## 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?

1. phi

think 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)

2. anonymous

alright..

3. phi

now pour out 6 that is like "subtracting" x/3 - 6

4. phi

what we now have is it is 1/9 full. any idea how to write that using x?

5. anonymous

=x/9?

6. phi

yes. 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)

7. anonymous

if i do x/3-6=x/9 then x would equal 27

8. phi

the point of doing this is not the answer, it is how you get the answer.

9. anonymous

okay so I would multiply each side by 9 and get rid of things then it would be 3 multiplied by 9

10. phi

like this $9 \cdot \frac{x}{3} - 9 \cdot 6 = 9 \frac{x}{9}$

11. anonymous

so then because it equals 27 (3 times 9 does) would i subtract 6 and have the answer of 21?

12. phi

the first term $9\cdot \frac{x}{3}$ or $\frac{9 \cdot x}{3}$ you can divide 3 into 9

13. phi

or, 9/3 is ?

14. anonymous

wouldnt it be 9 times x/3

15. phi

yes 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

16. phi

Is this confusing? If it is , it is worth figuring it out, because algebra uses this a *lot*

17. anonymous

yes im super confused

18. phi

If you have time, you can learn the idea You know how to figure out $\frac{4}{2}$ = 2 right?

19. phi

4 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

20. phi

or , another example, $\frac{30}{5} = \frac{2\cdot 3\cdot 5}{5}$ if you divide 5/5 you get $\frac{2\cdot 3\cdot \cancel{5}}{\cancel{5}} = \frac{2\cdot 3}{1}= 6$

21. phi

and 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 $\frac{\cancel{3} \cdot 3 \cdot x}{\cancel{3}} = \frac{3x}{1} = 3x$