Question

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?

Answer 1

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)

Answer 2

alright..

Answer 3

now
pour out 6

that is like "subtracting"
x/3 - 6

Answer 4

what we now have is
it is 1/9 full.

any idea how to write that using x?

Answer 5

=x/9?

Answer 6

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)

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

or, 9/3 is ?

Answer 14

wouldnt it be 9 times x/3

Answer 15

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

Answer 16

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

Answer 17

yes im super confused

Answer 18

If you have time, you can learn the idea

You know how to figure out
\[ \frac{4}{2} \]
= 2
right?

Answer 19

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

Answer 20

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

Answer 21

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
\[ \frac{\cancel{3} \cdot 3 \cdot x}{\cancel{3}} = \frac{3x}{1} = 3x\]