Question

Simplifying Algebraic Ratios. I do not understand flvs version of explanation. so if someone could explain using the equation 18y^3 over 36xy^2

Answer 1

\[\frac{ 18y^{3} }{ 36xy^{2} }\]So basically, we're reducing a fraction when doing these. We approach it by looking at the numbers separately and then each variable separately. Now, because the values on top and bottom are not separated by addition or subtraction, focusing on bits and pieces at a time will not affect the answer. So to start off, let's look at the number portion of the problem.

\[\frac{ 18 }{ 36 }\]We want to reduce this portion into lowest terms if possible. So we first want to see if there is a number that can divide evenly into both the top and bottomof the fraction. The number we choose will not matter, but we may need to reduce more than once if we do not choose the highest number that can be divided intoeach number. So an obvious choice for reducing this fraction is the number 2. 2 can divide both into 18 and into 36 evenly. So if we do divide both of those numbers by 2, we get
\[\frac{ 18\div2 }{ 36 \div 2 }= \frac{ 9 }{ 18 }\]Now this fraction can be reduced even further. (which means 2 is not the largest number that divides into 18 and 36). Either way, choosing the correct numbers to reduce will eventually turn 18/36 into 1/2. Doing that leaves us with

\[\frac{ y^{3} }{ 2xy^{2} }\]The one on top does not need to be written since it is just a multiplication of 1. So from here we would move on to the variable portions. Note that we cannot really do any reducing unless we have something common in the top and bottom of the fraction. That being said, there is nothing we can do with the lone x on bottom, it has nothing on top to reduce with. So instead we look at the y's. Now amore visual way of dealing with the variables is to expand it out without exponents. Basically, I mean writing the y's like this:
\[\frac{ yyy }{ yy }\] y^3 becomes 3 y's multiplied next to each other on top and y^2 becomes 2 y's multiplied next to each other on bottom. Now for every y that is both on top and bottom, you can cancel them out. The top has 3 y's and the bottom has 2, meaning we can only cancel out a maximum of 2 on top and bottom.

Answer 2

So if we reduce the y portion of the problem, we're left with simply 1 y remaining on top. Having reduced all the numbers and all the variables,Im left with the simplified form of:

\[\frac{ y }{ 2x }\]