-1) you must find a common denominator before adding or subtracting
-2) when trying to find a common denominator, you must do the same to the top as you did to the bottom.
Applying these rules: here are some examples :
1/2 + 1/5: Common denominator is lowest number that terms in the denominator both go in to (in this case, the common denominator is 10). If the common denominator is 10, then in the first term, the 2 in the denominator of 1/2 must be multiplied by 5 to reach ten. Then, rule number 2 must be applied, and the top must also be multiplied by 5, making the fraction equal 5/10. With the second term, the 5 in the denominator must be multiplied by 2 to reach ten, meaning that the top must also be multiplied by 2, making the new fraction 2/10. Now, we are able to do the equation 5/10 + 2/10= 7/10
Sometimes, a common denominator cannot be found, so the terms in the denominators must be multiplied together to form the common denominator.
Here, x and (x+4) did not have a common denominator, so they were multiplied together to form one.
There are also cases where the denominator of one fraction must be multiplied by a number to make it equal the other denominator.
x/x-1 + 1/1-x = x/x-1 + 1/-1(-1+x) = x/x-1 + -1/x-1 = x-1/x-1 = 1
Here, the denominator of the second fraction was multiplied by -1 so that it equaled the denominator of the first fraction.
Many examples and practice problems can be found on page 227
Here are some examples from page 227:
13. 1/2xy^4 + 1/x^3y^2 = x^2+2y^2/2x^3y^4
19. 1/4x^2 - 1/xy + 1/y^2 = y^2 - 4xy + 4x^2 / 4x^2y^2
Here is a video link that may help you better understand this: http://www.youtube.com/watch?v=FZdt73khrxA
This blog was a great recap of the concepts we covered in class. It was helpful how you wrote out the problems and solved them and then described your work in writing. Because it is sometimes hard to follow problems with fractions when they are typed out like this, perhaps you could have written them out in notability and then added them to the blog to make it easier to follow. The video you provided was also helpful. Nice work.
ReplyDeleteThis blog was very straight forward and accurately described what we started in class. It was easy to follow, and there was a good variety if practice problems/examples. Also your explanation was very good. The video was a nice touch and built off what you had already said. Good job!!
ReplyDeleteThis blog was a very great way of presenting and reflecting on the information we have gathered as a whole in class. What specifically I thought was a great key point to mention was the two rules you must start with when adding and subtracting rational expressions. It helps to know so then the student won't make a mistake in the process of solving the problem. Overall I thought this was well written and established the key components to this study of math. Great Effort Will!
ReplyDeleteWill, your post is well organized and shows a good variety of examples. I like that you started off by outlining the process and then an example using numbers before you got to variables. The variable examples are accurately done, but two things might have made them easier to follow: 1) Sometimes you left out the middle step, where each individual fraction has a common denominator but has not yet been combined with the other fraction, and 2) It might have been easier to read your examples had they been done with something like Notability instead of only typing them out. Finally, the video you included provided a nice, extra resource. Overall, nicely done!
ReplyDeleteGreat post Nelligan, the way you explained the common denominator process was very helpful especially when we did our group projects because finding the least common denominator was something we had to frequently find. One suggestion I have is you could try putting in the exponents as a superscript instead of using the ^ symbol. I have found that you need to use a different word processor instead of the blogger processor because it doesn't let you do superscript but if you open another word processor and superscript the exponent you can easily copy and paste it into the blogger processor. Although time consuming it makes the problems a lot easier to read.
ReplyDeleteWill, this was a great post. I was reviewing notes starting to get things together for the exam and I had to review this section. This blog really helped me understand the basic concepts of adding and subtracting rational expressions. You really broke it down making it easier to understand and apply it into equations. I also really liked how you started with the two major rules of this subject. Great job of pulling all together what we learned in class and breaking down the steps!
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