Equivalent Ratios | How to Find Equivalent Ratios

welcome to math with mr. J in this video I'm going to be covering equivalent ratios and as you can see on your screen we have four problems or examples that we're going to go through together in order to get this down on the left side numbers one and two we're going to find a few examples few equivalent ratios for each of those and then on the right side numbers 3 & 4 we're going to pick out the equivalent ratios out of the choices a b c and d so let's take a look at number 1 here where we have 8 to 12 now equivalent ratios are just like equivalent fractions we use multiplication or division whatever you do to one number of the ratio you have to do the same thing to the other using multiplication or division and you get an equivalent ratio so for example I can multiply both of these by 3 and I'll get an equivalent ratio so 8 times 3 is 24 12 times 3 is 36 so 24 to 36 is equivalent it holds the same value as the ratio 8 to 12 now I can multiply both of them by 10 and get 80 to 120 as long as I do the same thing to both numbers of that ratio I get an equivalent ratio so multiplication I can multiply both those numbers by anything in the world so you know an infinite number of answers there as long as I do the same thing to both the left and the right hand side now division is a little more limited because I need a common factor between the 8 and the 12 so for example I can't use 5 because I can't do 8 divided by 5 and 12 divided by 5 5 is not a factor I'm not going to get a whole number when I divide both the the 12 can you think of a common factor between the eight and the 12 hopefully you're thinking either two or four so for example division I could do 8 divided by 2 is 4 and 12 divided by 2 is 6 that would be an equivalent ratio or I could use the greatest common factor which is 4 and divide both by 4 so 8 divided by 4 is 2 and 12 divided by 4 is 3 this one would actually be 2 2 3 would be the simplest form of 8 to 12 and simplest form is an equivalent ratio as well as being simplest form so there's number 1 again multiplication or division and if you do the same thing to both the numbers of the ratio you get an equivalent ratio so let's take a look at number 2 27 to 18 let's use division first so can you think of a common factor between 27 and 18 hopefully you're either thinking 3 or 9 so let's divide them both by 3 to start and we would get 9 to 6 which is equivalent or like I mentioned you can divide both by 9 and get 3 to 2 or our other choice for equivalent ratios is multiplication so let's multiply both of them by 2 and we would get 54 to 36 now let's take a look at number 3 where we have 22 15 now we need to find the equivalent ratios out of our choices they're ABC and D so let's start with a which is 4 2 3 so let's think how would we get 22 equal this 4 here order matters so the when we're looking at equivalent ratios this 20 needs to be matched with this for the first number of the equivalent ratio and the 15 needs to be matched with this 3 so 20 divided by 5 gives us that 4 let's do the same thing to the 15 and see if we get 3 15 divided by 5 is 3 so this is an equivalent ratio now B 3 to 4 that has the same numbers right it has a 3 and a 4 just like a but it's not in the correct order order matters when it comes to ratios 20 divided by 5 does not give me 3 and 15 divided by 5 does not give me 4 so B is not equivalent because order matters see how do I get 20 to equal 40 right well I could do 20 times 2 what happens if we multiply 15 by 2 well we get this 30 so C does work out it is an equivalent ratio now D all right we have a 10 to start with we could do 20 divided by 2 would give me this 10 is 15 divided by 2 15 no so D is not equivalent number 4 we have 4 to 10 so let's take a look at a where we have 40 to a hundred so we have to think okay how do we get this for it equal 40 well we can multiply it by 10 what happens when we do 10 times 10 that gives us this 100 so we do have an equivalent ratio there with 40 to 100 B we have 5 to 2 hmm I can't really get this for two equal that 5 using multiplication or division but I can do 10 I can do this 10 divided by 2 to give me that 5 but just like number three order matters so I can't take that ten divide it by two and give me the first number in a ratio B does not work because order matters see we have 12 to 30 I could do 4 times 3 gives me this 12 and the 10 times 3 gives me that 30 so I did the same thing to both the 4 and 10 so that means I get an equivalent ratio so C would be equivalent now D 2 to 5 is very similar to choice B right and involves a 2 and a 5 but it's in a different order so let's see if this one works I know 4 divided by 2 gives me this 2 and this 10 divided by 2 gives me this 5 so I can divide both of them by 2 and I would get this ratio of 2 to 5 so D is equivalent all right so there you have it there's equivalent ratios hopefully that helped thanks so much for watching until next time peace you