Hello, my name is Fiona and I will be helping you on algebraic equations with fractions! 

The first question we will be solving is number 12 (letter JO) on page 32 of our Algebra worksheet.

 3e =    9   

            4

Since the opposite operation of multiplication is division, you will divide 3e by 3.  You have to balance out the question so you also divide 9/4 by 3/1 (which is the same as 3.) 

    3e      =      9    ÷   3  

    3               4           1

Dividing 3e by 3 will cancel them out and you will be left with the variable  e . You will just need to divide 9/4 and 3/1. First we'll start with dividing the denominators of both fractions. 

  e   =      9    ÷   3  

               4         1

Four divided by one will give you four. After that, we will divide the numerators. 

  e   =      9    ÷   3  

               4         1

9 divided by 3 will give you 3. You will be left with e = 3/4

  e   =     3   

              4

~~~

The second equation that we will be solving is number 12 (letter SW)

   5     =    1   v

   6          12

The first step we will do is that we will flip the equation. You can skip this step if you're okay with solving the equation as it is, but if you have difficulty and tend to get confused, like me; you can flip it as you like.

                ↔

   1   v    =     5   

  12               6

After that, you should simplify your equation. Put your variable in the place of the numerator so that the equation will be easier to solve. It will look something like this:

   v      =     5   

  12            6

Now it's all simplified, you can now solve! The opposite operation for division is multiplication, so you will multiply 12 in both sides.

   v   (12)  =     5    ( 12 )

  12                  6       1   

Since we're multiplying with fractions, you should write 12 as a fraction as well. I have written it as 12/1 which is equivalent to 12, so it did not change the value or anything. First, let us begin with multiplying the numerators, which is 5 and 12.

5 multiply by 12 will give you 60. Afterwards, we will multiply the denominators. 6 and 1 will give you 6. You will then be left with 60/6

 v =    60  

               6   

But we are not done yet! We have to do one more step, which is dividing! We will divide 60 and 6 and this will of course give us the answer of 10. 

v =   10  

If you'd like to learn more about this lesson, I recommend watching this video:

I hope this helped you! Have a great day fellow tortillas. :)