Strategies for adding two and three-digit numbers
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- Mike isn't sure how to add 189 + 608, help Mike by choosing an addition problem that is the same as 189 + 608. Now let's look at these choices. Let's just start with this first choice, actually all of these choices start with having 1 hundred, they all have 1 hundred, so where do we see 1 hundred here? Well in 189, we have a 1 in the hundreds place, so this right over here, that is one 1 hundred, 100, and then all of the choices actually have 6 hundreds, 6 hundreds, 6 hundreds, where are they getting that from? Well in 608, the 6 is in the hundreds, so that 6, represents 6 hundreds, 6 hundreds, so that's where they got the 1 hundred, and the 6 hundreds from, and then all of them have 8 tens, so they're actually all looking pretty similar, up to that point, they all have 8 tens, 8 tens, 8 tens, where do they get that from? Well in 189, this 8 is in the tens place, so it represents 8 tens, 8 tens, and then what else do they have? Well this is where they all start to be a little bit different, so let's go one by one. So this next one then has 9 ones, 9 ones, where are they getting that from? Well in 189, the 9 is in the ones place, so it's reasonable to write 9 ones, and then finally, they have 8 ones. 8 ones, where do they get that from? Well in 608, the 8 is in the ones place, so it's 8 ones, so this first choice is looking quite good. Now you might be saying, 'Okay, we took into account, all of these digits, except for this 0 over here, how come we didn't, how come there's a 0 here in the tens place?' Well that would just be 0 tens, 0 tens, which is just zero, so it's not going to change the value of this, so this first choice is indeed the same, as the original addition problem. If we want to see where the other ones break down, this one has 8 tens written twice, we only have one, we have an 8 tens here, but this 8 is in ones, so this should say 'ones', right over here, and this choice, we have the 8 ones, but this 9 right over here, this is ones, this isn't tens, so this should be 'ones'. So that's why we wouldn't pick either of those. Let's do another one of these, or related type of problem. Which addition problem is the same as 525 + 379? Let's just break it down. So we have a 5 in the hundreds place, so that would be 500, and then we have a 3 in the hundreds place, so + 300, then we have a 2 in the tens place, so it's two 10, or 20, and then we have a 7 in the tens place, so that's + 70, and then last but not least, we have a 5 in the ones place, so that's just going to be 5, and then we have a 9 in the ones place, so that's just going to be equal to 9. So which of these choices is the same of what I just wrote over here? 500 + 300, so this first choice has no 500 or 300, so we can rule that out. 500 + 300 + 20 + 70 + 5 +9, that's exactly what I wrote down. This last choice breaks down, they wrote 90 instead of 9, and then they wrote 5, and then they wrote 7, instead of 70. That 7 is in the tens place, it's not in the ones place, we ruled that one out as well.