Video Transcript
Use the symbol for is less than, is greater than, or is equal to, to fill in the gap. 1963 plus 6279, what, 3017 plus 6225.
In this problem, we have two additions. Both of them involve adding four-digit numbers together. And, in between the additions is a gap. And in that gap, we need to use one of the three symbols that we’re provided with.
Let’s remind ourselves what each of these symbols means. The first thing to remember is that we always read these symbols from left to right. So whatever the number is on the left, we would say that first, then the symbol and then the number on the right. The second thing to remember is that the wider end of each symbol always points to the larger number of a larger value. One way to help us remember this is to imagine putting counters inside each symbol.
We can see with the first symbol that the number here will be less than the number here. So, the first symbol starting narrow and getting wider to the right means is less than. Our second symbol would begin with a larger number, and the smaller number would come second after the symbol. So, reading the second symbol from left to right, it means is greater than. And the values on both sides of an equal sign are the same. We know this means is equal to.
The most accurate way to compare these two calculations is to work them out and to find out what they’re worth. But just by looking at the numbers, we could make a prediction about what the answer we think is going to be. The number 6279 is roughly only about 50 more than 6225. So, perhaps the calculation on the left-hand side of the gap is greater. But now, if we compare the first number that we had each time, we can see that the number on the right-hand side is over 1000 more. So even before we start, we can predict that the value on the left is less than the value on the right.
Let’s calculate each addition to see whether we’re correct. 1963 plus 6279. First, we add the ones. Three plus nine equals 12. Six tens plus seven tens equals 13 tens plus the one ten that we’ve exchanged equals 14 tens. Nine hundreds plus two hundreds equals 11 hundreds plus the one hundred we’ve exchanged, 12 hundreds, which is the same as 1200. And finally, one thousand plus six thousand plus the one thousand we’ve exchanged equals eight thousand. The value of our first addition is 8242.
Now let’s add our second two numbers together, 3017 plus 6225. Seven ones and five ones equal 12 ones again, which is the same as one ten and two ones. One ten plus two tens plus the one ten we’ve exchanged equal four tens. If we compare our numbers so far, they’re looking the same. Both have four tens and two ones.
Now let’s add the hundreds. Zero hundreds plus two hundreds equal two hundreds. Still, the answers are looking the same. They both end with 242. It’s all about this final digit. Three thousand plus six thousands equal nine thousands. The value of the calculation on the left is less than the value of the calculation on the right. 8242 is less than 9242. And so, we were correct with our prediction. The symbol that we should use in between the two calculations is the one that represents is less than. 1963 plus 6279 is less than 3017 plus 6225.
