Video: Comparing Addition Expressions

Use <, >, or = to fill in the gap: 369 + 203 _ 414 + 357.

04:49

Video Transcript

Use the symbol for is less than, is greater than, or is equal to to fill in the gap. 369 plus 203 what 414 plus 357.

This problem doesn’t give us two numbers to compare. It gives us two additions. We need to work out which is the larger out of 369 plus 203 and also 414 plus 357. Or maybe neither of them is larger. Perhaps they’re both the same size. Anyway, we can find out for sure by actually adding the numbers together and finding out the value of each addition. But if we look carefully at our numbers, we can make a prediction.

Let’s just look at the hundreds digits of our numbers. In the first addition, we’re adding a number with three hundreds and a number that has two hundreds. Now, compare this with our second addition. We can see a number with three hundreds, just like there was in the first calculation. But instead of another number with two hundreds, the second number in this calculation contains four hundreds. So perhaps, we can predict before we start that our first number is going to be less than the second one. Let’s check our prediction by adding both sets of numbers together.

Firstly, 369 plus 203. And this is the sort of calculation that we could do mentally quite quickly. But in this video, we’re going to practice using column addition. So, to begin with, we’re going to write both numbers. And we’re gonna set them out vertically so that the digits are in the correct columns.

And we start by adding the ones. We have nine ones in the first number, and the second number has three ones. Nine plus three equals 12. But how can we write 12 ones in a column where we’re only supposed to write one digit? What can we do? Well, 10 ones are the same as one ten. So, we can exchange 10 of our ones for one ten. And we can write the remaining two ones in the ones column. Nine plus three equals 12.

Now, let’s add the tens. Six tens plus zero tens equals six tens. But we’ve already exchanged a ten. We need to include that too. So, instead of six tens, our answer needs to be seven tens. And finally, let’s add our hundreds digits. 300 plus 200 equals 500. So, the value of the first addition, 369 plus 203, is 572. And we think we can see just by looking at these two numbers that we’re going to get a total greater than 572. Let’s add them together anyway. 414 plus 357.

Once again, we’re going to start by adding the ones. Four plus seven equals 11. And remember what we need to do now. We’ve made a number with two digits. We’re going to exchange 10 of our ones for one ten. And we’ll write the remaining one one in the ones place. Four plus seven equals 11. Now, let’s add our tens digits. One ten plus five tens equals six tens. And we’ve exchanged one ten as well. So, that’s seven tens.

And then finally, we’ll add our hundreds digits. 400 plus 300 equals 700. And so, the value of our second addition, 414 plus 357, is 771. Our first number contains five hundreds. Our second number contains seven hundreds. So, we know that our first number, 572, is less than 771. And so, we can say, 369 plus 203 is less than 414 plus 357. The correct symbol to use to fill in the gap is the one that represents is less than.

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