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Finding percentages with a double number line

CCSS.Math: ,

Video 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%.