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## 6th grade

### Course: 6th grade > Unit 3

Lesson 3: Visualize percents# Finding the whole with a tape diagram

Keisha can run 170 meters in one minute today, which is 125% of her distance from three years ago. To find her previous distance, we convert 125% to 5/4 and divide 170 by 5, obtaining 34 meters per fourth. Multiplying 34 by 4 reveals that Keisha could run 136 meters in one minute three years ago. Created by Sal Khan.

## Want to join the conversation?

- it is soo confusing(15 votes)
- ok it might be hard at first but keep trying.(22 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.(8 votes)

- i need so much help this did nothing to help(8 votes)
- so the first step you did is point out that 100% of 170m of distance was completed in both cases.

then for the today’s section you combined the 125% with the the first “whole” into a fraction which is 125/100 and then simplified it which gave you 5/4.

This 5/4 im assuming gave us details as to how many “wholes” todays and the 3 years ago “wholes” distance % has. Which is indicated by the denominator.

And since we know in both cases that 170m was completely ran. they will share the same denominator/“wholes” which is 4. However the numerator will be different because well im not really sure why. Lol this logic is escaping me.

After that the logic you used to create the diagram was off to me in the sense that i am unfamiliar with too many concepts :((8 votes) - this doesnt help(4 votes)
- It might not help but that means you can do it or is it the other way around?(8 votes)

- If you divide 170 by (125/100) you also get 136. Why does it also work this way?(7 votes)
- batman solos and nobody can change my mind(5 votes)
- change your mind ha ha ha(3 votes)

- what is a tape diagram(5 votes)
- It was just the thing he drew with sections of equal amounts. I dont think you had to know it beforehand.(1 vote)

- how ? i know how but how do you get the numbers ?(4 votes)
- its like turning the percent in to fraction and find the amount. just like previous workings reversal?(4 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.