Interpreting a tape diagram showing a fractional increase
About this video
A tape diagram shows X as 4 equal units and Y as 7 units. So Y is 7/4 of X, or 3/4 more than X. The matching context is a bird that collected X twigs and then 3/4 more twigs the next day; '3/7 more' is a tempting wrong answer.
You'll be able to
- read a tape diagram to see how much bigger one quantity is than another.
- describe an increase as a fraction of the original amount, like 3/4 more.
- pick a real-world context that matches a tape diagram.
Key words
- tape diagram
- A drawing of bars split into equal units, used to compare quantities.
- original amount
- The starting amount that an increase or decrease is compared to.
Transcript
- [Instructor] The tape diagram shows a relationship between X and Y. All right, we see that. Select the context that the tape diagram could represent. So pause this video, have a go at that. Now, before I even look at the choices, I just like to think about what's going on here.
So X is four of these units, and Y is, let's see, one, two, three, four, five, six, seven of these units. Or another way to think about it, 'cause I know this is all about what fraction you are greater than, or what fraction you are of the original, so another way to think about it is Y is equal to seven fourths of X, seven fourths of X.
We can see that X is four units, Y is seven units, so if you took four here, multiply it by seven fourths, you're gonna get seven. Another way to think about it is Y is, lemme write it in words, Y is, so the amount that Y is larger than X, it is three units larger than X, and that is three fourths of the lengths of X, is three fourths larger, or three fourths X, larger then X.
So now, let's see which of these make sense. A store sold X balloons. The next week, it sold three sevenths more balloons than the previous week. This is tempting, but when we think about how much more it's selling, we're not thinking about the fraction of the amount that we're increasing to, we would think about it as a fraction that we sold in the first week.
So if this said three fourths, I would go for it, but this does not, so I don't like this choice. Navi has X number of flowers in their vase. Ina has three fourths of the number in her vase. Well, that would be if we saw something else that was like this. That would be Ina.
But I don't think that choice makes sense. So hopefully, it's C. A bird collected X twigs. The next day, the bird collected three fourths more twigs than that amount. Yeah, that makes sense. Here, the bird collected X twigs, you could say that four units of twigs, and the next day, the bird collected three fourths more than those four units, which would be three more units.
That's exactly what we had written right over here. And so I like choice C.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.