multiplication, including regrouping.
- find the step where a multiplication mistake was made.
- explain why a placeholder zero is needed when multiplying by the tens digit.
Key words
- regroup
- Carry extra tens or hundreds to the next place, like writing 8 and carrying the 1 from 18.
- standard algorithm
- The usual written way to multiply: one row for each digit, then add the rows.
- error analysis
- Checking someone's work step by step to find where it went wrong.
Transcript
- [Instructor] So we have a situation here where someone is attempting to multiply 586 times 43, and what we wanna do together is figure out if they did this correctly or whether they made a mistake. And if they made a mistake, what step did they make a mistake on?
And actually, why don't you pause this video and have a go at this on your own before we work through this together. All right, now let's work through this together. So let's start at the beginning. Here we have 3 times 6 is 18, so you put the 8 here, regroup the 1.
That all looks good right now. Then you have 3 times 8 is 24, plus that 1 that we just regrouped is 25. Put the 5 here, regroup the 2. All looking good so far. 3 times 5 is 15, plus 2 is 17. Wrote the 17 here. So step one all looks good to me. Now let's look at. We're now now going to.
Now let's move on to the 4, which is really a 40, so we're gonna put a zero right over here. And then we're gonna say 4 times 6 is 24. Put the 4 here and regroup the 2. 4 times 8 is 32, plus 2 is 34, put the 4, regroup the 3. 4 times 5 is 20, plus the 3 is 23.
So it looks like a mistake was made in step two. And of course step three is gonna break down because they forgot to put the 3 right over there. So definitely a mistake, and the mistake is in step two.
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