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Math Bootcamp 10/5/20: Decimal Fraction Review

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are you guys still alive welcome back sooner math boot camp in this session we're going to be going over our decimals and fractions section but whenever some practice questions let's get right into it so on the first question we have a a wooden flooring strip is 20 and 1/2 in long and they're saying if we cut off four and three quarters of an inch from one end what will the new length of the strip what will be the new length of the strip in inches so let's start off with our I'm starting off with this amount Andre subtracting this amounts from it right what we need to do is we need to focus just on the fraction part I'm so sokis on the fraction part and I'm going to copy down we have 1/2 - 3/4 so what's the first column that you guys do with this problem common denominators are not the same common denominator you can use as a least common denominator in this problem 4 * 1/2 by in order to get 4 subject 2 on top four on the bottom and I would get 34 it's right here right so when I have a 2/4 - 3/4 I get a negative 14 Ray so now that I have stuff that subtract what subtract 220 from the forest what's 20 - 4 1616 right salmon have 16 - 143 516 - 1/4 that's going to give me 15 and 3/4 does that make sense I will work it out so so let's put it over one right so Century think of it this way. Let me put it in terms of reading decimals or fractions 1/4 or 1/4 is how much as a decimal how much is 1/4 21 how much is 1/4 like a quarter $0.25 right so 1/4 is 1/4 if I have 16 and I remove 1/4 permit I have 15 and 3/4 that's why I didn't do any of that that's why I was just like 15 15 and 3/4 decimals or in terms of money we have $16 and we subtract 1/4 from it then we're going to have to change 3/4 and 3/4 does that make sense you have a dog that'll be just because it's a common fraction we could think of it as a as a as a decimal right 1/4 you know it's $0.25 3/4 mean $0.75 because of the negative right yeah the one fourth the negative one for us from the 16 if if we were to solve it like let's say let's say the long way we would say what would be a common denominator here in route City will for right so we have to multiply by 4 and we would have what's a what's 16 * 4 is I don't know go ahead 64 and then we would get 63 / 4 and then we'd have to go by the top the bottom so weird again 63 / 4 goes in once for the 6th add reminder 3 down here right abc15 yeah. That's me working it out all the way if you don't need to if it's a common fraction like one order 1/2 or 3/4 those are common fractions that were familiar with so sometimes you can just subtract if you subtract 1/4 you know you have 3/4 do you subtract 3/4 at 1/4 left but that's how we would work that problem out all right question number two says they have a box of Siri the cost $4.69 package label says that the box contains 19 servings what is the cost of one serving to the nearest cent so what kind of problem is this what what operation am I going to be using here yeah I'll be using division 2 I'll be taking my total cost 469 and dividing it by 19 for this one 4.69 / 19 and we get this right get Point 246 right when we're talking about since we only go out two decimal places so if I'm going to round to this decimal place to look to the one to the right since it's five or more this is going to go up to 0.2 that's me rounding yeah but what should I say to this a 0.24 684 to 110 whatever who has been around since the nearest cent so since when we talked about since it only goes out to decimal places then are you going to the nearest dance one sister so it should be coming 2018 so we're running to the nearest cent here so let me go back to my calculator and see yeah so the phone number is 024 024 684 211 red but when we're rounding the nearest cent the nearest cent is only going to be out two decimal places right so so that means I'm going to need to focus on this number right here but in order to figure out if I round this up or down I need to look to the number to the right of that a new-look to this number answer this number how I didn't read if it's 5 or greater that means that my number underlined is going to go up by 1 is that make sense not much so do you see the number that's highlighted in red the  right. Number if it's 5 or greater than the number underlined is going to increase by one if it's 4 or less then it's scary by 0 I see the number of highlighted determines if the number underlined increases by one or not in because it's the number that's highlighted in red is greater than 5 it's an increase the number underlined this number underlined right here by 1 and so we're going to get 0.25 okay what's good third the second or the third lesson in the book right now beginning do brown alright let's check out question number 3 so question with me is saying how much would a computer system cost if it is priced as shown below so here's the deal you pay 200 down and you make 12 monthly payments of only 99885 so let's set it up as an equation we're going to have 200 down Plus 12 * 98.85 so this is Nike run that's your down payment this right here 12 monthly payments of only 1985 this is right here and then and means over adding an addition right there so that's what that's when the assault and we're going to solve the multiplication first so first we're going to take care of the parentheses which is 12 * 98.85 to go to calculator 1186.2 200 listen to give me 2386 different song I don't get that one yeah I did it different but yeah I was pretty much the same answer all right. As check out question before this unleaded gasoline which sells for 2.869 per gallon how much would 10 and 1/2 gallons cost round your answer to the nearest cent so again if 1/2 is one of those fractions that is easily converted into a decimal we know that 1/2 equals what what happened equals so what we're doing in a calculators are going 1.54 10.50 * 2.869 and let's see what we got as an answer is there one get 30 points 1245 would be right here right decimal places. So I'm going to be rounding to this place so I need to look at this number right here if it's 4 or less than a everything else gets dropped two zeros if it's 5 or greater than this number under line goes up by 1 so because it's 4 or less we're just going to be left with 30.12 as their answer 30 points. Is a good gas price I don't see that in our area is right Alright so now we got these three packages no way 1 1/2 lb 4 and 3/4 lb + 2 3/10 what is the average weight in pounds of the boxes and the weights then divided by the number of packages okay so they have it they haven't given to us in terms of of the fractions in terms of the weight but our answer is given to us in terms of decimals right so it's go ahead and write the weights out in terms of decimals let me know what the first package is going to be 1.5 Packers number one Target's number 2 is 4.75 and package number 3 should be point 30 but let me just confirm 3 / 10 yeah so we need to do is we need to add these all up together first until we get to go 1.5 + 4. + 1.5 + 4.75 + 2.3 is a 8.55 and then to find the average we divided by the number of taxes that we had so we have three packages and if you divided total by 3 sorry answer comes out to 2.85 I'm sorry okay I get it here wasn't written out a number for Merced three packages yeah yeah so three packages to all we doing is they're giving it to us as they giving it to us as a fraction but our answers are in decimal form so all we did is Dubai the top by the bottom to get into decimal out of all our total weights to get 8.55 and then divide by 3 since there's three packages don't waste your problems like that like fraction wise but the decimals we should break them down or solving decimal you're going to have to convert your answer to two decimal so you're better off just converting to decimal from better confused I of course wooden yeah yeah definitely question number 6 Gina is paid $8 an hour if she earned 258 in 1 weeks how many hours did she work it doesn't matter that it was in two weeks all that matters is that it's a 3-hour and she made 258 I need to find out how much you was making the hourly no we we know if she makes $8 an hour we need to know how many hours did she work so I'm going to take total earnings 252 / 858 / 8 take me to 1320 colony Asian Garden Grass happened to calculator and then what did you guys get 3225 25.25 1/4 is 1/4 right we got 32.25 which is the same as 32 and 1/4 so so here we're doing the opposite right we going to answer as a decimal in we're converting it to a fraction so that's okay number 7 says a developer plans to build homes on 20 and 1/2 acres she estimates at 6 in 1/4 Acres will be used for roads the remaining land will be divided into 1 and 1/2 size 1/4 acre lots how many Lots can the sub Asian include okay so we need to start with her total 20 and a half and we need to subtract the amount for the roads right which is 6 in 1/4 is this your total land right here right total land and then the road is 6 and a quarter a little bit - because it's so she would estimate will be you so here that will be like taking away from okay and so let's let's focus on the facts and part here so I have 1/2 - 1/4 what do what can I use as my least common denominator here for right so I can multiply this by 2 to get for Target we can just give me one fourth grade so I subtracted naproxens subtract the whole number so what's 20 - 6 14 right 3116 20 - 6 is 14 so we have 14 and 1/4 and then she's going to be divided divide the remaining Lots by 143 so if you want to use our calculator we can type it in as 14.25 / 5.25 right right right questionable why was injured / the one for the divided over here Mister let me just holler at it for are the video okay so let's go to a calculator 14.20 5 / 2.25 equals 57 I'll make sense we just took the total amount of land that we had which is highlighted in yellow subtract the amount of land are using for the road and then once we have our remaining land that's can be divided into 1/4 of an acre lots so we just divide 14 in and 1/4 by 1/4 and we got 57 all right so question 8 says it's cool buys a thousand whiteboard markers below is the price per marker for two brands how much in school how much did did the school save by buying brand a instead of Brandy okay so the bond a thousand of each so for Brandy so for a it was 27 * 1000 and for being it would have been quite there. 6 * 1000 we need to subtract one from the other to figure out what the difference is right so for the first brand brand Avis on 270 right and the second brand they spent 360 right we need to find out that's a difference of 90 so they saved well this should be actually switched around should be 360 -270 it was a difference of 90 receive $90 does that make sense and this is all going to be posted up press some on the cross website I'll type it in the chat or I'll just I'll show you how to get there after I'm done with the video okay so right here we got this little grass and it says Ray is a veterinarian A Small Animal Clinic she has four he has for appointment schedules for Monday morning to a new patient appointments a serious injury visit in Dental add a dental scaling in hours how much I'm should be zip women's take so let's see Chelsea new patient okay so for this one we need a highlighter for sure CS2 new patient appointments right the new patient appointments are three and a half hours videos two of them right here's two of these is Serious injury visit scariest injury visit he has one of those and a dental scaling he was one of those two so in total how much time is this so let's let's save myself some time and use let's use it as I don't really know what since they're all in the same format we could either address fractions or we can. It as decimals for me and my mind is quicker as decimals because I think of it in terms of of money right let's ride the most common way we see it but that's how it's so how many 3/4 equals $0.75 right so for the first one the new patient appointment she has two of those right side and 75 on the calculator * 2 that's one point five and then the dental he has one dental scaling which is another point 75 so I go + 2.75 now I'm at 2.25 and then I do another + 1.25 which brings me to 3.5 3.5 as a fraction I know is 3 and 1/2 right how's that easy easy peasy question number 10 Jennifer Works two and a half hours each morning at the clinic how many routine physicals could she complete in one morning so see how long the routine physicals are physical is 1/3 of an hour so let's all this one by hand 3 + 1/2 divided Vine 1/3 so my 3 and 1/2 is a mixed fraction right so what I need to do is I need to convert it into its improper fraction and I do that by multiplying the denominator times a whole number and then adding that to numerator so let's let's do that now so what's 2 * 3 what's 6 + 1 7 / 1/3 so what I do is I do the inverse mean I just flipped the second equation and I change it to a multiplication add and multiply straight across so what's 7 * 3 2121 2 * 1 question almost all connected yeah the 1/3 is the amount of time that it takes to do a routine physical Salina channels are connected survive 21 and so now let's let's divide that outside 21 / 2 10 goes into 101 what the question was how many can she complete so she can complete 10 right lance210 Fried Chicken complete 10 and 1/2 1/2 is in completing it only 10 would be a complete 11 has nothing to do with the grass 11th and new personal and son so a minor league baseball stadium has 6,000 seats on beach towel night the stadium sold 5500 available seats the seats were sold so what is the total number of seats do they have and how many did they sell restaurant and so one quick tips or tricks when it comes to reducing is that if you have the same number of zeros on top as you do below and you can cancel those out so there's no cross no such color negative I can cross bees out I can cross things out and I'm just down to 55 over 60 right and what can I divide 55 and 60 by I'm trying to simplify these so what number can a book into 555 and 60 five five so up top I would have 11 and down below that have 12 55 / 5 is 1160 / 5 is 12 and I answer is 11 / 12 so the two-step it was pretty quick went from a very large number to very small number very quickly by Crossing out the corresponding zeros if you have the same zero stop is you to blow this cancel out and then you're down to a smaller number 55 or 60 and then Brandon told us then 5 can go into both of those 3 / 11 / 12 number 12 says the City Center Parking Garage charges 3:15 for the first hour and a dollar twenty-five for each additional half hour how much would it cost what would it cost to park at the garage for 2 and 1/2 hours so for the first hour or so so they when do two and a half hours right so the first hour IS350 right first hour and then it's going to be a dollar twenty-five 3 half hour so how much would it cost for if it's a dog 25 for 30 minutes how much would it be for an hour 25 what would it be 24 or 125 for 30 minutes so how much would it be for an hour Derby double. Right 3254 the second hour and then for that half hour and being there a Dollar twenty-five did he see how I broke that down the first outside the 1st hour is $3.50 right and they're saying that it's a dollar twenty-five for every half hour right which is here but for the second hour if it's a dollar twenty-five for 30 minutes then double that would be 250 for an hour right so all we have to do now is decide these all up together so we have three 15 + 256 and then we just add 1.25 to that + -7.2 5 alright so you got question 13 that says Susan scheduled 84 appointments for patients at a hospital Outreach Clinic only 56 patients kept their appointment what fraction of the schedule women's workouts destruction 56 / 84 / something right to simplify it so what can we divide both of numbers by 2 your call so you can go into both 56 and 84 show me the numbers of top I get 28 and I'm down below I get 42 so now what can I divide 28 and 42 by to ya good job there we go we have 14 / 21 okay now what can I divide 14 and 21 by we can divide 21 by 3 but we can't divide 14 by 3. Maybe larger number 7 nothing to give me two over three right there we go Stockton 14 says this portion of the gas bill comparison household natural gas usage for December of this year and last year how many how many more therms of natural gas to the household use in December of last year then December of this year Express answer as a decimal so it's a subtraction problem right you go to a calculator 3.90 which is how much do you use last year in these more last year and we subtract 3.13 which is what they use this year Point 84 sound of the sea straightforward just subtract what number from the other when the problem had too many words is very simple but when he has a little words so complicated yeah that could be it sometimes yeah sometimes they do try to throw in a big story and sometimes like for example this one even had a graph you know how to graph a how to story and really all they're asking is what is this China Star number the number one state .84 write 0.84 go to 15 says I have until 1 p.m. to load 250 Boxes by 12:30 175 of the boxer loaded what's wrong in the boxes has not been loaded I think should we have knocked and loaded whatever this is an English this is much so if they loaded 175 of the boxes then then then they want to know how many did they not load so they had 250 boxes and they loaded 175 they have 75 boxes but they did not load right mine is 75 / 250 that's the fraction but what can I simplify this 7550 / 75 no I didn't put it on me 75 + 1 what about a 25 mile at work are we divided by 25 we get three of top and then we get 10 below call Sonia thank you number 16 says on a number line below what is the value of a minus B so 7/8 - 1/4 so what's the problem here before what's the problem before I can solve the problem the problem is I don't have the same denominator right so what can be my least common denominator here 4 binary to get AIDS pretty simple red so that's that Scott is driving about 380 miles from Los Angeles to San Francisco he plans to three fourths of the distance before noon how many miles does he plan to drive before noon so we need to figure out is what is 3/4 380 right so what I do is I cross-multiply this is a total right here this is my part cross multiply and divide by 4 a 380 * 3 is me 11:40 or 1,000 140 and I divide that by 4 magazine 285 Missouri flying cross like that the multiplication because you have your when you have your this this could be like your charger whatever you want to call it is right here you have 3/4 right so that's that's the ratio that's the ratio and your totals go at the bottom right so your total cut the bottom and your part goes up top so your total of this fraction v380 right cross multiply and then divide by this number or you could also just go points 75 * 380 but also works point 75 cuz we know that 3/4 is 75 so far is 75 / X 18 divided by 4.75 times or okay 18 a cookie recipe calls for 1 and 2/3 of a cup of sugar if if you wanted to make half the quantity showing the recipe how much how many cups of sugar would you use services and what's half of 1 and 2/3 what they saying so so we're doing is we're doing one and two thirds / what's half of it so we want to do first is convert this into an improper fraction so what's 3 * 1 3 + 2 525 / 3 / 2 and anytime you have a phone number you can place it over one to make it a fraction and so now all we have to do is flip the second fraction and turn into multiplication we must fight Crossing we have 5 over 6 go ahead Three Steps step one step two step how did you get the two because my cousin cuz they want to divide in half so divided in half means to cut in half means 2 / 2 half of the of the recipe for the half half of the sugar the whole thing will be 100% or four quarters and a half a b 50 right so the full the full a lot of sugar for one cookie recipe would be would be this right here 1 cup + 2/3 1 and 2/3 of a cup of sugar but they want to know if you want to make half of that so if you want to half of that is done in / 2 Jamaican all right so if you just want to hear how many miles will a map map distance of 5/8 of an inch represents if 1 in equals 40 miles so again set apart total is our part is our total so we cross multiply and / babes so do to 40 * 5 + 1200 9 / 8 50 Cent I want to put it in a decimal way how would you write that out of the decimal 5 divided by 8 we get 0.625 and then we go times 240 150 best ways to do it the way I did it on paper was I set up my chart 5/8 and I-240 at the bottom and what I did was I cross x * 5 * 240 and then I divide it up 8 the second way that I didn't was as a decimal and as a decimal I go 5 / 8 7 * 240 so you can either divide your duck your fraction the top by the bottom and then multiply times a number where you can set it up like this cross multiply and divide by I just believe the way that is right now you know that is confusing you rather go the other way the 5 / 8 * 240 I mean but it was still be too confusing as far as how would you do even gets her five of them by 8 to get what I'm saying originally like the problem be ridden like this 5 5/8 means 5 / X 240 so if you wanted to put into a decimal form so you just go 5 divided by 8 to decimal representative 124 next Once done within 10 minutes that's going to be legal which of the following shows a drill bits arranged in order from least to greatest in size okay so we don't need to look at any of this right the prices don't matter organ that matters is is a size so we need to convert these all into the same into the same denominator right so am I so 32 is going to be my least common denominator here so what I multiply 16 by to get 32 2 2 Target 18th 18 / 30 to write my core is 5/32 which is fine right what I multiply 8 by to get 32 4 and I will get 12 / 32 and multiply 2 by to get 32 16 / 32 so the larger than the larger the size of this right so my smallest one is going to be this is going to be smaller five and then the next one is the 12 and the 18 best below 16 16 18 / 32 the first one is going to be the core box lullaby the bevel Falls brand quarterback thank U quarterbacks classic bevel cutter so now I know it's hard to tell just because the fractions have different denominator so we can we can look at and say okay this one's bigger this one smaller so we're doing is we're putting them all with the same denominator and then we're putting it in order from the smallest numerator to the larger Tomb Raider Joe is going to order a pizza you eat at least half of it if he's very hungry he will eat as much as 7/8 of the identify the two points Identify two points on the number line between that represent the minimum fraction of the pizza Joe might have silver in the maximum fraction of the pizza that you might have left over Sauvie's half of it how much is going to have left the other half right so that's going to be now if he needs seven out of the eight slices how many how much is going to have left over what one of the eight slices right so my answer is here VW and why right depending on how much he needs for the pizza plane to San Jose projects take no more than 60 hours if John can spare a seven and a half hours per day to work on a project what is the maximum number of days it will take him to finish this is a division problem right we have 60 and we're dividing it by the number hours that you can work per day to find out the total number of days that's going to take him so you got her calculator 60 / 7.5 288 days all right let's see if we can finish these last ones for 5 minutes a survey shows that two-thirds of all homeowners have a pets of those meaning of those 2/3 3/4 have either a dog or cat of the homeowner surveyed what fraction has either a dog so you start off with the original fraction which is 2/3 and of those 3/4 David auger can't see X and when you multiply how do I know I know you know because it's it's it's a fraction of those of the total fraction to a fraction of a fraction whatever you want to find that you're going to do a multiplication so if I if I say if I say like let's say half of the students less 1/2 of the students Drive to school right and if I say and that's a lot of those all the students who drive half of them on a truck so let's see if I have left I like all the students here half of them is 1/2 and then if I say half of the students that drive to school have a truck that's a 1/4 and I would get one for is 5 * 1/2 * 1 1/2 * 1/2 whatever you're trying to find out what a fraction of a fraction is you multiply multiply straight across 2 * 363 * 4 is 12 simplified by 6 1 / 6 that's how I want a man answers no it's not Stakes is 02 what's 12 / 6 is 2 there we go there we go now it's making sense Wyman shipping 104 employees work during the day shift at night to cruise 2/5 of the size of the day shift how many workers are scheduled to work the night shift we have this is our total here's our part X cross in / 5 I go to my calculator like two times 140 equals to 80 right divide that by 5 which is a 56 okay question 25 is all about that map so the map shows the distance in miles between foreshore Maya. Maya drives a van that deliver supplies to each of the store's 024 stores I said for Shores for stores my address is Van that deliver supplies to each other on Friday she travel the following route store A to B B to C C D D D to C CDA how many miles did you drive in all oh okay so the number in between represents so from A to B is 2.4 what's your point for right here and then from B to C it's four point 4.3 from C to D is 3.6 and then from DTC back is the same 3.6 and from seed hey is for what in the world and then all we have to do is total up these distances we have 2.4 4.3 + 3.6 + 3.6 + 4 17.9 yeah so did I make sense with you sound out the distance from each store and then I had it all together to find out the total distance that she drove the scene from a wooden dowel 12 and a half feet long Jamie cut two pieces each three and three quarters how long concede is the remaining pieces okay I'm really tempted to just do it as a decimal right so 12 and 1/2 it is 12.5 and he could two pieces that are 3.75 so here we go you have 12.5 cut his first piece which is 3.75 and we have a point 75 then he cut his second piece three-point -3.75 vs 5 write 7 as a decimal 27 says Lewis bought 20 shares of stock price at 26.38 per share him he also paid an $8 transaction fee how much do they pay repeat the $8 transaction fee plus 20 shares at 26.38 so first we do the multiplication so Chris can go to a calculator and we go 20 * 26.38 I gives me 527.6 have the $8 transaction fee right which gives me 535 and sixty cents see if you guys can do number 28 so 28 says a mat board is 60 inches wide how many strips measuring 75 inch wide can be cut from the board assume no waste from the cuts so you're taking us all what kind of problem is this like what operation are we using here division yeah yeah dividing 65.75 let me know when you guys get 83 * final questions of his take-home pay each month Jerry spends 1/6 on a car payment and 1/4 on food what fraction is taking payment is left after paying for these two items so first you need to combine these two that that's his expenses so what I can do as I can make the least common denominator 24 right now I can do that when multiplied this by 4 and this by 6 so I'm going to have for over 24 + 6/24 + 10 / 24 yeah and then I can reduce that I can divide that by 295 / 12 Roberts of the question is what fraction of his take-home pay is left so he pays 5 to 5 out of the $12 Skeeter she has won $12 for the sake of argument five out of the 12 that he has gets spent on his car payment is food so what's the remaining portion I don't get it so we know that it's kind of like the it's kind of like the pizza question where if I eat so if I spend five with this a huge for the sake of the argument for the sake of the question that $12 is all he makes right if 5 out of $12 is spent on bills and how much does he get to keep 777 out of those $12 suit is take home of his take-home hey so he sends 5 or 12 and he doesn't take 7 out of 12 Sarah thank you so much

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