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## 6th grade (Illustrative Mathematics)

### Unit 3: Lesson 5

Lesson 12: Percentages and tape diagrams# Finding the whole with a tape diagram

Use a tape diagram to find the value of the whole when given the value of a part. Created by Sal Khan.

## Want to join the conversation?

- it is soo confusing(11 votes)
- ok it might be hard at first but keep trying.(13 votes)

- What job is this used in? In other words why do we need to know this? Also u are really smart(7 votes)
- Any job really. In basic conversations it's common to hear percentages. So it's crucial to understand percentages.(3 votes)

- batman solos and nobody can change my mind(5 votes)
- change your mind ha ha ha(4 votes)

- this doesnt help(3 votes)
- It might not help but that means you can do it or is it the other way around?(5 votes)

- i need so much help this did nothing to help(4 votes)
- If you divide 170 by (125/100) you also get 136. Why does it also work this way?(4 votes)
- its like turning the percent in to fraction and find the amount. just like previous workings reversal?(4 votes)
- what is a tape diagram(3 votes)
- It was just the thing he drew with sections of equal amounts. I dont think you had to know it beforehand.(2 votes)

- how ? i know how but how do you get the numbers ?(3 votes)
- no but It kind of do not make sense mrs.skillman kind you put some thing up so I can understand what it mean.(3 votes)

## Video transcript

- [Instructor] We are told that Keisha can run 170 meters in one minute. This is 125% of the distance that she could run in one
minute three years ago. How far could Keisha run in
one minute three years ago? Pause this video, and see
if you can figure this out. All right, now let's do it together. And my brain wants to make
sure I know the difference between three years ago and today. So today, she can run
170 meters in one minute. And what we want to figure out is how much could she run in
one minute three years ago? Well, we know this 170 meters
is 125% of the distance that she could do three years ago. And the distance she
could do three years ago, of course, is 100% of the distance that she could do three years ago, because it's the exact same distance. But I like to think in terms of fractions. So 125%, I could rewrite
that as 125 over 100. If I divide both the numerator
and the denominator by 25, this is equivalent to five over four. So that 170 meters, that is five-fourths of what
she could do three years ago. And what you could do three years ago would be four-fourths of what
she could do three years ago, because that's 100%. And so to figure out if
five-fourths is 170 meters, what is four-fourths? Let us set up a tape
diagram right over here. And I'm going to try to hand
draw it as best as I can. I want to make five equal sections. And I know it's not exactly, but let's say for the sake
of argument for this video, this is five equal sections. And so if we imagine that
each of these are a fourth, this is five-fourths. And then this distance right over here is going to be 170 meters. That's what she could run today. And what we want to do is
figure out what is four-fourths? That's the distance that
she could run in one minute three years ago. So this is our question mark. Well to do that, we just have to figure out how
big is each of these fourths? And if five of them is 170 meters, well, I just have to divide five into 170. Five goes into 17 three times. Three times five is 15. Subtract, I get a two
here, bring down the zero. Five goes into 20 four times. Four times five is 20, and
it works out perfectly. So each of these
five-fourths are 34 meters. 34 meters, 34 meters, 34 meters,
34 meters, and 34 meters. And so the distance that she
could run three years ago is going to be four of these fourths, or four of these 34 meters. So 34 times four, four times four is 16, three times four is 12, plus one is 13. So the mystery distance that
she could run in one minute three years ago is 136 meters. And we are done.