Video Transcripts: Operations with Decimals

Adding decimals 

Let's see if we can add 9.087 to 15.31. And I encourage you to pause the video and try to do  it on your own. So I'm assuming you have tried to do it on your own. And now let's see how  we could actually tackle this. Now, one thing I want to point out, some of you all might have  seen these numbers all lined up and immediately want to say, hey, 7 plus 1 is 8, and 8 plus 3  is 11, carry the 

1, et cetera, et cetera. And if you did that, you would be making a mistake. Because, you see,  right over here, these decimals aren't lined up. Here, if you did that, you would be adding the  7 thousandths to 1 hundredths. You would be adding 0 tenths to 5 ones. You would be adding 9 to 1 tens, or essentially, this is a 10 right over here. So the places would be all mixed up. So what 

you need to do is to actually align the decimals so that your place values are aligned. So what you want to do is you want to align things up. So we could write 9.087. And then we want to  align the decimal. So let's align the decimal. This is what has to match up. And this is going to  be 15.31. And this should hopefully make sense to you as well. This is 9 point something plus  15 point something so it's going to be-- If you add 9 to 15, it will be 24 point something, give  or take a little bit. And you see that here. Here you have a 9 plus the 15. So you have lined up the appropriate place values. And now we are ready to add. It's a good idea to st+art with the  smallest place value, so if you have any extra at a certain place, you can bring something into the next place value. So here you say 7 plus-- well, this is 7 thousandths. It's in the  thousandths place. And you might want to-- you say, well, what do I add it to? There are no  thousandths right over here. And you're right. There are no thousandths. So we could literally  write 0 thousandths. So 7 thousandths plus 0 thousandths is 7 thousandths. 8 hundredths  plus 1 hundredth is 9 hundredths. 0 plus 0 tenths plus 3 tenths is 3 tenths. We got our  decimal. Then you have 9 ones plus 5 ones is 14 ones. Well, 14 ones is the same thing as 4  ones and 1 ten. So 

we'll carry that 1 right over there. This is just 1 ten plus 4 ones, which is 14. And so then  finally, you have 1 ten plus another ten is 2. So we get 24.397. 

Adding decimals: 0.822+5.65 

We're asked to add 0.822 to 5.65. So let me rewrite this. And when I rewrite it, I want to line  up the decimals so that we add the right place to the right place. And so we could write either  number first, although I like to write the larger number first. So let's write 5.65. And remember, the important thing is that we line up the decimal points. So if we write 0.822-- so we line up  the decimal. Let me line up the decimal first. So I'll write the decimal right below the other decimal. And it is 0.822. And now we are ready to add. So let's see what's going on here. So I like to start in the smallest place. That way, the carrying works out well. So you might say,  wait, I need to add this 2 thousandths to something. I don't see anything up here. Well, you  could say there's just a 0 thousandths right up here. Then it makes it very clear. Well, 0  thousandths plus 2 thousandths is going to be 2 thousandths. 5 hundredths plus 2 hundredths is 7 hundredths. 6 tenths plus 8 tenths is 14 tenths. Well, 14 tenths is the same thing as 4  tenths and 1 one. Another way of thinking about it is you're carrying the 1. But really, what  you're saying is, look, this is 14 tenths. I could write it as 4 tenths and a 1, or a ones place, a  1 in a ones place. Then you have 1 plus 5 is 6. And of course, you cannot forget the decimal.  The decimal goes right there. And this is 6.472. 

Adding three decimals 

We need to add 7.056 to 605.7 to 5.67. Now when you're adding any number, you always  want to make sure you line up numbers in the same place. And especially when you're 

dealing with decimals, the easiest way to do that is to just line up the decimals. So let's do  that. So the first number right here is 7.056. This second number right here is 605.7. And then this last number is 5.67. So now we have everything lined up. Everything that's in the ones  place is below or above everything else in the ones place. Everything in the tenths place is  below or above everything else in the tenths place, and so on and so forth. So we can add.  So let's add it. So you want to start off in the smallest place. So you start off here. This is the  tenths, hundredths, thousandths place. This is literally 6 thousandths, and you want to add it  to the other thousandths. There aren't any other thousandths. So you can view it two ways.  You can just bring in this 6 down, or you could view this 605.7 as the same thing as 605.700.  You can add as many zeroes to the right of this decimal, to the right of the 7, as you want,  since we're sitting on the right side of the decimal, without changing its value. You can also do it here. This 5.67, you can write it as 5.670. When you write it like this, and you have 6 plus 0  plus 0 is 6. And you keep going. 5 plus 0 plus 7 is 12. You write the 2 in the hundredths place, and carry the 1. 1 plus 0 plus 7 is 8, plus 6 is 14. Write the 4, regroup the 1 into the ones  place. 1 plus 7 is 8. 8 plus 5 is 13. 13 plus 5 is 18. This is 18. Carry or regroup the 1. 1 plus 0  is just 1. And then finally. You have the 6 in the hundreds place. Nothing gets added to it, so  you can just bring down that 6 and it's right there. And you don't want to forget the decimal.  And so when you add the numbers you get 618.426, or 618 and 426 thousandths. And we're  done.