Identifying equations from visual models: tape diagrams
About this video
The video turns tape diagrams into equations and solves them. A tape with n and 18 making 42 gives n + 18 = 42, so n = 24. A tape of six equal p's making 84 gives 6p = 84, so p = 14. Both are solved by doing the same thing to both sides.
You'll be able to
- write an equation that matches a tape diagram.
- solve n + a = b by subtracting a from both sides.
- solve a x p = b by dividing both sides by a.
Key words
- tape diagram
- A drawing of bars or strips that shows how parts make up a whole.
- equation
- A math sentence saying two expressions are equal, using an equals sign.
- variable
- A letter, like n or p, that stands for an unknown number.
Transcript
- [Instructor] The tape diagram represents an equation. Write an equation to represent the tape diagram. So pause the video, have a go at that. And then you can actually try to find the value of n that makes the equation true. So if we wanna represent this equation, we could really say that n plus this 18 is equal to 42.
And maybe I'll color code this just for kicks. So this is n right over here. N. And then to that I am going to add 18. That's this part right over here. So n plus 18 is going to be equal to, all of this is going to be equal to 42. And we could see that, that this width plus that width is equal to this entire width.
Now if we want to figure out what n is, there's a couple of ways you could do it. You could just say, okay, what plus 18 is equal to 42? Some of you might be able to do that in your head. Or another way to do this is we could say, okay, if these two things equal each other, what if we were to subtract 18 from both sides?
They'd still be equal since I'm doing the same thing to both sides. So if I subtract 18... Let me do it from both sides. If I subtract 18 from this side and subtract 18 from that side, another way to think about it is we're saying that these two things are equal.
So if we subtract 18 from both of these, so we take out 18 on top right over here, we'll be just left with n. And if we take 18 away from 42, what are we left with? So we're going to get n is equal to, these cancel out 'cause we just got rid of the 18 there. And what's 42 minus 18?
See, 42 minus 20 is 22, so this is going to be equal to 24. And you can validate that. 24 plus 18 is indeed equal to 42. Let's do another example. Let me delete what I had written before. All right. So we have another situation where a tape diagram represents an equation.
Write an equation. Find the value of p. So pause the video again and have a go at it. Okay, so what I have here are one, two, three, four, five, six p's. We could literally write p plus p plus p plus p plus p plus p. That's six. Is equal to 84. Or we could recognize that that is the same thing as 6 times p.
So we could write this equation as 6 times p is equal to 84. What's the value of p that makes the equation true? So what number times 6 is going to get to 84? Once again, you might be able to do that in your head. But another way to think about it is if I just divide the 84 into six equal pieces.
Let me show that right over here. Or another way, divide both sides of this equation by 6, which I'm doing visually with this tape diagrams. So let me divide both sides by 6. Remember, if two things are equal to each other, as long as you do the same thing to both sides, they'll still be equal to each other.
So on the left hand side, you'll just be left with a p. So you get a p is equal to. And so it's going to be equal to just this, whatever 84 divided by 6 is. And some of you might do that in your head. You might recognize, well, let me just do it for you. 6 goes into 84, 6 goes into 8 one time, 1 times 6, right, is 6.
We get a 2. 8 minus 6 is 2. Bring down the 4. 6 goes into 24 four times. 4 times 6 is 24. And we have no remainder. So p is equal to 14. So this is 14, 14, 14, 14, 14, 14. And you can validate. If you add six 14s together, you will get to.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.