Let's explore adding two 3-digit numbers using place value and carrying. We walk through the process step by step, starting with the ones place, then the tens place, and finally the hundreds place. We emphasize the importance of understanding what carrying means and how it relates to place value. Created by Sal Khan.
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- why did he add a one above the nine?(3 votes)
- because you add it when it is over 10, so you add it to any number when you have 2 digits in your answer(2 votes)
- so we carry because of if it were to be 14 if we added 127+347 we add 7+7 =14 so that 1 would go to the top of the other number then 4+2 then plus 1 correct?(2 votes)
- Correct. 7+7=14. The one would be added to the tens. Now you have 2+4+1=7. Then you add 1+3= 4. Your final answer would be 474.(2 votes)
- Why do we have to do carrying?(2 votes)
- When adding 2 numbers, carrying is required when the numbers in the 1s place add up to 10 or more, or when the numbers in the 10s place add up to 100 or more, or when the numbers in the 100s place add up to 1000 or more, and so on.
If we want to add 98 and 3, we have a several steps to take:
98 + 3 =
90 + 8 + 3 =-- because
98 = 90 + 8
90 + 11 =-- because
8 + 3 = 11
90 + 10 + 1 =-- because
11 = 10 + 1
100 + 1 =-- because
90 + 10 = 100and this the same as our carry step
101-- our answer
This is a lot to do just to add 3 to 98, so we have this shortcut method called carrying to speed things up:
1) Add 8 and 3 to get 11. This gives us 1 in the 1s place and we carry 10 to the 10s place. So we add a 1 over the 10s place.
2) Add the carried 1 to 9 to get 10. This is equivalent to adding 10 to 90 to get 100. This gives us 0 in the 10s place and we carry 100 to the 100s place by adding a 1 over the 100s place.
3) Add the carried 100 to the 0 to give us 1 in the 100s place
4) We end up with 101
1 <- carried from 10 + 90
1 <- carried from 8 + 3
- In adding why do you have to do it from right to left?Could we also do left to right?(1 vote)
- Actually, sometimes the numbers to the right go over 10. 144 + 379 does. You go from left to right so that if those numbers add up and have to go in over to a number to the left, you can do that without having to re-add that.
So basically, you could, but it would be very hard.(1 vote)
Let's add 536 to 398. I'm going to do it two different ways so that we really understand what this carrying is all about. So first we'll do it in the more traditional way. We start in the ones place. We say, well, what's 6 plus 8? Well, we know that 6 plus 8 is equal to 14. And so when we write it down here in the sum, we could say, well, look, the four is in the ones place, so it's equal to 4 plus one 10 So let's write that one 10 in the tens place. And now we focus on the tens place. We have 1 ten, plus 3 tens, plus 9 tens. So what's that going to get us? 1 plus 3 plus 9 is equal to 13. Now, we have to remind ourselves, this is 13 tens. This is 13 tens. Or another way of thinking about it, this is 3 tens. This is 3 tens and 100. You might say, wait, wait. How does that make sense? Remember, this is in the tens place. When we're adding a 1 ten plus the 3 tens plus 9 tens, we're actually adding 10 plus 30 plus 90, and we're getting 130. And so we're putting the 30. The 3 in the tens place represents the 30. So this is the 3. The 3 represents the 30. And then we're placing this 1 in the hundreds place. 10 tens is equal to 100. And now we're adding up the hundreds place. 1 plus 5 plus 3 is equal to-- let's see, 1 plus 5 is equal to 6, plus 3 is equal to 9. But we have to remind ourselves, this is 900. This is in the hundreds place. So this is actually 100-- I want to make all colors the same. So this is actually 100 plus 500 plus 300. Let me get the color coding right. Plus 300 is equal to 900. And that's exactly what we got here. 100 plus 500 plus 300 is equal to 900, and we're done. This is equal to 934.