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we're asked to select three ratios that are equivalent to seven to six so pause this video and see if you can spot the three ratios that are equivalent to 7 to 6 all right now let's work through this together and the main thing to realize about equivalent ratios is we just have to multiply or divide the corresponding parts of the ratio by the same amount so before I even look at these choices for example if I have 7 - 6 if I multiply the 7 times 2 to get 14 then I would also multiply the 6 times 2 to get 12 so for example 14 - 12 is the exact same ratio now you might be tempted to pick 12 - 14 but that is not the same ratio order matters in a ratio this could be the ratio of oranges to apples and we're saying for every 7 oranges there are 6 apples you wouldn't be able to say it the other way around so you would rule this one out even though it's dealing with some of the right numbers it's not in the right order now let's think about 21 to 18 to go from 7 to 21 we would multiply by 3 and to go from 6 to 18 you would also multiply by 3 so that works if we multiply both of these numbers by 3 we get 21 - 18 so let me circle that in that one is for sure' equivalent what about 42 - 36 well to go from 7 to 42 we're going to have to multiply by 6 and to go from 6 to 36 we also multiply by 6 so this once again is an equivalent ratio we multiply each of these by 6 and we keep the same order so that is equivalent right over there 63 to 54 let's see to go from 7 to 63 you multiply by 9 and to go from 6 to 54 you also multiply by 9 so once again 63 to 54 is an equivalent ratio and so we've already selected 3 but let's just verify that this doesn't work so to go from 7 to 84 you would multiply by 12 to go from six to sixty to go with it you'd multiply by ten and to six or ten and a third so this one is definitely not an equivalent ratio let's do another example so once again we are asked to select three ratios that are equivalent to 16 to 12 so pause this video and see if you can work through it alright let's look at this first one so 8 to 6 so at first you might say well gee these numbers are smaller than 16 and 12 but remember you can to get an equivalent ratio you could multiply or divide these numbers by the same number so to get from 16 to 8 you could view that as well we just divided by 2 and to go from 12 to 6 you also divide by 2 so this actually is an equivalent ratio I'll circle that in what about 32 to 24 well to go from 16 to 32 we multiply by 2 to go from 12 to 24 we also multiply by 2 so this is an equivalent ratio what about 4 to 3 well to go from 16 to 4 we would have to divide by 4 and to go from 12 to 3 we are going to divide by 4 as well so we're dividing by the same thing each of these numbers so this is also going to be an equivalent ratio so we've selected our 3 so we are essentially done but we might as well see why these don't work now let's think about it to go from 16 to 12 how do we do that well to go from 16 to 12 you could divide by 4 and multiply by 3 so this would be x 3/4 you would get 12 and to go from 12 to 8 let's you could divide by 3 and multiply by 2 so this you could view as my x 2/3 so you'd be multiplying or dividing by different numbers here so this one is not equivalent and then 24 to 16 to go from 16 to 24 you would multiply by let's see that's 1 and 1/2 so this right over here would be you'd multiply by one and a half and to go from 12 to 16 you would multiply that is by one and one-third so times 1 and 1/3 so you're not multiplying by the same amount so once again not an equivalent ratio