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anonymous
 one year ago
The container that holds the water for the football team is
1/3
full. After pouring out
6
gallons of water, it is
1/9
full. How many gallons can the container hold?
anonymous
 one year ago
The container that holds the water for the football team is 1/3 full. After pouring out 6 gallons of water, it is 1/9 full. How many gallons can the container hold?

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phi
 one year ago
Best ResponseYou've already chosen the best response.0think like this: let "x" be the number of gallons when full. How many gallons in the container when 1/3 full? you write x/3 (that means we divide the number of gallons by 3)

phi
 one year ago
Best ResponseYou've already chosen the best response.0now pour out 6 that is like "subtracting" x/3  6

phi
 one year ago
Best ResponseYou've already chosen the best response.0what we now have is it is 1/9 full. any idea how to write that using x?

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes. we have \[ \frac{x}{3}  6 = \frac{x}{9} \] now we switch from "what is going on mode" to "algebra mode" to solve I would multiply both sides (and all terms) by 9 (this will get rid of the fractions)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if i do x/36=x/9 then x would equal 27

phi
 one year ago
Best ResponseYou've already chosen the best response.0the point of doing this is not the answer, it is how you get the answer.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so I would multiply each side by 9 and get rid of things then it would be 3 multiplied by 9

phi
 one year ago
Best ResponseYou've already chosen the best response.0like this \[ 9 \cdot \frac{x}{3}  9 \cdot 6 = 9 \frac{x}{9} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then because it equals 27 (3 times 9 does) would i subtract 6 and have the answer of 21?

phi
 one year ago
Best ResponseYou've already chosen the best response.0the first term \[ 9\cdot \frac{x}{3} \] or \[ \frac{9 \cdot x}{3} \] you can divide 3 into 9

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldnt it be 9 times x/3

phi
 one year ago
Best ResponseYou've already chosen the best response.0yes 9 times x/3 which you write as \[ 9 \cdot \frac{x}{3} \] or \[ \frac{9\cdot x}{3} \] or \[ \frac{9}{3} \cdot x \] all different ways of writing the same thing. but the important part is it means you can divide 3 into 9

phi
 one year ago
Best ResponseYou've already chosen the best response.0Is this confusing? If it is , it is worth figuring it out, because algebra uses this a *lot*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes im super confused

phi
 one year ago
Best ResponseYou've already chosen the best response.0If you have time, you can learn the idea You know how to figure out \[ \frac{4}{2} \] = 2 right?

phi
 one year ago
Best ResponseYou've already chosen the best response.04 is the same as 2*2 so we could write the problem as \[ \frac{2\cdot 2}{2} \] and we know the answer is still 2

phi
 one year ago
Best ResponseYou've already chosen the best response.0or , another example, \[ \frac{30}{5} = \frac{2\cdot 3\cdot 5}{5} \] if you divide 5/5 you get \[ \frac{2\cdot 3\cdot \cancel{5}}{\cancel{5}} = \frac{2\cdot 3}{1}= 6\]

phi
 one year ago
Best ResponseYou've already chosen the best response.0and you know 30/5 = 6 we got the correct answer. we use that same trick with \[ \frac{9 x}{3} = \frac{3 \cdot 3 \cdot x}{3} \] or, using the trick \[ \frac{\cancel{3} \cdot 3 \cdot x}{\cancel{3}} = \frac{3x}{1} = 3x\]
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