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Multiplying and Dividing Rationals - Problem 1
Remember that a rational expression means that you have a polynomial on the top and or the bottom of a fraction. In our case we have monomials on top and bottom here and monomials on top and bottom there. This is really a problem that you might see in your study of exponents. Let me show you how to approach it.
When I teach exponents I’m kind of cruel I make my students write out all of the numbers and letters so that nothing gets confused. If you're really good at memorizing you might have memorized the shortcut rules of the exponents but don’t mess them up. The best way to do these problems is to write everything out. Let me show you what I mean.
This first guy I’m going to write as 3xyy on top, on the bottom I’m going to have 10yyy. In my second fraction I have 4xxxz, on the bottom I have xxxzzz. Okay now that everything is written out I’m going to cross out anything that’s the same on top and bottom and it’s okay when I’m multiplying since I have a multiplying sign if I had something that was the same here and here, even though they were in different fractions I could still cancel them out. That’s only true if I’m multiplying not true if adding or subtracting.
Okay let me show you. So on top here I have an x so let’s look for an x on the bottom I can get rid of, there is one, gone. On top I have 2y's so let me get rid of those 2Y's. Okay on top here I have 3x's I can get rid of two of them with those two. On top I have a z I can get rid of that z there. I think that I have everything crossed out that I can. It’s a good idea to go back and try to clean this up like rewrite stuff make sure I didn’t miss anything.
So on top I have 3 times 4 I think that’s it, I think I just have 12 on top. Everything else got crossed out oops! There’s an x, okay 12 and then x. Okay on the bottom I have a 10 a Y and zz which is 10yz². I’m almost done the last thing I’m noticing here is that the fraction 12/10 could be reduced to 6/5 so my final answer is going to 6x on top 5yz² on the bottom.
So again I’m a Math teacher and I’m cruel as many Math teachers are and I make my students write out all these letters when it comes to exponents. Your teacher might not do that, you might be trying to use the properties of exponents that you might have memorized either way you just got to be really careful to keep straight your properties like if you had 2Ys on top and 3Ys on the bottom you need to make sure are remembering that that’s going to result with one y of the denominator.
Be careful with that stuff, reduce everything and you guys will do well on these homework problems.