SAT Math Part 20 - Simplifying Complex Fractions - By The Organic Chemistry Tutor
Transcript
| 00:0-1 | 71 . Which of the following answer choices is equivalent | |
| 00:05 | to the expression shown below . So what we have | |
| 00:09 | here is a complex fraction . How can we simplify | |
| 00:14 | this complex fraction ? What do you recommend that we | |
| 00:18 | should do ? So feel free to pause the video | |
| 00:22 | and try this problem yourself . What I like to | |
| 00:27 | do in a situation like this is I like to | |
| 00:30 | clear away all the fractions within the larger fraction . | |
| 00:34 | So let's analyze the denominator of the smaller fractions . | |
| 00:38 | Here we have an X , A Y and a | |
| 00:41 | three . So to clear away all of the many | |
| 00:45 | fractions , We need to multiply the top and the | |
| 00:48 | bottom by three X . Y . So let's multiply | |
| 00:52 | three X . Y by two over X . Notice | |
| 00:59 | that the X variable to cancel . So we have | |
| 01:02 | two times three which is six and times wide . | |
| 01:06 | Yeah . Yeah . Now let's multiply three X . | |
| 01:11 | Y Times one of why the Y variables will cancel | |
| 01:16 | . Given us three acts . Now let's multiply three | |
| 01:23 | X . Y by X over three . So here | |
| 01:29 | we can see that the threes will cancel and then | |
| 01:32 | we have X times X . Which is X squared | |
| 01:35 | . And then times why next ? We have three | |
| 01:40 | X . Y . Times five over Y . So | |
| 01:44 | why cancels ? And then five times 3 is 15 | |
| 01:48 | . And we also have an x . so 15 | |
| 01:50 | x . Does this right ? Here is the answer | |
| 01:56 | which as we can see , it corresponds to answer | |
| 01:58 | choice A . So when simplifying complex fractions multiply the | |
| 02:04 | top and the bottom of the fraction . Bye . | |
| 02:08 | The common denominator 72 . Which of the following answer | |
| 02:13 | choices is equivalent to the expression shown below . So | |
| 02:19 | here we have another complex fraction . Let's follow the | |
| 02:24 | same procedure . So let's identify the common denominator first | |
| 02:30 | . So we have an X plus five , even | |
| 02:33 | though we have two of them , We only need | |
| 02:35 | one and we have an X plus four . So | |
| 02:40 | we're gonna multiply the top and the bottom of the | |
| 02:42 | fractions by X plus five times X plus four . | |
| 02:52 | Seven over X plus five . If we multiply it | |
| 02:55 | by this what will we get ? The X-us five | |
| 03:01 | factors will cancel . So we're going to have a | |
| 03:03 | seven Multiplied by X-plus four was Now what about the | |
| 03:13 | denominator ? We can multiply two over X plus five | |
| 03:20 | by this . And so the X plus five factors | |
| 03:24 | will cancel given us two times X plus four . | |
| 03:30 | She now if we multiply negative three over X plus | |
| 03:36 | four by X plus five times X plus four The | |
| 03:41 | X-us four factors will cancel . We're going to have | |
| 03:44 | negative three Times X-plus five . So at this point | |
| 03:50 | all we need to do is simplify , Let's distribute | |
| 03:56 | the 2 , 2 x plus four . So that's | |
| 03:58 | going to be two X plus eight . And if | |
| 04:02 | we distribute negative three , two x plus five , | |
| 04:06 | That's gonna be -3 X -15 . Now let's combine | |
| 04:14 | like terms so we have to ex monastery acts , | |
| 04:20 | that's gonna be negative acts And then 8 -15 is | |
| 04:26 | negative seven . So what I'm gonna do is I'm | |
| 04:29 | going to factor out a negative one So I'm going | |
| 04:33 | to get positive x plus seven With a -1 in | |
| 04:36 | the front . Now I can move the negative sign | |
| 04:39 | to the top so I can find my answer like | |
| 04:41 | this so as we can see answer choice B is | |
| 04:48 | the correct answer . So that's it for this video | |
| 04:52 | . Now , you know how to simplify a complex | |
| 04:54 | fraction . So I hope you find it useful . | |
| 04:57 | And don't forget to subscribe when you get a chance | |
| 05:01 | . In addition I'm going to pull some links in | |
| 05:03 | the description section below . Feel free to take a | |
| 05:06 | look at that . When you get a chance , | |
| 05:07 | you might find some videos that might be of interest | |
| 05:09 | to you . Also check out my S . A | |
| 05:12 | . T . Math playlists for more videos on this | |
| 05:16 | type of topic . Thanks again for watching . |
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