Find the difference between 871 and 319.
When we’re asked to find the difference between two numbers, we need to subtract them. If we start with 871 and then subtract 319, the number that we’ll be left with will be the difference between the two numbers. We can subtract these two three-digit numbers by using column subtraction. This means we have to write out both numbers vertically. We need to set out the digits so that they’re in the hundreds, tens, and ones places. Let’s model 871 using place value counters too. We’re going to need eight hundreds, seven tens, and only one one. So as we find the answer using vertical subtraction, what we’ll do is model what we’re doing using the place value counters. We’ll start by taking away the ones. 871 has one one, and we need to take away the nine ones through 319.
But how can we take away nine ones if all we have is one one? It’s not possible, is it? Well, if we stop and think about it, we know we can take away nine ones from 871 because 871 is a large enough number two take away nine from. We just need to regroup the number a little. Let’s look to the next column to help us. If we look at the number of tens in 871, we can see that we have seven tens. What if we took one of those tens and exchanged it for 10 ones? Watch what happens to our place value counters when we do this.
We’ll take this tens counter here and we can exchange it for 10 ones. One ten is exactly the same as 10 ones. Let’s show what we’ve just done using our column subtraction. We’ve taken one ten. So instead of seven tens, we now have six tens. And we exchanged it for 10 ones. Instead of one one, we now have 11 ones. And we can now subtract nine ones from our 11 ones. One, two, three, four, five, six, seven, eight, nine ones. 11 ones take away nine ones leaves us with two ones. Now, we can take away our tens. We did have seven tens, but, remember, we’ve regrouped the number. So we now only have six tens. Six tens take away one ten, we know that six take away one leaves us with five. So six tens take away one ten leaves us with five tens or 50.
Finally, we need to subtract the hundreds digits. We have 800 and we need to subtract 300. 100, 200, 300. 800 take away 300 leaves us with 500. We used column subtraction to help find the answer. And when we couldn’t subtract the digits in one of our columns, we regroup the number to help us answer the question. Remember that regrouping a number doesn’t make it larger or smaller. It’s just another way of partitioning it to help us to subtract. We started off with 871. And then after we regroup the number, it looked like 800 and 60 11 which might sound a bit strange. But if we stop and think about it, 800 and 60 11 is actually the same number as 871. But regrouping the number like this helped us to subtract those nine ones. And so the difference between 871 and 319 is 552.