Modeling expressions with mixed numbers: bracelets
About this video
Josiah used 22 beads to make 2 3/4 bracelets. The video draws a tape diagram of bracelets split into fourths, sees that 2 3/4 bracelets is 11 fourths, so each fourth has 22 / 11 = 2 beads, and a whole bracelet has 4 x 2 = 8 beads.
You'll be able to
- use a tape diagram split into fourths to model a mixed number.
- find how much is in one whole group when I know how much is in a fractional number of groups.
- count how many fourths are in a mixed number like 2 3/4.
Key words
- tape diagram
- A bar split into equal parts to help show and solve a problem.
- fourth
- One of 4 equal parts of a whole.
- mixed number
- A whole number with a fraction, like 2 3/4.
Transcript
- [Instructor] "Josiah is making identical beaded bracelets for each of his friends. So far he has used 22 beads to complete 2 3/4 bracelets. How many beads are there on one completed bracelet?" And to help us answer this question, I'm going to use a tape diagram.
And since what we have here is an expression that's dealing with fourths, I wanna think about, well, let's take three whole bracelets and divide it into fourths. And so if I did that, it could look something like this, where if these are each fourths, then this right over here would be one bracelet.
So that's one. That over here would be another one. And then what's shaded in is going to be the 3/4 of our bracelet. So that is three fourths of our bracelet. So if you add these together, this is 2 3/4 of our bracelet. And we know that that's equivalent to the 22 beads.
That's equivalent to the 22 beads. So let me draw that here. So the 22 beads are equivalent to 2 3/4. So it doesn't go, if we went over here, that'd be equivalent to three bracelets, but it's equal to 1, 2, and 3/4 bracelets. So that is this right over here is the 22 beads.
So the question is, how many beads are there per bracelet? Well, to think about that is, we could think about how, how many beads are in each of these fourths, and then four times that is going to be in a bracelet, 'cause there's 1, 2, 3, 4. How do you figure out, as in how many of these fourths?
Well, let's see. How many of these fourths make up 22 beads. We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. So 11 of them make up 22 beads. And these are 11 equal. So if you have 11 equal things making up 22, then each of these are going to be two beads because 2 x 11 is equal to 22.
Or another way you could think about it is, 22 divided into 11 equal sections is equal to 2. So each of these are two beads, and we already saw that this is a fourth of a bracelet. So if you take four of these, so 2, 2, 2, 2. If you add all of those together, you are going to get eight beads.
Eight beads per bracelet. And we are done! Exclamation mark. (chuckles) All right, you don't have to write an exclamation mark.
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