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Math 7 - Equivalent Ratios, Percent to Fraction, Percent of a Number

Added Dec 11, 2020 •

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Models on how to shoe work for Make/ Find/ Write equivalent ratios/ fractions Change a Percent to a Fraction (in Simplest Form) Calculate the Percent of a Number

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find makes or rights equivalent ratios fractions ratios are just another way of saying fractions fractions ratios we're going to write make find equal ratios case in point let's start out with 36 / 48 simplify a fraction ratio. an equivalent fraction ratio in this case look at this 3648 you want to look for factors that they share that you can divide by such as 2 both of these are even numbers I can divide both of these by 2 I can factor out a factor is a number that you can divide out and you want to look for a common factor for both the numerator and the denominator and if you look at 2 / 2 2 / 2 makes 1 we are technically / 13648 / 1 one made up of 2/2 when you divide any number by one you just get itself so that's why whatever we get the quotient that we guess it is equal to 36/48 is equal to let's do this 36 / 21848 / 224 3648 equals 18/24 o these two ratios equal 36 / 48 equals 18/24 these are not two different fractions they look different but they are equal so I have just made an equivalent ratio an equivalent fraction we do not have to just divided by 2/2 but we have to divide by an overall value of 1 and Tayson 36 / 48 again instead of / 2 / 2 let's / 3/3 fattest still a value of both of these 36 and 48 can also be divided by 3 so both of these are having factor of 3 and then that we can divide out doing that we get well over 16 * 12/16 equals 36 / 48 so 36 / 48 what we started with is equal to 12/16 logic then if 36 equals 18/24 and 36/48 equals 12/16 that means 18/24 equal to 12/16 cuz they're all equal to each other their equivalent is a just two and three now it's best when we're talking about simplifying fractions to find the greatest common Factor the GCF is the biggest number we can divide both for 36 and 48 by in this case it is 36 and 48 can be divided by 2/3 biggest number that 36 and 48 share in common that you can / is a 12 12 / 12 that is another value of one so we're just divided by 1 so that's why this resulting ratio is going to be equal 36 divided by 12 is 3 48 divided by 12 is 4 do all of these fractions simplify down to 3/4 this is the simplest version of 36 / 48 so what we can do to make equivalent ratios the by top and bottom the numerator number by a ratio of one as long as both of these numbers are common to both of them we can divide top and bottom two these are both divisible by 3 divisible by 12 want to find a common multiple that you can divide out GCF greatest common factor another way we don't have to just divide week the X instead of jet instead of dividing by 2/2 we could have * 2 / 2 / 1 + x one gets us an equivalent thing so let's instead * 2/2 * 1 when you multiply anything by one you get back that anything we're not changing the value changing the way the fraction looks by multiplying by 1 so 36 * 27248 * 296 that means 36 36 48 is equal to 72 over 96 but you saw even within my mental math kind of slow down why do you want a x if I know that this 3/4 is equal to 36 / 48 let's find equal ratios from the simplest version of 36 / 48 so look at this I can * 2/2 again that's the value of one 3 * 264 * 28346 6/8 I don't have 2 x 2 ft x done yet let's go 3/4 * 5/5 and look at this right here that is equal to 3 x 5 at is 15 for x 5 that is 20 cuz we x value of one made up of 5/5 + 15 over 20 of these ratios are equal to each other we started out with 36/48 we simplify and we got let's do math so I can see all these for somebody got was 18 over 24 so 36/48 is equal to 2/24 is equal to 12/16 is equal to if you have a 3/4 that way out here cuz that the simplest version 3/4 which is equal to help me multiply this we got a bigger one let's go 72 over 96 which is equal to 6/8 m which is equal to 15/20 all of these ratios fractions are equal to each other all we did was multiplying / one we change the way 36 / 48 looked we didn't change the value of what it's equal to so that is how you find make and write equivalent ratios writing a percent or changing a percent to a fraction in simplest form 8% a number out of 140 translate the statement one of the easiest thing to know the word is equal so are percent is equal to some number out of 100 and that's pretty how you change a percent to a fraction let's do a quick simple example so 44% that is equal to so that's your percent and what's the number number is 4440 4 out of 100 there we go that is a percent to a fraction but we need to change it to its simplest form so let's zoom in style he's sorry so right here this right here is the work you always social work in math so we changed it to the percent to a fraction but the fraction should be written in its simplest form the last example we showed work how to make any fraction while to find equivalent action forms to make a fraction to its simplest form if possible you need to divide by the greatest common factor what is the biggest number that you can divide out in both 44 and 100 that's the same in this case it is 4 since we are dividing by a value of one made up of factors of 4 we're going to end up the simplest fraction form the simplest form of the fraction so this right here is the work we change the percent to a fraction but the fraction is not the simplest form that still work though but little bit more work dividing the greatest common factor 44 divided hundred and we're going to divide by 4 and by 4 we end up with 44 / 4 that is 11100 / 4 that is 25 and we check is there a number that both 11 and 25 can be divisible by that's the same no so now this right here is 44% as a fraction in its simplest form and this is the work that you need to show can you always do you always have to simplify it sometimes the percent is already Amplified case in point let's do 37% to change this percent into a fraction again take the number and just put it over 100 and all you got to think 36 and 100 the number sets is there a number I could divide 37 and 100 by that's the same so I can make a one I can simplify you got to think no because 30 when is prime there is no number that 37 100 share that you can divide both top and bottom by to make an equivalent fraction there is no value of one that you can / 37 100 come make it simpler this right here is the fraction in simplest form sometimes that's all you can do and not all percents are less than 100 sometimes we got bigger percent say 250 / sent does not matter what the number is to change a percent into a fraction just write the number and put her over 100 how do you change a percent into a fraction or right here look at this we can see that we can simplify 2250 over 100 we could divide by a 10 that leaves us with 25 over 10000 shares a simple way of simplify what is 25 / 10 I can do some more work both of these can be factored by find if you factor out a 5 so 5/5 is a 1 we're not changing the value which is changing the way it looks 25. by five 5:10 / 5 to sew 250% as a fraction in simplest form is 5 / 2 finding the percent of a number you need to realize and if you remember in our lesson the word of mean multiply X so percent of a number so percent times a number anytime you see percent of a number percent times number but percent can't really do that why you can find the percent but most of the time percent is used for calculator purpose so what on the last example we did we were able to convert a percent to a fraction we know how to multiply a fraction with a number so it's a fraction times a number a fraction of a number so see that percent of a number is just percent times number but let's convert a percent to a fraction so we could show the work on paper so fraction times number let's do 28% of 52 so 28% of 52 that just means it's 28% find 52 but again look at is 28% * 50 you can't really do that but we can do is change 20% into a fraction and that was our last example for 28 over 100 look at that and then we multiply this by 52 and how do you multiply any fraction to a number that's not a fraction well let's change this 52 into a fraction so we got 28 / 100 X 52 / 1 on now we got to Francis we multiply and that's pretty simple all you have to do is multiply the numerator X in numerator and denominator comes and Donna are whatever that fraction if you simplify your done but do you really want a * 28 * 52 and that's why I'm at last example even though we change the fraction into a percent percent into a fraction this fraction can be simplified so let's simplify that and I'll show you why that will help you out so let's do the work off to the side so 28 / 100 and I see that was 28 100 can be divisible by 4 value of one made up of 4/4 we're not changing the way we're not changing the value of 20 and over 100 just changing the way it looks so 28 / 4 100 / 425 so we know that 28/100 is equal to 7/25 so instead of having 28 of 100 we can substitute 7 / 25 there again these are the same value we're not changing anything that's we're not changing that were just making it easier for us to simplify look at this and this is why 28 * 52 that sounds a lot better 100 times 125 times 1 but this right here the new X in numerator now that is a lot simpler so let's do that 7 * 52/25 * 1 let's do the work off to the side we're going to go 52 * that was 7 carat over that is 364 so we get 360 for over 25 and that is 28% of 52 right there but that's fraction doesn't look good we gotta somehow changed we can change it to mixed number as I can help but let's just remember. infractions are the same thing as a fraction is just another way of writing a division problem so 36/25 / 364 25th is the same thing as 364 divided by 20 we can't really show do work with this right here this division expression we got to put it in our nice little algorithm so let's go 25 out here 364 so 2364 / 25 + how many 25 are in 3 how many are in 36 1 * 25 and less subtract we get one and get one with spring down this for all right how's your 14 how many 25 are in 114 or 25 * 4 that's 100 subtract and we get 14 there's a remainder but we can't do that we need to go further on with think about it like money we need dimes and pennies so let's put a decimal place right here and then a 0 let's bring this 0 down so now we have one 40 how many quarters are in 145 x 25 we subtract and we get 15 now we're in the pennies spot how many quarts how many 25 are in 150 6 so think about it like money what is 28% of $52 $14.56 that is how you change or find the percent of a number so let's look at this in order to find the percent of a number you got to know how to change the person into a fraction and it helps to know how to make equivalent fractions are ratios by simplifying and then substituting equivalent ratio and its place then you need to know how to multiply fractions and then when you multiply fractions you get this right here you can simplify if possible but then right here to change a fraction into division you need to know long division and then you have your percent of the number

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Math 7 - Equivalent Ratios, Percent to Fraction, Percent of a Number

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