A recipe for oat meal cookies calls for 2 cups of flour
for every 3 cups oatmeal. How much flour is required
for a big batch which uses 9 cups of oatmeal.
So 2 cups of flour for every 3 cups of oatmeal.
Now we are going to a situation where we are using
9 cups of oatmeal. I will let you know a couple
of different ways we can think about it. One way to think
about this is we know if we use 3 cups of oatmeal ,
we need 2 cups of flour. We do not know
how much is required if we use 9 cups of oatmeal
If we are going from 3 cups to 9 cups of oatmeal
how much more oatmeal we are using?
we are using 3 times more , 3 x 3 = 9
If we want to use flour in the same proportion
we need to use, 3 times the flour
we need flour times 3 ; 2x3 = 6 cups of flour
Another way to think about it
You can say 2 cups of flour over 3 cups of oatmeal
is equal to ? cups of flour over
9 cups of oatmeal. I like the first way of doing it
It is common sense. If you triple the oatmeal, you have to triple the flour.
Once youset up an equation like this, is
to use a little bit of algebra.
In cross multiplication, whenever you set a proportion
like this, 2 x 9 = ? x 3 or we get 18 = ? x 3
so the number of cups of flour we need to use
times 3 needs to be 18. You divide both
sides by 3 to get the answer which is 6
So we get ? = 6 cups of flour.
You might we wondering cross multiplication does not
make sense. If you have setup a proportion like this,
why should cross multiplication work. That comes from algebra.
I am going to rewirte this part as x to simplify
we have 2/3 = x/9.
In algebra, all we are saying this quantity over here
is equal to this quantity over there.
If you do anything to the left , we need to do the
same thing to the right to keep it equal.
So what can we multiply this by, so that
we are left with just "x".
So we multiply this times 9, If you multiply right side
by 9, you need to multiply the left by 9
for both sides to be equal.
on the right hand side the 9 cancel out, you are
left with x. On the left hand side, 9*2/3 = 18/3 = 6
So these are all legitimate ways of doing this.
For really simple problems like this
you can use common sense. If you are increasing
oatmeal by 3 times, increase flour also by a factor of 3

找到比值上面的未知數 2 (英)

找到比值上面的未知數 2 (英) : 找到比值上面的未知數 2