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Math-8, Video Notes 7.2, Equations with Rational Numbers

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hello everybody in this is mr. Sun Tiana and these are your video notes for 7.2 this is for a math 8th Class Fisher students please label your your notes 7.2 solving rational equations the targets were going to be covering in these notes so many questions so I can rational equations clearing your fractions and decimals in an equation collecting the like terms so here we go  why so here is the first problem it's about I think she's about clearing your fractions and we have 5 6 y + 1 equals 1/2 y + 1/4 here's your first determine what the LCM is going to be of the denominators by LCM case you forgot it's least common multiple least turn multiple right here comes the mathematics make this a little bit bigger to take a look at what those denominators are going to be well we have a we have a 1 we have a two-way of four for a denominator okay so what's going to be the process for clearing those out well  you have to think about the multiples for each of those numbers so let's make a list 6:15 to 6 fixing to 1218 North skip counting by 624 for one well one goes to every number goes into 1 goes into 2 goes in three and so forth I'll go into every single number need to find a common multiple 2 goes into 2 four six eight 10 12 14 and keeps on going 4 goes into 4 listen to 12 listen to 16 Otis that hear this would keep going on to 10 11 and 12 what is the common multiple adenomatous fit into 12 12 12 12 there it is okay so we just found power least common multiple it's going to be  12 nights now that we've found no we found that let's use that InStep number to here's what we're going to do we're going to clear the fractions by multiplying by that least common multiple so going to mold do I the entire equation 512 here we go  by 12 and I multiply this 512 animal supply list  512 and I'm gonna multiply this by 12 all right what will that look like one step I guess you can see we're just going to go ahead and solve this 6 fits into itself one time but it fits into 12  twice 1 * 12 is 12 - 15 - itself one time but if into 12 six times for fits into itself one time what is 15 - 12 3 times so what numbers will I multiply will over here I'm going to want to fly two times five here and then 12 x 1 here I'm going to multiply 6 x 1 and here I'm going to fly 3 * 1 let's go ahead and do that 2 * 5 is 10 y + 12 x 112 on this side 6 * 1 is going to be 6 y + over here three times one it's going to be three alright now that I have this equation going to go ahead and use our skills that we had before  to solve for that variable so I have a 6 wires go ahead and subtract 6y from both sides  just like that and The Six Wives cancel out 10 - 6 is going to give me for y + 12 equals 3 let's keep subtracting subtract 12  besides here what will I get well the 12s cancel out and I'm left with for what equals 3 - 12 is -9 one last step here I'm going to divide both sides by 4  Force cancel out in your final answer is y equals -9/4 songwriter type of problem here we have decimals how do we clear the decimals all right step number one very similar to before we're going to figure out the place value of the largest decimal so we have 55 and no decimal here take a look at the process here well we need to look at the place values the nine is in the  since the five is hundreds  alright the five here is in the turn in the fight here is in the  hundreds alright what place value is the largest clearly it's the hundreds that means 100 all right now that we saw the process for clearing  let's go ahead and clear it sent to clear the decimals by multiplying 100 because that was the largest  that was the largest place value solar multiply everything  bye 100 by 100 if the largest decimal would have been the tents we were x 10 if it was the we were * 1000 and so forth and so forth so we go ahead and multiply here and then multiply the last step is going to be to solve as usual so 100 * 95 is 95 x equals 100 * 55 5x + 100 some 6600 now we solve as usual I'm going to drop my algebra wall should I do I should subtract 55  x from both sides is the process that you've done before could you five this is canceled out go ahead and solve 95 - 55 is in fact 40 x that equals the 600 that I have here keep using your opposites are going to divide both sides by 40  besides Forest cancel out Andrea test with x equals let's see what is that drop a zero 60 is let's see 40 into 6120 1540 * 5 gives you the 600 there it is what do you notice here well I have a k over here 3K over there and have 15K over here so wait a minute I have a 3K here in a positive 15K over there go ahead and combine those like terms before anything else what's 3 + 15 + 18 so that turns into 18K drop down the plus 28 drop down your equals and your cave -6 notice how we elected the like terms now what do we do now we solve like we've solved be for drop down your algebra wall let's go ahead and subtract K from here change from their case canceled I'm left with a negative 6 equals 17 k + 28 how to keep your equation balanced so I'm going to subtract 28 from both sides extend my when's River Waltz cancel out I have 17 k equals -6 and -28 gives me a -34 my last step here's going to divide both sides by 1717 cancel out and you are left with k equals -2 all right three different types of problems three different skills are related to solving equations alright thank you very much I'll see you guys soon bye bye

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Math-8, Video Notes 7.2, Equations with Rational Numbers

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