找到比值上面的未知數 2 (英)
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找到比值上面的未知數 2 (英): 找到比值上面的未知數 2
- 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