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Video transcript

Let's add these two mixed numbers. 2 and 5/13 plus 7 and 6/13. And the way I like to think about in my head, I like to separate out the mixed numbers into the whole number component and the fractional component. So we can rewrite 2 and 5/13 as 2 plus 5 over 13. And then we can write that plus. And then 7 and 6/13, we can rewrite as plus 7 plus 6/13. So all I did is I rewrote this. And I essentially expanded it out. I broke up the mixed numbers into their whole number parts and their fractional parts. And then what I like to do is I like to add the whole number parts. So this 2 plus this 7, so I'll do that. So I'll do the 2 plus 7 over here. I'll add those up. And to that, I will add the fractional parts. So to that, I will add the 5/13 to the 6/13. So if we add the whole number parts, 2 plus 7 is 9, and the fractional parts, they already have the same denominator in this problem. 5/13 plus 6/13, same denominator. You're going to get 11/13. 5 plus 6 is 11. So you get 9 plus 11/13. Well, that's just the same thing as 9 and 11/13. And we are done.

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Adding mixed numbers with like denominators (video) | Khan Academy

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Factors and Multiples

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Finding factors of a number (video) | Khan Academy

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Instructor] What we're going to do in this video is refresh our understanding of place value but we're going to dig a little bit deeper and think about place value in the context of decimals. So just as a refresher if I have the number 973, this should be review for you.

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Angles Song | Acute, Obtuse, & Right Angles | 3rd & 4th Grade

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Write fractions as decimals (denominators of 10 & 100) (practice) | Khan Academy

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Let's multiply 6 times 7,981. And the way we're going to do it right now is just to represent or expand out 7,981 as 7,000 plus 900 plus 80 plus 1. And so multiplying 6 times 7,981 is the same thing as multiplying 6 times 7,000 plus 6 times 900 plus 6 times 80 plus 6 times 1. You'd essentially distribute the 6. And to help us keep track of things, let me draw a little grid right over here. So this is the 6, and we're going to have to think about what 6 times 7,000 is, 6 times 900, 6 times 80, and 6 times 1. So I'll make a little square for our rectangle for each of them. Let me do that. So here we go. And so we just need to think about, what is 6 times 7,000? Well 6 times 7 is 42. So 6 times 7,000 is 42,000. 6 times 900, well once again, 6 times 9 is 54. So 6 times 900 is 5,400. 6 times 80, well 80 is eight 10s. So 6 times 8 is 48, but since it's six times 80 or eight 10s, this is going to be 48 10s, or 480. And then finally, 6 times 1, of course, is equal to 6. So to find what this product is, we just have to take the sum of each of these numbers. What 6 times 7,000 is plus 6 times 900 plus 6 times 80 plus 6 times 1. So let's do that right over here. So it's going to be 42,000 plus 5,400 plus 480 plus 6. And we get, let's see, in the ones place, we just have a 6. In the tens place, we just have an 8. In the hundreds place, 4 plus 4 is 8. In the thousands place, 2 plus 5 is 7. And then finally, the ten thousandths place, we still have a 4. So we get 47,886. So this Is equal to 47,886. And what I encourage you to do is to think about how this is really underlining what we're doing here. It's not that different than what you might have done with the traditional multiplication techniques. And this is a useful way of thinking about it because now you really understand what's going on. And actually, when you start doing things like this in your head, at least for myself, this is actually how I try to tackle the multiplication problem. When someone says 6 times 7,981, if I was just looking at this and I didn't have any paper, I would say, OK, what's 6 times 7,000? I'd say, OK, that's 42,000. I'll try to remember that. What's 6 times 900? Oh that's 5,400. Well if I add that to the 42,000, I get 47,400. Then, what's 6 times 80? 480. Have to add that to the 47,400 to get to 47,880. And then, what's 6 times 1? Well that's 6. Well add that to the 47,880, which I've been keeping in my brain, and that's going to be 47,886. So this helps you understand what's really going on when you multiply multiple digits, and it's a useful technique for doing mental multiplication.

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Multiplying with area model: 6 x 7981 (video) | Khan Academy

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Division with area models (video) | Khan Academy

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Partial Quotient Division Help video.mp4

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Equivalent fractions (video) | Khan Academy

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Video transcript

what I want to do in this video is think about the difference between a line segment a line segment a line a line and array and array and this is kind of the pure geometrical versions of these of these things and so a line segment is actually probably what most of us associate with a line in our everyday lives so a line segment is something just like that for lack of a better word a straight line but what why we call it a segment is that it actually has a starting and a stopping point so most of the lines that we experience in our everyday reality are actually line segments when we think of it from a pure geometrical point of view and I know I drew a little bit of a curve here but this is supposed to be completely straight but this is a line segment the segment the segment is based on the fact that it has a ending point and the starting point our starting point and an ending point a line if you're thinking about it in the pure geometric sense of a line is essentially its it does not stop it doesn't have a starting point and an ending point it keeps going on forever in both directions so a line would look like this a line would look like this and to show that it keeps on going on forever and in that direction right over there we draw this arrow and to keep showing that it goes on forever in kind of the down left direction we draw this our right over here so obviously yeah you know I've never encountered something that just keeps on going straight forever forever but in math that's the neat thing about math we can think about these abstract notions and so the mathematical purest geometric sense of a line is this straight thing that goes on forever now array is something in between array has a well-defined starting point so that's its starting point but then it just keeps on going on forever so then so the Ray might start over here but then it just keeps on going then it just keeps on going so that right over there is array now with that out of the way let's actually try to do the Khan Academy module on recognizing the difference between line segments lines and rays and I think you'll find it pretty straightforward based on on our classification right over here so let me get the module let me get the module going let me let me where did I put it where did I put it there you go all right so what is this thing right over here well there's two arrows on both ends so it's implying that goes on forever so this is going to be a line let's check our answer yeah it's a line now it's taking some time out correct next question all right now what about this thing well once again arrows on both sides means that this thing is going to go on forever in both directions so once again it is a line fair enough let's do another one here we have one arrow so it goes on forever in this direction but it has a well-defined starting point so it starts there and then goes on forever and if you remember that's what a ray is one starting point but goes on forever so it goes or one written think about it goes on forever and only one direction so that is a ray so let's do another question this right over here you have a starting point and an ending point or you could call this the start point in the ending point but it doesn't go on forever in either direction so this right over here is a line segment there you go so hopefully that that that gives you enough to work your way through this module and you might notice when I did this when I did this module right here there is no video and that's exactly what this video is it's the video for this module

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Lines, line segments, & rays (video) | Khan Academy

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