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### 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?

- What job is this used in? In other words why do we need to know this? Also u are really smart(18 votes)
- Any job really. In basic conversations it's common to hear percentages. So it's crucial to understand percentages.(18 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 :((16 votes) - i need so much help this did nothing to help(15 votes)
- just divide 170 by 125 and you get 1.36. it works for every % just divide the number that you're trying to find the % of by the % like if youre trying to find 34% of 100 or 100% just divide 34 by 100 and you get 0.34. try it for yourself(10 votes)
- what is a tape diagram(8 votes)
- It was just the thing he drew with sections of equal amounts. I dont think you had to know it beforehand.(2 votes)

- Could you please slow down. I would really appreciated it 😁(8 votes)
- you can adjust the playback speed in settings(1 vote)

- If you divide 170 by (125/100) you also get 136. Why does it also work this way?(8 votes)
- When you divide 170 by 100125

, you indeed get 136. Let’s break it down to understand why this works:

Percent Conversion:

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 a fraction: 100125=45

.

This means that today’s distance is 5/4 of the distance from three years ago.

Finding the Previous Distance:

Divide 170 by 5 (the numerator of the fraction): 5170=34

.

Keisha’s distance from three years ago was 34 meters per fourth (since the denominator is 4).

Total Previous Distance:

Multiply 34 by 4 (the denominator of the fraction): 34×4=136

.

Keisha could run 136 meters in one minute three years ago1.

In summary, dividing by 100125

works because it helps us find the original distance based on the percentage increase. The logic behind it is consistent and applicable to other percentages as well! 😊(1 vote)

- The way how the video explains it isn't enough when doing the exercise because this video only gives you one example to do it. Also, the exercises are a little different. He should have done more problems like 3 instead of 1 and solved some ones from the exercises.

Step 1. But for anyone, who needs some help a simpler way is to first make a line chart.

Step 2. 170 = 125%. 170 is just a number that equals 125%

Step 3. So to find out the number that equals 100% we first need to find out how many squares or lines make 100%

Step 4. So we divide 125% by 100% which equals = 1.25 (Which is just 5/4 in decimal form or 5 over 4)

Step 5. So 5/4 just means that there are 5 total squares or lines. And the number 5 equals 125% and 170

Step 6. If the problem is about finding who amount of numbers for each square then lastly you find out the amount that goes into each square which would equal 170.

So you divide again. We divide 170 by 5 which gives us 34. So now we know that 34 goes into each of the squares 5x time which all equal to 170 (34 x 5 = 170)

Now if you are dealing with number lines then continue.

Step 7. So since we now know there are 5 total lines we need to find out the number percentage that will equal 125%

Step 8. To know what percentage makes 125% we now must divide again. So we 125 divided by 5 = 25. So now we know 25% would be the first percentage out of 5. (25 x 5 = 125%)

Step 9. Since we now know each number line or square will be 25% to find out any other percentage like 50% or 75% you'll just need to multiply by the same amount of lines or squares you have.

For example 25 x 3 = 75% and since we know that 34 is the total amount for each square we also multiply 34 x 3 = 102.

So I hope that I have given you an idea of how or what to do when doing the exercise problem.(7 votes) - its like turning the percent in to fraction and find the amount. just like previous workings reversal?(6 votes)
- how ? i know how but how do you get the numbers ?(5 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.