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# Ratios and double number lines

CCSS.Math:

## Video transcript

we're told the double number line shows that five pounds of avocados costs \$9 and so what is going on here with this double number line this shows how as we increase the number of avocados how the cost increases so for example when we have zero pounds of avocados it costs us zero dollars when we have five pounds of avocados it costs us nine dollars and so if you look at any point over here let's say you look right over here this would be let's see this is one right this is one two three four five if you look at one this point on the cost number line would tell you how much one pound of avocado would cost two pounds of avocados how much would that cost you would look at this second number line right over there so they ask us based on the ratio shown in the doubler based on the ratio shown in the double number line what is the cost for one pound of avocados so pause the video and think about it remember one pound of avocados on this top number line we look at the second number line the cost would be right over here what is this going to be well we could just set it up as a ratio the ratio of pounds of avocados to cost is going to be let me do this in some colors so if I have five pounds of avocados it is going to cost me nine dollars so the ratio of pounds to dollars is five to nine so if I were to have one pound of avocado one pound of avocado I have divided by five to get 1 pound of avocado I would have to do the same thing for the cost so if I divide 9 by 5 this is going to be nine fifths dollars of nine fifths dollars would be the cost of one pound well nine fist isn't always the most natural way to write money so you could view this nine fifths is equal to one and 4/5 which is equal to one and eight tenths which is equal to one point eight or you could say this is one dollar and 80 cents so if you were to go on to this double number line the cost of 1 pound of avocado this point right over here would be one dollar and 80 cents if you said 2 pounds of avocados well now you would double it so this would be three dollars and 60 cents and you would go on and on and on all the way until you got to nine dollars here let's do another example so here we are told the double number line shows how many model trains Eirene can build in a week so we can see in zero weeks you can't build any trains but and then one week she can build nine trains and they ask us which table represents the rate of Irene building model trains so pause this video and see if you can figure it out so once again every week she can build nine trains so one way to think about it is the ratio of week two trains would be one to nine so let's see if I look at this table I just want to see where the ratio between weeks two trains stays at one to nine so five to forty five that is still one two nine to go from one to five I've multiplied by five and then to go to nine to 45 I've also multiplied by five so this one checks out now and another way to think about it is 45 is 9 times five so nine times and not that might be easy way to think about it over here 12 to 108 well that's once again 12 times nine is 108 and then 26 to 234 let's see 26 times 10 would be 260 minus 26 yeah it would be 234 so this is nine times so in all of these cases the ratio of trains or the ratio of weeks to trains is one to nine so this one is looking good so I'll just circle that in but let's just make sure that this one doesn't work well over here the ratio of weeks to trains is 9 to 1 not 1 to 9 the train should be 9 times the weeks while here the weeks is 9 times the train so just looking at that first one we know that this is not going to work out let's do one last example the number the double number line shows how many snowballs Jacob and his friends can make in one minute in no minutes they can make zero snowballs in one minute they can make 12 complete the table to show the same information as the double number line so once again pause this video and see if you can work this out well we can think about it as a ratio the ratio of minutes to snowballs is one to twelve so minutes to snowballs is one to twelve or another way to think about it is the snowballs is going to be twelve times the minutes and so over here if I have twelve snowballs well we already know that's going to be one minute if I have forty-eight snowballs well let's just think about it to go from 12 to 48 you have to multiply by four see if four times as many snowballs is gonna take you four times as many minutes and then if you go to five well to go from one to five you multiply by five so you're gonna have five times as many snowballs then you would be able to make in one minute so five times 12 is 60 and we're done it could be one to twelve four to forty eight five to 64 every five minutes you can make sixty snowballs or they make sixty snowballs