3/4-9p=-3/5

Question

i dont understand the equation

Answer 1

This problem is algebraic, and we are understood to be solving for the variable "p."

I find it easier to always move the variable to where it is positive.  In this case, let's move him to the right side of the tracks (=).
>> 3/4 = 9p - 3/5

Great!  He's happy to be positive.  Now, we have two equations with uncommon denominators who don't really agree with each other.  Let's make them agree.  The lowest number they both agree on (and therefore are "factors" of) is 20!
>> 15/20 = 9p - 12/20

Sweet!  They agree.  Now let's get those fractions to live on the same side of the tracks (=).
>> 15/20 + 12/20 = 9p
>> 27/20 = 9p

Now all we have to do, is put poor "p" into solitary confinement, and put the number 9 with the others on the other side of the tracks.
>> 27/(20•9) = p
>> 27/180 = p

The only problem is, 27/180 feels fat and could use a diet.  Let's trim him down.  He likes 9s!
>> 3/20 = p
OR (in other words)

ANSWER: p = 3/20

Wondering how you can switch sides in an algebraic equation?  Do the opposite process.  Negative numbers should be ADDED to the opposite side.  Positive numbers, subtracted.  Multiplied numbers, divided... and divided numbers (or fractions), multiplied.

Hope this helps!

Answer 2

I would first multiply the entire equation by the least common denominator to get rid of the fractions.  The equation then becomes 15 - 180p = -12

Next I would subtract 15 from both sides of the equation.  The equation then becomes -180p = -27

Finally, I would divide both sides of the equation by -180.  p = 27/180  Dividing the numerator and denominator by 9/9 (which is like dividing by 1) gives the fraction in the simplest form: p = 3/20

I stressed "both sides" and "entire equation" because a lot of students make these mistakes of NOT doing operations on both sides of the equation and not multiply the entire equation.  I think the concept of "both sides" is one of the most important, if not THE most important concept in Algebra.