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If you're comparing quantities that have different units then
your ratio is a special ratio known as
a rate. Let's see how this works with a couple of examples.
If I want to write 12 miles in 10 hours as a ratio in simplest form,
I'm gonna write 12 miles
over 10 hours,
and then I'm going to look for a common factor.
Common factor is 2, so that's going to allow me to reduce
to 6 miles over 5 hours.
So that would be
my ratio, which in this case is also a rate
because the units are not the same. In the next example
I have a bag of mixed nuts, and I want to write the ratio
of peanuts to almonds. So I have
15 of the nuts were peanuts,
so let's put that in the numerator, and in the denominator
we have 20 of the nuts
were almonds, and if I reduce that, it's a common factor of 5,
so I get 3 peanuts
to 4 almonds
is my rate in simplest form.