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Course: Pre-algebra > Unit 4
Lesson 2: Visualize percentsFinding percentages with a double number line
In this math problem, we determine the percentage of students taking the bus to school in a class of 28. By using a double number line, we find that 21 out of 28 students take the bus, which is 3/4 of the class. Converting this fraction to a percentage, we discover that 75% of the students ride the bus to school. Created by Sal Khan.
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This is so confusing(22 votes)
I know right!?(10 votes)
- how I can improve my math's skill?(10 votes)
- it does not (sadly)(2 votes)
1:20Couldnt you just turn 21/28 into 3/4 then 3/4 into 75%?(10 votes)
Indeed, but I think Sal purposefully showed us how to use the double number line(4 votes)
What's a douber-no, tubble number line?(7 votes)
i know right!(2 votes)
- How do you find an answer if you don't have a clue to it?(5 votes)
this is so hard he does not even tell us how to do it(5 votes)- so to find out 21 was 75% of 28 what I did was divide 100 by 28. I then took my sum (3.571.....) and multiplied it by 21 to and got the whole number 75.
so it looked like this on paper:
100/28= 3.571 3.571....*21=75
my question is, does this work everytime, are there exceptions?(2 votes)- To show anything that works, we can prove it, or simply do operations with variables.
So now assume we have
a = result after percentage (21)
p = percentage (75%)
b = initial number (28)
So first you did
100 / b
Then multiplied it by a.
a * 100 / b
On the other hand,
a = (p / 100) * b (Converting percentage to decimal)
a / b = p / 100
a * 100 / b = p
p = a * 100 / b
Since your "formula" is simply a result of rearranging the terms,
so yes, it works every time except when b = 0.(2 votes)
- Please help wait I kind of get it(2 votes)
I wonder if math back than was more similar(1 vote)- Probably. Maybe we could borrow a time machine and see if its true.(3 votes)
that's a number ray(2 votes)
1:20Video transcript
- [Instructor] We're
told that Omar's class has 28 students in it. 21 of them take the bus to school. What percentage of the
students in Omar's class take the bus to school? Pause this video, and see
if you can figure that out. All right, well, I'm going
to try to visualize this with what we call a double number line. So let's say that is zero, and 28 is the total number of students in this classroom right over here. As a double number line, because I'm going to
make another number line right below it. But I'm going to write these
points in terms of percentages. So zero students would be 0% of the students in Omar's class, and 28 students would be 100% of the students in Omar's class. And so what we really need to do now is, we know that 21 of them take the bus. 21 is going to be roughly around here. So that's 21. So we really just need to figure out, is what percentage is this going to be? One way to think about it is
what fraction is 21 of 28? Well, if I write 21 over 28, we know that we can
divide both the numerator and the denominator by seven, they're both divisible by seven, 21 divided by seven is three, and 28 divided by seven is four. So 21 is three-fourths of 28. So let's divide this number line from zero to 28 into fourths. So that would be halfway, and now we have it divided into fourths, and we can see that 21 is one,
two, three of these fourths. Well, if 21 is three-fourths
of the way to 28, then whatever percentage this is here, that would be three-fourths
of the way to 100. So let's divide this into fourths as well. Now we know that one-fourth of 100 is 25%. Two-fourths of 100 is 50%. Three-fourths of 100 is 75%. So what percentage of the
students in Omar's class take the bus to school? 75%.