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Math 7 - Module 2B - Lesson 13 - Problem Set and a Better Method

Added May 05, 2021 •

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alright let's get on with us so we can finish be done all right so we're going to do this right here terminating the next lesson lesson 14 we're going to do with nonterminating and we're going to how to do all this stuff with the vision but today it's all terminating means it's easy to convert each terminating decimal to a fraction in its simplest form so we got this right here .40 is 0.4 / for if you look at it it's just one member look at this so changing a decimal into a fraction just see how many numbers are in the decimal place we have one number for the decimal place so you make a fraction play one right here and however many numbers you have in your decimal place that's how many zeros you put after the one so one decimal number one decimal place 10 pence notice that's the time for 10 there's your fraction but it says write it in its simplest form so to write it in its simplest form we got to simplify it for and 10 means we could divide both of these sister even by the book by two thank you a lot of guys put that in the chat good so 4 / 2 is 210 / 2 is 5 so this is the fraction in its simplest form so you will have a problem like this on it is going to be this easy I might give you one like the next one which is just a little bit harder not too much harder put on your headphones go login years in class if you're not going to be about doing my so sweet 16 we don't read it as Point 16 the correct way read it is 16 100 that makes it easy but again let's say you don't know that to write this as a fraction we put it over something with the one and how many decimal places two decimal places and then just put the numerator of top 16 100 but we got to simplify 16 / 100 both of these right here at yes we can. bye-bye too but I want you guys to Tracy number sense I can't divide 100 by 4 I could divide 16 by 4 so even though they're both even number senses if you see a bigger better number to / / that show us / 4:16 / 4 you get for 100 / 4 you get 25 + 25 there's nothing that they share so we don't divide us we leave it 4/25 this one is not as easy but still do it so that right there for you take away the decimal that 625 but if you know the position the placements the place value the last number 625 tenths hundredths thousandths 625000 you can go straight and write the fraction there but again write your fraction line little one in front Ira many decimal places you have that's how many zeros you got 1 2 3 1 2 3 / 1000 this will help you guys start with this message you start realizing tens hundreds thousands just start knowing the names and right here just put the numerator up there 625000 and what can we divide by we could divide by 5 cuz both of these numbers end in a 5 + 0 / 5 notice * 25 + 900 / 25 / 25 isn't too bad I can't do it in the top of my head but let's just do that 625 / 25 there are 2/4 and 6 that's 50 we get 12 bring down the 525 there are 25 1000 / 25 even though I simplified a Divison simplification I'm not done I could divide another five out so just because I did some work doesn't mean you're done always check 25 what can I simplify some more yes I could / 5 25 / 5 that's 540 / 5/8 if what you got a lot of it so I saw homework so he was treated in a lot 25 / 40 if that was a test I would take away a whole point because 25 over 40 can be simplified some more to get 5/8 simplest form means you can't simplify it anymore simplify one more time 5/8 there's nothing left to simplify nothing left of the bye. That's why it's the simplest form 0.08 Prince Hans 8 / 100 but again let's say you don't know what position it is we have we're going to make it into a fraction cuz run right over it put a one in front how many decimal places do you have have two decimal places and all we have to do is put this number in the numerator again get rid of the decimal place that's the number you put out the look we don't write a zero in front of a number so that's a placeholder when you put it on it's just eight we can divide by 4 if you see 8 / 2 but we know it's four times to we can divide one hundred by 4 also 8 divided by 4 to 100 divided by 4 2502 / 25 and then right here very similar 0.0 one to the lazy way to read it yes accepting what we're here I'm being asked to call home what am I going to tell him now what am I going to say to him .012 it again don't read it read a decimal get rid of the decimal cover it up and read the number if you have a zero in front we don't read this around front we read it as 1212 what you need to know the position tenths hundredths thousandths 12 12 over a thousand but again so you don't know how to read it but a one there and how many decimal places you got that's how many zeros though that thousand 12000 again let's / 4 you can divide by to somebody's just said can I just buy two yes you can but if you see a bigger I saw a bigger I guess that's Mastery Hill assisted / 2 will get the same number divided by two steps at work if you don't the Bible the biggest number you just got to do a couple more steps it's not too much 12 / 2 6 what's half of 1000 500 but notice look right here I can divide by 2 again that's why I divided by 4 with a saved us just a little bit of work not much 6 / 2/3 half of 500 250 there's nothing else decimal to fraction you're going to get one problem on this on your module 2B test not too hard not too hard I'm not going to give you one like a easy stir going to get some like beat me or see something that's easiest but you got to remember simplest form convert each fraction or mixed number to a decimal using equivalent fraction equivalent fraction for me and set it over a base 10 put it over 10 100010 and so on and so forth do not put it over 500 even though it's a hundred that's 500 neither one not a 5 so this one super easy I'm not going to give you anything like this one I'll give you some might be though 4/5 so the question is you look at your denominator there's not a one remember you want numbers that look like 10 100 thousand 10000 salon so five does 5 times something get you 10 if it doesn't then you say can I get a hundred can I get a thousand going to try and find some number that get smoked alright five times to excellent so now we have this were multiplying by two five times to multiply fractions we have a fraction over a 10. The name of a decimal position tens hundreds thousands ten thousands so on that's why we want it as a base 10 but let's finish multiplying first five times who is 10-4 * 2 is 8/8 tenths so we got one zero that needs one decimal place so all we do is plug in that number in your numerator .88 we read the fraction and the decimal as the same if our fraction has a base of 10 8/10 The Collection got 3/4 that's not a tent too big to be a tent so we got a name try to make it 40 is bigger than 100 so any bigger than 10 some can't make it at 10 40 times nothing gets us a hundred so we need to aim for a thousand that's a trick you go through all right what do I multiply what do I multiply to get close to thousand I can sit while some of you guys already what Melissa you go a little bit all right there's no air but you're doing each one of the separate problem so 340th you want to most of us already ends in a zero but want to put more zeros than we want to try and get you a siletz * 5 that gets you 15 over 200 so we're getting closer to a thousand 3/40 equals 15/2 equivalent fraction with X another 5 and somebody said I should have just * 25 or 4 I started this yes you can a x 25 it's one of those things you do 40 * 25 is 1000 but if you don't see that just keep on multiplying so you get to some 0-0 number that's the hardest part of doing this right here trying to find numbers to X to get you to one of these that is the hardest part but after you get there it's not hard at all look at is 5 * 2 is 10000 15 * 5 that is 75 75 / 1,000 so now change your fraction now that it's over at base 1075 1000 if you know how to read it and you know your directions there is but again if you don't is your decimal we have three zeros that means we got three decimal places but we have a two digit number of top start filling from the back so Point x.75 But the  needs to be a zero so that's an important placeholder .07 5 but if you read it 75 tenths hundredths thousandths 75000 read your decimal or fraction of base 10 they should be the same thing okay again I got weather FaceTime on same base 10 base 10 is having something is 10 * 10 10 * 110 * 1010 * 10 * 10 10 * 10 * 10 * 10 is an exponent a base-ten is 10 ^ anything so the first number always be A1 the number behind it will be a zero this will tell you how many zeros behind it so 75 1000 know how to read it based on or is your next one I definitely would give you play something like sea scratch paper I would definitely give you a problem I see I'm going to show you two different ways to do see there's a hard way and well there's a little hard or easy way it's just different ways this way right here 8/200 we want to make it over some base 10 all the work we've been doing so far we've been multiplying multiplying so let's do that first and I'll show you another way in a second after that we * 5 5 * 200 is 1000 8 * 5 is 40 so weak three decimal places and we got a two digit number so fill it in from the back but since there's an X there you got to fill it in with the don't forget that if you leave it as a point x number I'm going to take points away if you leave it as 0.04 T I still give you full credit but numbers behind zeros behind them you don't need you could drop it off why did that come watch this next one I'm going to do this problem again we're always thinking about X sometimes we already have a hundred how does 200 become let's bring it down instead of bringing it up let's / 2 200 / 2 we have it as 108 divided by 2 for yes even though I hear the tears of the hard part about this stuff even though we can simplify this fraction you don't want to cuz we're changing it to a decimal if you have it as a base 10 that's the type of fracture you want even though we can simplify it for over 100 for 100 two decimal places put in this number right there feeling in in the back that means that number becomes a zero if you can simplify by dividing out of 10 and you still have a base 10 that means you're always going to have an extra zero back if you don't take it out if you did that beforehand hey so which one this one I think is a better way to think about it you don't have to worry about that extra zero on freak out and we made it smaller simplify so times you could divide instead of multiply I would definitely give a problem like feet BMC some people will get D and freak out I'm going to tell you you shouldn't but he does involve a little bit more work so I'm going to let you know if you have a mixed number it's better than an improper fraction so don't you don't need to is 3 right here you know your answer is going to be three point something three-point something so you don't need to worry about the three you just need to put the 3 in front of your decimal that's not right that you forget your three take away half a point some of the guys that sell some of you guys get out and get a mixed number one but if you forget the whole number I will have to take away to half a point that is very important it's three-point not something we don't just want to know 5/16 let's do it off to the side somebody already remembered it lets * 25 and see what we get to Summerset * 25 right away 5 * 25 is 120 I don't know 16 x 25 right off the bat I'm going to do it also decide down here 3 30 + 1212 + 150 can you get a 020-5010 carrier one 700 is it 700 somebody that there was a mess up somewhere 16 * 25 oh that's a 400 look at that so we're getting closer to just a base 10 but that's 400 we need well we can go down to make it into a 100 conversely / we can divide the top by force if you're going to do the division thing you got to make sure the numerator and the night can be divided by the same number yes 200 we could divide 400 by 4 to make 100 but 125 does not divide by 4 so you got to make sure you're dividing by the same number so we can't make it in the 100 but we can make it into a thousand I believe four times what is that another 25 another 25 4 * 25 is 100 but we got two zeros in the back so becomes 10,000 125 * 25 I got to do the work off of the side 125 * 500-600 6:25 625 0 they're 10 carrier 145 3125 so there is 5 / 16 as a fraction we needed as a decimal but we had to remember that's why you always want to go I need to write this as a decimal to put back connect it so how many Jasmine with one two three four 4 decimal places perfect number 3125 that was this combined it we get 3.3 1253 and 3125 ten-thousandths that would definitely give me when I'm saying give give you something something with the mixed number in front so you don't forget that watch out it is very easy easy to do but it's also easier mess up and forget all right so there would pretty much done now we got the word problem anytime Sunday time word problem Anja Tanger Tanya how do you spell it I don't know is converting a fraction into a decimal by finding equivalent fraction that has power of 10 in the denominator so they're using this get us to see are there tricks are there shortcuts Sarah looks at the last step of Tanya's work shown below and says that she cannot go any further is Sarah correct if she is explain why if there is incorrect complete the remains test so she wants to say try and find a power of 10 have things to do so what they're trying to do is also what time is doing is trying to write it as a fraction over 10 have something over 10 at the same time simplify so they decide to do what's called prime factorization so I'm going to show you why they did this so they went they skip a couple steps 72 can be broken up into eight or nine times eight which is 9 can be broken up into three times three some of you guys remember this is called the factor tree and you break it into Prime factors 2 * 4 + 224 is 2 x 2 so you break it down to the smallest possible numbers and this is what 72 is made up of prime numbers 3 * 3 * 2 * 2 * 2 and why they skipped this is sixth grade stuff review here you can write repeated multiplication of exponents I got two threes b x 3 x 3 that is 3 ^ 2 and then I got this I'm still multiplying but now it's a different number 2 x 2 x 2 I got to I got three sets of two's repeat it that's 2 ^ 3 that's why and they switched it around they always put the small number in front Cedar power 3 * 3 ^ 2 that's why they wrote it like that right there and they broke apart 48th and they got 2 ^ 5 * 3 * 5 all right they're trying to write it with some fraction of 10 that's how they want us find at 10 and they said I could go yes and no cuz they want a power of 10 down there sometime so I'm going to run to rewrite it I'm going to rewrite it as and here's a thing this is this is why this last promise challenge question this is number sense understanding her so now this is as quarter code simplified as you can write it with prime numbers but the whole thing is what if you don't need to write it as simplified form how do you write it halfway that's a mess of people up I'm going to write this as I'm still going to keep this is 2 ^ 3 and I'm going to write it as instead of 3/2 power to I'm going to write it as three times three and I'll show you why down here when I rewrite down at the bottom instead of 2 ^ 5 I'm going to write 2 ^ 3 + notice I have two that are left I'm going to write X to Eminem right so that's a one but I need one more to do and I'll do that right here after second I'ma hold off on 1/2 I got this * 3 * 5 and here's my last two and I'll show you why look at this right here 2 ^ 3 / 2 ^ 3 who cares 13 / 3 that's the one that can go away so what's left right here we have a 3 / Let's rewrite what's left here I have a 2 * it is 5 * 2 I have a 10 sorry when you cross out these values of one that go away unless it the 3 / 2 * 5 times 2 but look at this I made this five times to attend so now I have a 10 what they're saying is I never thought of this by doing this so if you can make a ten we already got a 0 and a 1 in front I need to make this what do I multiply 2 to make 10 I got a * 5 what I do down here I do up here 2 * 5 that's a 10 x 10 down here 3 * 515 / 100 15 / 100 1500 there is your decimal Tanja is converting a fraction into a decimal so she got stuff and she didn't know what to do and I never thought about simplifying like this I do it one of these other old problems that way let's go is 5/16 + 2 + 5/16 using this method 5/16 that's all 5 is already pry but 16 is 5/2 * 2 * 2 * 2 so we need to change each one of these into a 10 that makes it so much easier 2 x 5 to x 5 to x 5 to x 5 and then together already got a five up here I got to put four more so that's going to be 5 ^ 5 / 10 * 10 * 10 * 1010 ^ 4 so I got four zeros 1 2 3 4 1005 ^ 5 5 * 5 is 25 25 * 25 is 62565 now that's so much quicker I never thought of doing this so even I learn some new stuff print let's go look at another one prime factor eyes Let Me Go sing let's look at another here let's just look at this 34343 / 40 and break this apart into tens so this is going to be 3 / for Domino 10 times for cuz I already have them for the ten in the front I have a in front and is there and back I don't need to worry about this one I need to change 40 into some number with a 1 in the front is there in the back of base 10 * 25 4 * 25 is 100 75 / that's one that's 10 on 100 so much easier 75 / 3 75000 I never thought about doing it this way that's me let me go look at some other phone let's go look at one from exercise to the one over Thursday 11 / 32 let's break this apart 11 is already Prime so I don't need to worry about that I just need to X other stuff 32 I'm going to change it to * 4 * 2 4 * 4 is 1616 * 2 is 32 in prime factor eyes at all the way and that's the whole thing that's that's actually practice right there why because if I break it down to two yeah I can multiply by 5 but look at this for * 25 for x 25 2 * 5 and this is all I need some multiply 11 by that's 100 x 100 * 10 selling a 1 2 3 4 5 0 1 2 3 4 5 zeros and put a one in front it's over a hundred thousand but you wouldn't understand this without doing the long way that I've done it so there's like a shortcut 25 x 25 is that you still need to multiply this part that part still not great so I will this is better than the long division way but you would still have to do some work at multiplying the numerator out 25 * 25 is 625 5 * 11 is 55 so you have to do 25 * 8525 Kerry 8 to 12. 13125 the same number 52135 734 we had that earlier to 34375 any change that to a decimal one two three four five five spots I like this method this is a good method right here this is better than Javid long division but it's better than my trying to guess you don't have to guess what number this is actually a great message how much are other method I showed you had to guess what number what number can I multiply to put to make it a zero in the back all right what number can I multiply you don't have to worry cuz we make simple small numbers 2 * 5 get us a 10-4 * 20 I guess it's a hundred we just need to worry about tens and 100 we'll try some other number out over 36 if we break it apart we got seven over or * 9 3 * 3 now 3 x 3 4 x 5 get this 100 so we can rewrite that  V I don't care what that is right now I'm not trying to figure out 7 * 25/100 * that's why this method would actually show you if it does or doesn't work I cannot multiply 3 times any number to ever get me a base 10 number meaning with the one in the front is on the back three times nothing will even get me a hundred thousand ten thousand it doesn't work so I can stop here and just do long division this is a great test to see if we could do this writing equivalent fractions with like I was trying to find another number let's go I think if we have a 3 seven I think the only one the only odd number we can if you break it apart if we break it apart and we can simplify. And we're left with the only odd numbers we can have in Spa 213 only odd number we can have is 5 only odd number we can have has to by Sophie prime factorize and we have a non five odd number it won't work or multiple of 5 but if we have any other odd number it ruins we can't have us three we can't have 707 X nothing will ever get onsrud and have a 9 we have a 1 but one cancels out if we have a problem we have a three 7 well neither 3 * 337 11 or 13 any prime number that's odd it's not going to work unless the only odd number that works is a five let's look at would break it apart 3 gets us let's go 4 * 20 we need to make bases of 10 4 * 25 gets new 100 so I can stop I-25 and then 20 * 5 gets me 100 * 5 show 15 * 25 and then right here we got 4 * 25 is 120 * 5 is 100 and so we get 10,000 15 * 12 and 15 quarters 16 quarters is 400 3737 50 374 there it is yes I'm correct was just 375 I was just 375 not 3750 so 370 5 / 10375 ten-thousandth we got four decimal places 1234 but we only got three digits 03759 Spencer this totally works I'm going to show an example where it doesn't work just like this one so your denominator needs to break apart into just choose choose and fives are the only ones dozen ones don't count choose and fives how many numbers you can have if you have any other number it doesn't work back to this one right here let's look at tonjes problem wrote it choose and threes but look at this the three please cancel out so it leaves you with tutus and five is a bias to become a 10 and become base 10 Susan 5 so you can only have 2 hours and 5 when you break it up this mess breaking it into equal fractions only works if your base your denominators breaks in the only twos and fives let's stick a Part 42 V can't be broken up 42 how is 6 * 7 I don't see nothing 2 * 3 * 7 by having these two numbers down here are this is not a 5 so this should not work even though we can make this a 10 2 * 5 and then multiply that by 5 and I still have the three times seven so I get a 25/10 times 3 times 7 but there is no way. either at 3 or 7 into a ten or a hundred or a thousand nothing we can multiply the change that is if I multiply 30 times 70 is still liquor store 21in Front what the 500 300 x 700 no one in front so prime factorization I got to remember this myself

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Math 7 - Module 2B - Lesson 13 - Problem Set and a Better Method

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