One popular of proportions is in something called dimensional analysis, and what happens
in dimensional analysis is we will have some quantity that has a unit and will try to convert
that quantity into a different unit, here�s just a short list of some popular conversions
that we do a lot, we can go between pounds and kilograms, or feet and inches or miles
and kilometers or grams and ounces or there�s many others as well like I said this is just
a short list and so basically what happens is they�ll provide you with for example
how many pounds are in a kilogram and then they�ll ask you how many pounds are in 7
kilograms or something so what you�ll have to do is set up a proportion with a variable
in it and solve for that variable which will be the number of pounds that are in 7 kilograms
or something so let�s work through a couple examples and see if we can wrap our minds
around dimensional analysis, so here is our first example it says how many kilograms does
an adult male weigh if he weighs 184 pounds so they gave us an amount in pounds of 184
they�re asking us to convert that into kilograms and so we can make a ratio for this information,
we can say that our adult male weighs x kilograms which is equivalent to 184 pounds, alright
now what will that be equivalent to if that x number of kilograms is equal to 184 pounds
then how many kilograms is equal to 1 pound for example, you could say 0.454kg is equal
to 1 pound and that was part of the provided information they told us that 1 pound was
equal to .454kg or you could say 1kg was equal to 2.2 pounds either one of these you would
like to use is fine. So we set up a proportion x kilograms is equal to 184 pounds just like
0454kg us equal to 1 pound so let�s solve this proportion here the typical way that
we usually solve proportions is using cross multiplication and that�s what we�re gonna
do as well. So we will take x times 1 that�ll be x and that�ll be equal to 0.454 times
184 and so let�s take our calculator here we�ll do 0.454 times 184 I�ve already
typed this in and we get 83.536, 83.536 and that unit for x was in kilograms. Alright
now truth be told we could have used this information to write the proportion as well
but if you�re comfortable looking a step ahead it was wiser to use this relationship
why we�ll notice when you had one in the denominator when you cross multiplied this
just gave you x times 1 which was immediately just your answer x, if we would have said
1kg, 1kg was equivalent to 2.2 pounds and cross multiplied we would have had 2.2x and
we would have had some extra steps. Is that wrong? No, it�s not wrong at all but you
know we are always trying to make life as easy as possible so think about which proportion
you want to set up to make the math easier in the following step. Let�s do one more,
how many liters are in 5 gallons? And they give us 2 relationships one liter is the same
as 0.264 gallons those are the same or you could say 1 gallon is equivalent to 3.785
liters so either one of these are ok so if we see the words how many that�s a key right
off the bat, that�s a key indicator that we don�t know that amount and that should
be the variable so we will say how many liters that x number of liters, that�s our variable
is in 5 gallons, x number of liters is equal to 5 gallons and that should be equal to a
certain number of liters that equals 1 gallon, so let�s ask ourselves how many liters are
in one gallon well we scan our information here, here we go 3.785 liters is in 1 gallon.
We cross multiply here and here and then x times 1 is x and then we�ll 5 times 3.785,
so we�ll take our calculator out 3.785 times 5 gives us 18.925, 18.925 go back and see
what the units were for x we have x liters so this is 18.925 liters here so that�s
how many liters are in 5 gallons.