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# Solving ratio problems with tables example 2

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 three miles every 17 minutes. And we see that right over here. This is Ryan, after 17 minutes, he's run
three miles. And Sabrina runs five miles every 29
minutes. And we see it right over here. After 29 minutes, she has run five 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. Three miles every 17 minutes versus five
miles every 29 minutes. So what you wanna do is find a point on
this table where the, 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 where 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 took Sabrina two 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 over 100. Fair enough. The table shows equivalent fractions to 99
over 1,000. And then they ask us which fraction is
greater, 9 over 100 or 99 over 1000? And this actually is not so hard to
compare, even without the tables. You can multiply the numerator and the
denominator here by 1000, and, or by 10, and you would get 90 over
1,000. And comparing that to 99 over 1,000. And 90 over 1000 is clearly smaller. So you could say that 9 over 100 is less
than 99 over 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, where you have the same
numerator as denominator. And you see that 9 over a 1,000 is the
same thing as 450 over 5,000. And 99 over a 1,000 is the same thing as
495 over 5,000. So you have the same numerator in each in
the, you have the same denominator, but this
numerator is larger. 99 over 1,000 is a larger number, and we
mark that right over there.