Video: Evaluating and Comparing Subtraction Expressions

Use <, >, or = to fill in the gap: 210 − 170 _ 325 − 181.

04:30

Video Transcript

Use the symbol for is less than, is greater than, or is equal to, to fill in the gap. 210 subtract 170 what 325 subtract 181.

Here, we’re given two subtractions. 210 take away 170 and then 325 take away 181. We need to then complete the gap between the two subtractions using one of the three symbols. Is the difference between 210 and 170 less than the difference between 325 and 181? Is it more than the answer to the second subtraction? Or are both answers equal? You might have an idea just by looking at the numbers themselves and thinking about how they change from calculation to calculation. But really, the only way to be sure is to work out the answer to both subtractions. Now, this is an interesting question, because we don’t have to use the same method to find the answer for both subtractions.

With the first subtraction, we could actually work this out mentally. Let’s go over how we know this. Well, what we can notice about the two numbers in this subtraction is that they’re both multiples of 10. We know this because they both end in a zero. So, really, what the calculation is asking us is what’s the difference between 21 tens and 17 tens. And, of course, to find the answer to this, all we have to do is to take away 17 from 21. We know that the difference between 20 and 17 is three. So the difference between 21 and 17 must be four. 21 tens take away 17 tens leaves us with four tens. And so 210 take away 170 equals 40. The value of the calculation on the left-hand side of the gap is 40. So let’s write this down.

The numbers in the second calculation aren’t quite as easy to work with. They’re not multiples of 10, are they? So perhaps, it might be best to use a written method to calculate the answer with these two numbers. First of all, we’ll write them out vertically. So, the hundreds, the tens, and the ones are all in the right places. First, let’s subtract the ones. Five ones take away one one leaves us with four ones. Now, we subtract the tens. We have two tens or 20 in the first number, 325. And we need to subtract eight tens. But how can we subtract eight tens from two tens? We haven’t got enough tens to take eight tens from. And of course, we know we do have enough tens in the whole number, because we have 325 to take eight tens from.

So what we’ll do is we’ll look across at the hundreds column. And we’re going to take one of those hundreds and to move it into the tens place. Instead of three hundreds, we now have two hundreds. And 100 is worth 10 tens. So we’re going to put 10 tens in the tens column. Our first number is still worth 325. But we’ve just regrouped it in a different way to enable us to subtract those eight tens. The difference between 12 and eight is four. So 12 tens take away eight tens leaves us with four tens. And finally, we can subtract the hundreds. We did have three hundreds. But remember, we regrouped the number slightly. So we now have two hundreds. Two hundreds take away one hundred leaves us with 100. So the value of the second calculation is 144. You may have guessed that the answer to this was going to be larger than the first number as we worked through the calculation.

So to solve the problem, we need to use the correct symbol to fill in the gap. We know that the first subtraction is less than the second one because 40 is less than 144. We’ve used the symbol for is less than to fill in the gap. And so we can say 210 subtract 170 is less than 325 subtract 181.

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