Understanding the standard algorithm when subtracting within 1,000
About this video
Monica is using the standard algorithm to find 804 - 365, and we must find the missing number X in her work. Because there are 0 tens and only 4 ones, the 8 hundreds are decomposed into 7 hundreds and 10 tens, then the 10 tens into 9 tens and 10 ones. X is the 9 tens, and the full answer is 439.
You'll be able to
- explain why I need to regroup when subtracting.
- decompose hundreds into tens, and tens into ones, to subtract.
- follow and check someone else's subtraction work.
Key words
- standard algorithm
- The usual step-by-step way to subtract, place by place.
- decompose
- To break a number into smaller parts, like 8 hundreds into 7 hundreds and 10 tens.
- regroup
- To move value from one place to another so you can subtract.
Transcript
- [Instructor] We're told, Monica starts to use the standard algorithm to solve 804 minus 365. Here is her work. What number should Monica replace X with? So pause this video and have a go at this before we do this together. So it looks like what Monica is trying to do is because she's going place value by place value and she needs to figure out a way to subtract six from zero and five from four.
So she decomposed certain numbers and then regrouped parts of it to others, but it's sometimes a little bit confusing to look at someone else's work and to see what's going on. So actually, what I find useful to do is to just do what I would've done doing the standard algorithm.
And that's just a fancy way of saying the standard way of subtracting numbers. And let's just see if I did it, what it might look like. So as I just mentioned, I can't subtract five from four, I can't subtract six from zero, so I'm gonna have to do a little bit of regrouping.
Over here, I have eight hundreds. I can decompose this eight hundreds into seven hundreds and 10 tens, so then this is going to become 10 tens. Notice 10 tens plus seven hundreds is 800. Now, I'm making progress, except I still need to subtract the five ones from the four ones, so let me decompose this 10 tens into nine tens and 10 ones.
And so if I add the 10 ones to the four ones that are already there, I end up with 14 ones right over here. And now, I am ready to subtract. And if I wanted to do it, I could say 14 minus five is nine, and I could keep going. I could say nine minus six, but I've actually already answered the question because what's pretty clear is is that this X here, this is this nine right over here.
What Monica did is first decomposed that eight hundreds into seven hundreds into 10 tens, and then she decomposed that 10 tens into 10 ones and nine tens, so this X right over here is a nine. And that's all they're asking us for. They're actually not asking us to complete the subtraction.
We could, nine minus six is three, seven minus three is four, and we're actually done, but X is this nine right over there.
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