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# Solving ratio problems with tables example 2

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.