Equivalent Ratios Proportions Middle Grades

equivalent ratios which are also known as proportions equivalent ratios is very beginning to working with with ratios and when you first learn how to work with ratios by looking at equivalence then you can start solving and you can do many more interesting things including problem solving as well which uses proportions again so before we get into all the more major types of complex questions what want to do first is explain what equivalent ratio is basically if you have ratio three quarters is equal to 6 8. those two are equivalent just as three quarters is equal to 6 8 written as fraction now some of you may have taken that in the past but i'm going to just go over this to show you why and then that basically is to say that you have the same ratio if the fractions are equivalent the ratio is equivalent so just have quick little thing here that want to show you first of all you've got three quarters and you want to show that's equivalent to six eighths basically here's one hole which are four quarters and another one whole which are eight eighths and you can see that the same height now if you only have three quarters that would be up to there and six eights would mean you take away two of the eights and notice they're still the same height now they're the same amount but they actually are written differently because this only has three pieces whereas this has six pieces when you have six eighths so that's why you say that they're equivalent because they're not exactly the same they have different meanings 6 8 means you have six pieces and each piece is an eighth three quarters says that you have three pieces and each piece is quarter but they have they are the same amount at the end that's equivalent fractions ratios therefore work exactly the same way where you have here three to four is equivalent to six to eight it's just different way of writing it now they're equivalent or proportional so if three to four i'm going to just do quick little little example you already know the answer to this but we're going i'm going to show you how to figure it out the 3 to 4 equals to 8 and this will be the type of question you get given you want to find what is well the very first thing you do is you write it as fraction so 3 to 4 equals to 8 and then you can solve for that well very quickly you can see here 4 times 2 is 8 so 3 times 2 would be 6. and that would be your answer so would equal 6. all right now another way you can look at this is you can say well if if you know what three quarters is equal to to eight then it's just like if you had question i'm going to ask you to come down here for second if you had 3 times 3 sorry 3 is equal to over 2 how would you solve that so you have something divided by 2 is equal to 3. well you know that something has to be 6. and another way you can think about that is do the reverse reverse operation divided by so you can do divided by 2 instead you can do the reverse operation do 3 times 2 would equal and 3 times 2 is 6. so you're basically sort of bringing that up here and you're multiplying during the reverse operation when you bring it to the other side of the equal sign so here up here if you come back here you could have done 8 times 3 divided by and that would equal your and this goes in once twice you have 6 is equal to that's basic fractions that you've learned and you know before this okay so that's quick one now let's go to the next one and this one you have to 7 and 21 to 49 are equivalent so therefore you can figure out what is you have to know their equivalent before you can figure it out but basically so what you want to do is to 7 as fraction is equal to 21 to 49. so 7 times 7 is 49 and so times or something times 7 is equal to 21. because you multiply this by 7 you need to do the same times 7 so what times 7 equals 21 well that's 3. okay again you can multiply up so you can say 21 over 49 times 7 and 7 goes into 49 7 times 21 divided by 7 would be 3 so you get your answer again okay so there's your equivalent fraction are rationals calculating for an unknown now in this case you've got 5 to is equal to 11 to 17. so i've written this in two different ways i've written it as that as fraction 5 over equals 11 over 17. i've made sure that the first two numbers are in the numerator and the last two in the denominator you can or you can do it the other way around you could say well let's do it the first two is the denominator and the second two as the numerator and if you do that sometimes students find this little easier to calculate and if you're to calculate that i'm just going to do this quickly this would be equals 17 over 11 times 5 and so 17 times 5 is 85 over 11 and would then equal 7 and 8 11. here let's just write that up here okay so that is equal to your and and so if you've got is equal to that you can actually check it out and you can get the same answer using this this one as well this way it's just little longer because what you have to do is flip them and then you can solve for that way but both ways work and wanted to just show you that okay in this case you've got to 18 is equal to 5 to 23 so you have to 18 is equal to 5 over 23 and you can multiply that out so you have equals 5 times 18 over 23 and 5 times 18 is 90 over 23 so you want to make that into an improper fraction 4 times 23 would be 92 that's just that's two larger than the 90s so we know that's going to be 3 and 21 out of 23. so look how you've solved for these ratios notice this is the the ratio of ratio form and this is in the fractional form so that you can actually find out what that number is back in this ratio now i've also done something very quickly here just in case you're having some difficulty with that multiplying if you have 2 times equals 8 then would equal the opposite operation which is 8 here 8 divided by 2 which is 4. 2 times what is 4 is equal to 8 which works and again here this isn't so obvious but what you would do again is 3 times something is equal to 10 so 10 divided by that 3 would equal that which of course is 3 and 1 3. all right so there is in ratios equivalent ratios you first of all have to write it as fraction if you can and then and then you need to solve somehow to figure out how you can get the same if you multiply 18 times 3 and 21 over 23 you will get 23 and and so you and so you need to figure out what this would be and and you've got it okay thanks bye