# Math Help - Finding Value of X division of fractions

1. ## Finding Value of X division of fractions

I am trying to help my son out and I am drawing a blank on this problem.

x ÷ 7/8 = 3/5

I know I have to do something like this:
X x 8/7 = 3/5

I am having problems with the solutions because of the reduced 3/5. Others we could eye ball and find the solution, but this one I am having difficulty with. Regards.

2. Originally Posted by zerbe
I am trying to help my son out and I am drawing a blank on this problem.

x ÷ 7/8 = 3/5

I know I have to do something like this:
X x 8/7 = 3/5

I am having problems with the solutions because of the reduced 3/5. Others we could eye ball and find the solution, but this one I am having difficulty with. Regards.
now there are many ways to do this problem, a lot of room for creativity. but lets keep it simple.

we want to get $x$ by itself. why waste time making the left hand side pretty. just get rid of the 7/8 right off the bat

$x \div \frac 78 = \frac 35$ .............multiply both sides by $\frac 78$ (do you see that this will cancel the 7/8 ?)

we get

$x = \frac 35 \times \frac 78$ ..............simplify

$\Rightarrow x = \frac {3(7)}{5(8)} = \frac {21}{40}$

3. Thanks so much. I have a tendency to make these problems more difficult than they are.

4. Originally Posted by zerbe
Thanks so much. I have a tendency to make these problems more difficult than they are.
yes, the objective is to get x on one side by itself, and move everything to the other side. we move things by performing their opposite operation on both sides of the equation. so i wanted to move the 7/8 from the left. i noticed it was dividing, so i had to multiply both sides by 7/8. that way, the division cancels the multiplication on the left and i get rid of the 7/8 while at the same time, it ends up on the right, which is where i wanted to move it to

5. There are two ways to do this, the guy above gave one, this is the other way:

your right with your 8/7, multiplying by this is the same as dividing by 7/8.

Thus you have x*8/7 = 3/5, this the same as 8x/7 = 3/5

so then we multiply both sides by 7 to get rid of it form the 8x

We do 3*7 which is 21

so we have 8x = 21/5

then simply divide both sides by 8, to get x = 21/5*8 which is 21/40.

I hope this helped, if you need any more help just PM me.