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Let's compare 2 tables of ratios and interpret them to solve the word problem. This is a fun! Created by Sal Khan.
Video transcript
We're told Ryan and Sabrina are running a race. Ryan runs 3 miles every 17 minutes. And we see that right over here. This is Ryan. After 17 minutes, he's run 3 miles. And Sabrina runs 5 miles every 29 minutes. And we see it right over here. After 29 minutes, she has run 5 miles. The tables below show each of their distance over time. Who runs at a faster rate? Ryan or Sabrina? So these are hard to compare directly-- 3 miles every 17 minutes versus 5 miles every 29 minutes. So what you want to do is find a point on this table where the ratios between time and distance are easier to compare. And the easiest ones to compare are when you have the same numerator or you have the same denominator. So let's see over here. Are there any points in which the numerators are the same or the denominators are the same? Well, it looks like over here, it took Ryan 85 minutes to go 15 miles, and it looks like it took Sabrina 87 minutes to go 15 miles. So it took Sabrina 2 more minutes to go 15 miles, so she is clearly a little bit slower. Ryan's a little bit faster. So Ryan runs at a faster rate. Let's check our answer. Let's do one more of these. These are a lot of fun. The following table shows equivalent fractions to 9/100. Fair enough. The table shows equivalent fractions to 99/1000. And then they ask us, which fraction is greater? 9/100 or 99/1,000? And this actually is not so hard to compare even without the tables. You could multiply the numerator and the denominator here by 1,000, or by 10, and you would get 90/1,000. And comparing that to 99/1,000, and 90/1,000 is clearly smaller, so you could say that 9/100 is less than 99/1,000. But another way to do it is to look at the tables, is to look at a point where you have the same numerator or denominator. And you see that 9/1,000 is the same thing as 450/5,000 And 99/1,000 is the same thing as 495/5,000 So you have the same denominator, but this numerator is larger. 99/1,000 is a larger number. And we mark that right over there.