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Added Apr 26, 2022 •

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Changing Forms

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already guys welcome back to another math Bridge lesson today were talking about changing forms so we have a decent sized lesson ahead of us with a good amount of it objectives so let's see what they are we're going to want to change fractions to mixed numbers and mixed numbers to fractions fractions to decimals decimals to fractions mixed numbers to decimals and decimals to make all right so really we're doing three conversions right it's 3 conversion between them both ways right so that's why it turns into all right so changing forms they have a guy baking bread I guess it's symbolism for from do to bread right changing forms what does baker has to say all right so they did just wanted us to put a little note there and say you know remember you know the mixed fraction I'm going to use the term mixed fraction because that's the trend lets you know most and I did the scribes a better write because yeah it's mixed numbers like numbers of two different them categories for the description of a mixed fraction is more accurate because it contains a fractured man I use the term mixed fraction you know they're just saying you're not the reason we convert into a mixed fraction is to make it easier to understand right if I say one and three quarters a dollar seventy-five that's easier to understand than me saying 7/4 7/4 in someone says you know 7/4 of a dollar okay well how much money do you really have to write and takes a moment comprehended so let's talk about under which circumstances we can do that conversion right from a from a fraction over 2 a mixed fraction so the word fraction is kind of generic for you know any number that contains a fraction line in your right but really in a fraction we really should be talking about you know a standard fraction write a standard fraction is always going to have a larger denominator and a smaller numerator right meeting the number at the bottom is the bigger number the number up top is smaller that's what we mean when we say the word fraction standard traction right if it were to be anything different anything other than than that scenario we would call it by different right it's the number of top is bigger than we would call it by its correct name improper fraction write we had a whole number we call it by mixed fraction but if it's if it's just you know approximately where we have a big denominator small numerator and that's just fraction or anything different would call it either improper or mixed so this fraction of Pop is actually improper fraction 4/3 is improper because the number of top is larger than the number below and you know to go load it further the number below will be called the denominator is is representative of the total right all of the parts did the total right all the parts combined together equals a total and the number of top is the portion the parts of the total the part can never be bigger than the total right it's kind of like you know you have a a group of like let's say five friends and you know I say oh how many of your friends are employed right it can't be more than five you only have five friends so you can say like a six of my friends are employed that can't be right so we can be five or less so the part should never be bigger than the total right that's why we call it in if it ever is you know because at that point if it no longer is a fraction that forms a whole number and that that's when do mixed fraction gets injured we have a whole number plus a fraction portion 20 ways only improper fractions can be converted into a mixed fraction that's one of the main sequence all right so let's let's review the steps and again really here you know we have to reiterate to change an improper fraction write a fraction or a regular fraction can't be chained into a mixed number do you have an example of an improper fraction write 5/2 in improper because the number of top is larger than the number below so we're going to divide 5 by 2 and you know this week's already be familiar with it because you know we did Division and one of the very first lessons so once you conduct your Division and you have your answer this is this like the final you know the final step of the division right we've already said two can go into 52 times and we have a remainder of one so you notice how they color how these numbers are colored differently we have the green to the blue one and the red to write so the green to the two that's on the top that becomes your whole number your remainder becomes your numerator and the number that you / that becomes your denominator so you'll see how they are they your answer to that surrounds the right to goes into * that's your whole number you're a Manger that's your numerator and the number you / that's your denominator so take a look at how this organized writes color coded so you can see I'm in here we'll get practice when we do what is you guys can see where those numbers are being placed okay perfect example. Let me bring up my pain right here and we'll do this by hand 5 out great yeah listen to go in five times all right so now we're done right we we have a remainder so now let me see if you guys remember the placement so what is the whole number going to be 5 or 2 I can't tell what is my numerator 2 yeah so the number you know my answer my answer would be five right my answer is the whole number my remainder is the numerator and the number that I / is the dinar you know if as long as you remember that your answer is a whole number and if you happen to forget you know okay which one are what's going to go where the one or the two where does that just remember the smaller number goes on top the larger number goes below when you have a mixed fraction it would have to be a proper fraction fraction portion of a mixed fraction is always going to be a proper fraction we originally start off with an improper fraction and then we converted I wanted to at least fix it right I don't know I'm trying to think of example I don't know this is similar but I guess you would be like if you had a bunch of bills in your wallet and you know typically the way you want to arrange your money is smallest bills in the front and then largest in the back so that you know when you spray it out in America order from smallest to largest and I guess like this would be like like let's say you have $100 in your wallet but it's it's broken down into like ones fives 10 twenties maybe a 50 and it's like all mixed up in a different order you know we might say I owe your money is a range in properly right it's not arranged correctly and so we would arrange it from smallest to largest so that you know you still have $100 in your wallet but now you know it's me you can pull out the money that he wants more okay we put three and then simplify all right so what is my phone number 3 or 2 monitor for so I just inserted the numbers as they are but now we can simplify so 2/4 simplified down to 1/2 yes in order to get that you know you just ask yourself you look at the fraction ESO what's the largest number that can divide and supposed to be that would be too and then and one thing a note is like when we do this when we simplify yes the numbers have changed from a to do one from 4 to 2 the numbers have changed but the value has not changed it's like you know when we go you know what say we took two $10 bills and then we swapped it for a 24 number change the numbers changed but the value is still the same we still had a total of $20 so you know we're not changing value at all it's just like we're I have a question if you were look at the improper fraction of 14 quarters 14/4 and 14 quarters right simplify that it would come out to three and a half so if you would like to take say seven of those quarters that would be roughly 16 quarter right there right or no no no where are you X or are you I'm just trying to see how we're getting that 14 quarters in another way becomes three and a half so if you want to take value yeah okay half of 7 quarters would be if you were to take my half as a decimal play 50.5 perfect but we would have 3.5 if we had a decimal right for you okay got it got it you don't even like you know how you saw these are all the same value 14/4 3 1/2 3.5 ways of representing you know I can say one hour 60 Minutes 1/24 of a day you know it's all the same time that's just and it just so fraction with a mixed number would be 3 1/2 decimal 3.4 in a fraction before teen for all right okay so now we're doing the reverse right we're going mixed fraction to improper fraction down at this box that we have are here we have four and 3/10 right and then if you look at the middle part the 10 * 4 + 3 that's the conversion that's where they're converting and then they end up with 43 / 10 let me explain what's happening here in the middle what's happening is they're taking the denominator 10 right here and regular did they take the denominator 10 * * the whole number four and then add the numerator 32 it so it's 10 * 4 + 3 denominator Times phone number numerator of working your way up you know you're starting at the bottom multiplying when you go one step up and then adding to the last step multiply and then add denominator Times phone number what's an annual noticed that the denominator the ten Remains the Same you know they had a 10 in the original problem the denominator remain the same through the transformation and if remain the same at the final stage after the transformation was done but that's the process and again and 3/10 is the same value as 43 / 10 they're just in a different format right now if I tell you I'm going to be here for another hour or I'm going to be here for another 60 minutes that's still the same so that's what's happening here same value just in a different okay so let's do it together so we're going to take the denominator multiply it times a whole number and then add the numerator so what is let's start with the first set of 6 * 4 what is a 24 now we had 25 and we get what 29 66 yeah Remains the Same throughout the entire process and you know it's like this you know we're doing the reverse of what we were just doing right and most of the time you're not going to do this it would be kind of like them you know most problems are going to go the other way the way we started because this is kind of like saying God I know this is like if we had you know lots of lots of you have like 5 bucks and he said oh can we get Nichols five bucks worth of Nichols you know it that's usually not what happened but normally you have changed bigger bills what is denominator X whole number what do we get there 43 40 + what is my denominator all right see how they're evil time this card in there too attractions usually change into a decimal when most of the numbers are working with our deaths are a so you know and we can say that for any the number that's in a different format if we have two different types of formats we're going to want to convert you know all the numbers so that they're in the same format and in this case we have you know you have two decimals one fraction to make s'mores convert 1 fraction into a decimal that we're dealing with all decimals all right yeah this is going to be probably one of the no more simple conversions this one is just divide the top number or the bottom number that's that's going to start process and again you know don't worry about that you doing it by hand that was an older lesson you know we're going to have time to get a chance to test so we'll be using a calculator and some of these you can just tell me what would this be as a decimal 2.5 you know this fraction right here you know you may recognize that this should be like 1/2 right close to but anytime you have a denominator that is double the numerator that's going to be 25 or 50 like 50 / 100 or 8 / 6 1/46 / 12/7 or 1416 all of these fractions they equal the same thing because their denominator is twice the amount even though you know they look wildly different they all have the same value okay what about this one what does this equal one quarter so you know this one reduced would be 1/4 right and this is going to be another coming to the one half 1/4 three Porters and the 1/3 are probably going to be the ones that you guys are going to see the most most this is pretty manageable to decimal to fraction this is more of a process that does really not too much calculations involve like I was in the other ones the first two that we did you know there's not a lot of calculation the right here they have 4.3 right so this is why become a mixed fraction of 4 is going to represent the phone number if three is going to represent the numerator in the proximal portion so they're going to have to get rid of this decimal point this appointment disappear before the fraction line under the three and then they're going to place a one immediately under the fraction line the next thing you do is depending on how many digits do you have on top that's how many zeros do you have 1 right here we only have one digit so they have 10 4.3 separate the 4 in the 34 is a whole number with 3 as the numerator the fraction line with the one you look at the numerator and see how many numbers do I have with only her how many digits I should say it's only a single digit number so I put a single 0 so if it were safe versus 4.10 than that would have ended up much different right would have been 31 if you had four points 4.1 is the same as 4.10 so you would have four and then your fraction line or one on top / 10 okay Global practice summer school okay so this one we have to go to step up so we'll go from decimal to mixed fraction by a whole number why does my numerator fraction line up in 15 is a single digit number so I put a 08 this can be reduced down to 2 and 1/2 5 / 10 / 2 now I can convert this mixed fraction over to nonprofit psycho 2 x 2 + 4 + 1 is 5 that's my new new murder five and below near me do we separate phone number show me decimal are the five becomes will it remains a phone number by the phone number in the fraction 90 as a numerator in a fraction line instead of 19 as a single digit number should I put a single 0 beer now I'm in mixed fraction format I'm going to convert from mixed fraction over to improper fraction and again I go 10 * 5 is 50 + 959 what's my number so is the answer right there like in the what you would just did there cuz I noticed it the the 5 / 9 enrite was like 2:59 or 10 is that correct or not themselves haven't changed in this case you know can you do that can you do that like that again you made please so yeah 5.9 what I do is I separate the five from The nine-to-five Remains a whole number 29 becomes a numerator in a fraction line I could have one and then since mine is a single digit number I put a single zero so when I see that that's the exact answer to that 59 on top after numerator and the denominator right same value 5.95 and 91059 over 10 in decimal mixed fraction so that's why you see a lot of the same o you know you see the same numbers 5 showing up against the 94 and then in the fraction it's because it's the same value just in different formats all right now we're going to do the opposite of what we just did you really just did three things forward and backwards all right mixed fraction into decimal so let's say we start off with in 14 right again I said this is going to be one of the one of those fractions you keep saying over and over again right even in in the way we refer to it verbally and one order you would want to order $0.25 to 22 some of these may be kind of can I try to answer this by looking at it just tell me what is a 2.25 yes all right they're going to run again so many fractions you know I mean you know you can come up with like these very are no one over 17137 right like I used your your money Siri that's how I got the answer answer these fractions is so uncommon you know you really just in the same one one quarter to one how one third one fifth The Palms will change that. this is an uncommon 158 so all you do is do 5 / 8 we got this and a whole number is 3 that doesn't change the smoke point 6 coupons all we did is go 5 / 8 okay look at this 7 or 14 we already saw this in this very same slide right you saw 7 or 14 is that 1/2 fraction write the denominator is double the number so this is a 5.5 right Eminem Just to be clear 5.5 can also be run as 5.50 same value because those digits are in the same place value when I add that 08 does n't change the place I leave any of the other kids all right now we're doing opposite right we're going from decimal over to mixed fraction 25 right we're going to 25 is the numerator of the fraction line that a 125 is a two digit number do we put two zeros and then we can simplify 25 / 100 simplifies down to 1/4 2 in 1/4 we're going through the steps for remember these steps aren't any different than the decimal to fraction right only difference now is that we have a phone number alright simplify if you can 25 over 100 equals 1/4 I mean you can bind it back with the phone number what's your last skills check all right my whole number is the same write 6 if I were to have 75 over a hundred what could that reduce down to read letters 5 / 100 reduced down to 3/4 alrighty guys

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