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# Rate problem using fractions

Video transcript

Odie the octopus swam home. He swam at a constant speed. He plotted how far
he'd gone every 1/7 of a second on the graph below. Not all octopi
can create graphs, but Odie was no
ordinary octopus. And actually, octopi are some
of the smartest creatures on this planet. What was Odie's speed--
after probably dolphins and great apes and
probably most primates, but they're still fairly
smart, smarter than most fish. What was Odie's speed
in meters per second? Note we use m/s to show the
units of meters per second. All right. So to figure out speed
in meters per second, we essentially need
to divide distance in meters divided
by time in seconds. So let's see if we
can pull that off. So the easiest thing-- let me
find a point that I can clearly read how far Odie has traveled. So it looks like this
point right over here. It's clearly that the
distance in meters is 4/7. So let me do that. So the distance
in meters is 4/7, so I'll do that
in the numerator. the distance in meters. Gee, I don't like
that con-- well, I'll just go with this color. You know, the contrast
with the white background is a little hard on the eye. And It took him 5/7 of
a second to get there. So 4/7 meters-- actually, let me
make sure I put the units here. 4/7 meters in 5/7 seconds. And so literally, we just
need to divide 4/7 by 5/7, and we're going to get
it in meters per second. So this is going to
be the same thing as 4/7 over 5/7
meters per second. And 4/7 divided by 5/7 is the
same thing as 4/7 times 7/5. So let me write that down. So 4/7 times 7/5. Dividing by a fraction
is the same thing as multiplying by
its reciprocal. So times 7/5, and we get
this-- well, this 7 and this 7 cancel out, and
you get 4 over 5. You could have also
done that by multiplying the numerator and the
denominator here by 7. If you multiply it
by 7, multiply by 7, you would get 4/5. But either way, his speed
in meters per second is 4/5 meters per second.