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Aztec Bridge

Added Apr 28, 2022 •

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Problem Solving Using Fractions

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are you guys welcome back to another math Bridge lesson today we are continuing to talk about fractions and we are in our final lesson evaru unit call operations with fractions problem solving using fractions so we can use addition subtraction multiplication division of fractions to solve real no problems I'm going to get my Albert handy it says tonight you are making hamburgers on the grill for dinner how many equal sides hamburgers hamburgers can you make you have half a pound of hamburger meat each hamburger is to be 16 thinks of a pound okay so first of all what kind of problem does this sound like what kind of operation design will using here division you know we have a CERN we have a total amount of meat we have to split it up into different thing into different pieces right piece for each Burger the end of the division unit you know I was getting X-rays and then I saw something I was like oh you know what I totally never noticed that it also works this way right so let me show you guys I'll demonstrate how we would solve it and then I'll I'm just going to share something that I noticed about the division problems that's kind of like a shortcut so Chris is the proper way to write the way we've been instructed to do it so we would say like this right I'm just having a setup a problem the total amount of meat divided into the Patty we can know how many patties we can make right and then told to to flip the second fraction so then want one of her 16 becomes 16/1 and then we switch to multiplication and then we danced bicros 1 * 16 being 16 2 * 1 being too and then finally reducing 16 divided by 2 equals 18 but here's one thing I noticed whenever we're dividing two unit fractions and I'll explain what a unit fraction is because we haven't haven't used that term in this lesson a unit fraction is a fraction that has a numerator as the number one number one as a numerator I should say 1/4 1/5 16 17 18 19 from 10116 those are all unit fractions because I have a 1 in the numerator so you know we're doing a lot of division problems with unit fractions and one of things I noticed was you know when will we end up solving for it you get the same answer as going and dividing from right to left right the same thing as if I were to just look at these two fractions ago okay what is 16 / 2 and work right to left of course that this isn't like a you know it's not a division math right was just something I noticed with with all of these units with all these unit fractions when we're doing two visions right so I'm not sure like if you look it up at that we might see this online has technique for you I know you said you know we can use as a shortcut because inevitably that's what ends up happening we end up here at the step where we do 16 / 26 in / 2 right off the bat when we set it up so you know try to try that out with your with your division problems that have unit fraction and I'll see if it saves you sometime sounds good. The traditional way okay Joe worked part of the year and part of that time was spent working on the assembly line with fractions did Joe spend on the assembly line him up for us they have the prom set up here you know one thing you may notice is they don't have Bantu that we're looking for as one of the options because the options are already simplified so we'll go ahead and multiply it and then we'll have to reduce do 5 * 3 is 15/9 * 763 your answer would be 15/63 but we would have to reduce that so 15 and 63 are both divisible by the number 3 so if I divide 15 do I get a numerator 5 and if I divide 63 by 3 by get a denominator of 21 so this is going to be our answer here 5 / 21 okay U remote supplying a fraction times a whole number and a hundred previous lessons we discussed that you know convert a whole number into a fraction simplify placing it over 107 becomes 7/1 as a fraction so if we multiply the numerator as we have to Temp 7:14 not the denominators 5 * 1 that's mine we have 14 / 9 where we can see the work here all right same scenario place that 7 over 13 * 7 is 2111 * 1 is 1121 / 11 is there answer there is a work down there okay it says a little while ago Susan had a quarter mile left to add to the finish line of a race she just finished an eighth of a mile how much further does she have to go okay so what we need to do is determine what operation was an easier so what operation do you guys think we're going to need to use to find out the remaining distance that she has would you guys say what what operation are we I used to find the remainder of her distance subtraction subtraction to take the total which is 1/4 and subtracted from the mount she ran 18 so let me go and write that down here we have 1/4 - 18 as we know with our subtraction and addition problems we need to have common denominator is the least common denominator if I were to skip count them again this how I find the Comfort Inn on me you know it's hard to skip count by 4 for a 12 and then skip count by 8 1624 the first number that shows up in both of those lines is the number 88 is the second number if I skip count by fours and 8 is the first number if I skip count by eights so 8 is going to be my least common denominator so that means I don't need to text the second fraction that's already in the Forum that I want it because they are already contains an 8 in the denominator I only need to modify the first fraction and so in order to get an eighth in the denominator X fraction by 2 so this is going to become the first fractions going to turn into 2/8 in a way that I got two of your 8 was by multiplying 1/4 by 2 1 * 2 is 2/4 * 2 is 8 so now I'm by the first fraction second Remains the Same so now I can solve 2/8 - 1/8 and that equals 1/8 oh okay original problem they found the LCD Emily song we can LCD stands for least common denominator okay you need a board that's 1/9 of a footlong you cut from a 1/4 foot board you bought how much bored do you have left okay so let's take a moment to understand what it is they're asking how much is 4 G you need a board that's 192 ft long you cut it from A1 order for 45 quarter of a foot we're going to remove One Nights of a foot how much do we have left that's what they're asking so they're asking what is 1/4 - 1/9 that's that's the problem so let's go -1 / not alright so we're going to meet to have the same denominator in order for me to solve this so what I'm going to do is I'm going to multiply the first fraction by the second fractions denominator that means 1/4 is getting what and then I'm going to multiply the second fraction by the first fractions denominator * 1/9 is getting multiple attempts for so becomes 9 / 36 turn the way I got that was 9 * 1 is nine nine times 4 is 36 now it's got my second fraction that's going to become 4 / 30 in a way that I got that was 4 * 1 is for 4 * 9 is 36 and then I can go ahead and do the subtraction 9 - 4 is 5 36 remains distance in a subtraction or in a an addition problem the denominators don't change only when I do that do you know my my problem is already in simplest Forum meeting I cannot I cannot reduce it any further is already in the in the simplest form and the way you know is you try to reduce him if you can't then you know it's in the simplest form 3 a you know I would only number that can go into 5 is the number 5 but 5 doesn't go into 36 at least not without giving me a remainder alright so here's the problem original problem they found the LCD and then they soft so here they doing 37 * 7 okay so that's fine we're going to place at 7 over a 13 * 7 is 21/7 * 1 + 7 1 divided by 7 is 3 say hurry up. Replace the whole number over 12 make it a fraction they multiply the numerator and get 21 and multiply the denominator and gets they simplify and get three okay you have an eighth of a pound of nails to divide amongst the two of you so how many are you going to get it so I'll tell you guys one thing when you're splitting when you have this is again this is a unit fraction write remember I explained the unit fraction is a fraction that has the number one in its numerator right our as its numerator when we're sick getting a unit fraction the denominator is going to double when we split a unit fraction the denominator is going to double so it's it's like if I have half a pound meat lettuce I have half a pound of beef and I'm going to split it between two people that means that I go from 1/2 and I split it each person gets one over four if I were to depart to take a quarter and then split it between two people even further than everyone gets an 81 / 1/8 write so each time you divide a unit fraction the denominator is going to double that's how you go from from what say you know using this measurement right I can go from a pound to half a pound so quarter pound to an eighth of a pound to one sixteenth of a pound to 1/32 of a pound red splitting it in half you know I'm getting half of the amount what happens to the denominator is that a doubles celebrity you got some kind of double okay we have an addition problem here so you know we'd have to find a LCD I'm going to do something first I'm going to put this answer here but I'm not going to submit it until we saw her the reason I'm I'm temporarily placing it in as the answer is because this the only option right that has the correct LCD what's the least common denominator between 2 and 7 so that's 14 so there's no way I'm going to have it. 15 and 16 right what does logically speaking I'm not sure what I'm going to have in the numerator just yet but I haven't done the math but I know it would have to be a 14. It's kind of like someone telling me I went to 2 hour to a vegan restaurant guess what guess what I ordered wrong not sure what you ordered but I know for a fact it wasn't animal meat red for sure was for sure wasn't fish if you had a vegan restaurant right so it's it's using your logic to can exclude options right so logically I'm excluding the 15 and the 16 right because I can't fit so anyways so I take the first fraction let's take the first fraction and I X the denominator so that means one half is in * 2 * 7 and * 2 times the denominator over the first so the first traction ends coming 7 / 14 and the second fraction becomes 2 / 14 next week at 9 or 4 all right we confirmed our you know whenever whenever I see an opportunity send corporate a test taking skill I always I demonstrated because you know passing the hiset which is really what we're all here for right now so you can pass your part of it is being off in in the material and then the other part is you know being being a Savage Tuskegee let me know when you can. Get your answer faster if I'm going to put this here the reason putting that there is because I know LCD but least common denominator is 9 so it would not make any sense for me to have an answer of an LCD that isn't you know you not 9 right maybe I could have a LCD that's three right either 3 or 9 because 9 to be reduced down to 3/4 by 3 but the smallest number that I can have is if nominal is 9 and that's that's the only option I have. So let's go ahead and solve it either way so I have my 1/3 and my one month so I need modify the first fraction so that I have a 9 in the denominator and you know usually if I need to modify both of them I do that thing where I most like a fraction by the second fractions denominator second fraction by the first fractions denominator but this isn't that scenario here I already have the LCD in one of my fractured so I just need to modify the first in order to get 99 M I need a x everything by City so this is going to become become three / 9 what's 1 / 9 so that's only three plus one is going to give me for I need or overnight all right another scenario so this one this one I can't put an answer right off the bat because all three of these denominators are fair game I could have a 6 right I could have a 6 as a denominator I could also have a 3 because 6 can be reduced down to 30 so have a to as a denominator because 6 can also be reduced down at 2 so I don't know what my my answer is going to be just yet but anyways we'll find out soon so this 2/3 I have to have a 6 at the bottom so what I'm going to need to do to this 2/3 cuz I'm going to need a double it so as if it were to be doubled would be 4/6 then I can decide the numerator as 4 + 1 is 5 and the 6 has remained the same so 5 / 6 again with this one just went off the denominators I couldn't get an answer right off the bat because you know we could have had what's the number for here right I had to if it was if my answer is four 6 that could have been reduced down cut in half and I would have had a 3 in the denominator if my answer was 3/6 I could have reduced it by 3 and I would have had a few in the denominator so I couldn't make decision right off the bat based off of the denominator in this okay your spouse bought a quarter of a gallon of milk at the beginning of week by the end of week only only 2/9 of the gown was left how much did your family drink during the week so what kind of celebration are we doing here solve this problem Robert Chevrolet original amount and we're subtracting what is left in order to figure out how much milk get up here we have one of her for -2 / 9 you know this is a subtraction problem so I need that LCD so I do that I do that first first fraction it's X the denominator 1/4 * 9 * the denominator of the first fraction so that means to 96 * 4 okay 9 / 36/9 * 199 * 4 36 s fraction becomes 8 / 36 2 * 4 is 8/9 * 436 and then finally 9 - 8 is 1 and the denominator remains consistent we had one thing when when I originally saw this problem I mean this is the first time I see this specific problem cuz it's the first time I work in the bridge but I've seen a problem set up exactly like there's just a different fractions and you know when I first saw this style a problem this is how I originally processed it in my head I thought again with a quarter right we had a quarter milk and we're left with tonight right so in my mind I thought this is what we begun with a quarter this is what we have remaining this is my house your brother and so what mess we have subtracted and then those - x do we don't know what this is this how I originally thought of it I thought minus the mystery of Mount Eagle tonight right and I don't recall us and I don't recall what happened to the wild things from butt yeah just in this case you would just take the starting amount subtract the remaining amount and will find out the the amount that was consumed by them okay ezpz Edition review all right so again first day I needed that Elsie but you know this is one of those problems we use our test-taking skills to just go okay 59 go to the next the reason we could do that is because we know that 9 is the least common denominator so that means that I'm going to need the first fraction to have a denominator of 9 plumbing supply house 911 in well as my options for the nominators 9 can only logically can only be the only option as an answer chauffeur you do for problems where you could use like reasoning or logic sometimes that's quicker than then actually are doing the math and solving it kind of like this one right here I know the LCD has to be 40 navigating bigger you know it it's it's quicker to just if you know something to be for certain right something to be true it sound like like example about that vegan restaurant which of these did they not only for sure do you need any animals if it was a vegan restaurant right you know, like saying old like I don't know a word problem that says Tom looked up in the sky and saw an animal which of these animals was it a bird a dog or a fish or logically can only be a bird right only Birds only bird would be in the sky fish would be in the water a dog would be on land using kind of like things things you already familiar with prior knowledge that's what stopped using prior knowledge to solve the question right which you know you could do with some of these do you know the LCD another one prior knowledge I know the LCD is going to be a team If I multiply these you know if I multiply the first fraction by the second fractions denominator in a second I know that it's 18 I'm not going to have a denominator that's bigger than that and besides 21 isn't even isn't even a number that would show up if I were it bounced my to write are still come by to anyone isn't going to show up in the same 4921 would not show up if I skip count by 9 so I know that logically all right cool sure all done

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