Modeling fraction equations with tape diagrams: bike route
About this video
Marcus has ridden 12 miles of an 18-mile route, shown on a tape diagram split into thirds. The video finds the fraction ridden as 12 / 18 = 2/3 and checks equations, choosing 12 / 18 = 2/3 and 2/3 x 18 = 12.
You'll be able to
- find what fraction of a whole has been completed by dividing the part by the whole.
- use a tape diagram to show a fraction of a distance.
- recognise equations that correctly link a fraction, a part and a whole.
Key words
- tape diagram
- A long bar split into equal parts, used to show how a part relates to a whole.
- fraction of the route
- How much has been travelled compared with the whole distance, found by part / whole.
Transcript
- [Instructor] Marcus is planning an 18-mile bike ride. He rides 12 miles and takes a break at a park. He uses the model shown to represent how much of the route he has completed. All right, so he's completed 12 miles. The whole thing is 18 miles. And it's interesting, they've at least visually broken this down into thirds of that 18 mile, which would be six miles each.
I guess each of these little sections is a mile. And so let's read what they're asking us. Which two equations can be used to determine the fraction of the root Marcus has ridden? Choose two answers. So pause this video, have a go at that before we do it together.
Okay. So if I wanna know the fraction of a route, I would say, how far have I gone divided by the total amount that I need to go. So we know he's gone 12 miles and he needs to go 18, so he's gone 12. And I would divide that by how far he needs to go, and 12 divided by 18.
There's a bunch of ways that you could think about what that is. That's the same thing as 12 over 18, which is indeed two thirds. And you can see from this right over here that he is two thirds of the way. This is one third, that's six, and then another six is two thirds.
So I definitely, I definitely like this choice. B, this is how far I need to go divided by 12. And that isn't two thirds. This is going to be over one. 18 divided by 12 is more than one. So I definitely don't like this. This is just mathematically incorrect. Two thirds times 12 is 18.
Well, that's not going to be right. Two thirds of 12 is less than 12, not greater than 12. So by process of elimination, we can assume that D is going to be right, but let's see if this makes sense. Two thirds times 18 is equal to 12, yeah. And so that's the fraction that we've gone times the total should be how far we've gone.
And we can see that right over here, two thirds of 18, this whole thing is 18, we divided it into thirds, and then if we take two of those thirds, that is exactly 12 miles. So I definitely like choices A and D.
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