Visualize equivalent ratios
- [Instructor] What we're going to do in this video is tackle some word problems involving ratios. So here, we're told that Yoda Soda is the intergalactic party drink that will have all of your friends saying, mm, good this is. You are throwing a party and you need five liters of Yoda Soda for every 12 guests. If you have 36 guests, how many liters of Yoda Soda do you need? So pause this video and try to figure it out on your own. Well, they tell us the ratio of liters of soda to number of guests. So you need five, it's five liters for every 12 guests is the ratio but we wanna have 36 guests. So if the ratio is five liters of soda for every 12 guests but we're in a situation where we have 36 guests, so this is three times as many guests, we're gonna need three times as many liters of soda. So three times five is 15. Five to 12. Five liters for 12 guests or for five liters for every 12 guests is the same thing as 15 liters for every 36 guests. So to answer that question, how many liters do you need, you need 15 liters. Let's do another one of these. Here, we just have a picture of a bunch of fish in a tank and it says there are eight big fish for every blank small fish and then it says there are four big fish for every blank small fish. So pause this video again and see if you can work through this. Alright, so let's just count the big fish first. So there's one, two, three, wait, let me count this way. One, two, three, four, five, six, seven, eight. So in this tank, there actually are eight big fish and so let's see how many small fish there are. There's one, two, three, four, five, six, seven, eight, nine, 10 small fish. So in the tank, for every eight big fish which you see in red, there are 10 small fish but here it says, there are four big fish for every blank small fish. So what would that be? Well, one way to think about it is we have half as many fish or half as many big fish so we divided it by two. So we're gonna have half as many small fish. So we're gonna divide by two. So for every four big fish, there are five small fish and one way to think about it, you could divide the fish evenly into two groups right over here. So let's see, if we can capture, so if you could have, this is, if I divide it like that, here I have one, two, three, four big fish and one, two, three, four, five small fish then in this group I have one, two, three, four big fish and one, two, three, four, five small fish. So every four big fish, there are five small fish. These are equivalent ratios. Let's keep going. So here, we're told an ice cream shop uses the following ingredients to make one sundae. So they use two scoops of ice cream, four spoonfuls of sprinkles, two tablespoons of whipped cream. How many sundaes did the shop make if they used 32 spoonfuls of sprinkles? So pause the video and try to think about it. So there's a couple of ways to think about it. Here, it says, let's see, we're talking about sprinkles. So that's what's relevant here. Four spoonfuls for every one sundae. So we could say that there, so the ratio of spoonfuls to sundaes is four to one. Four spoonfuls, spoonfuls of sprinkles, let me write it this way, let me write sprinkles, sprinkles. How many spoonfuls? How many spoonfuls for one sundae? But here we're talking about using 32 spoonfuls of sprinkles so that is eight times as many. So you're going to be able to use, create eight times as many sundaes. So you're gonna have 32 spoonfuls of sprinkles for every eight sundaes. So how many sundaes did the shop make? Well, they made eight. Let's do one last example. At a dog park, there are 10 black dogs, five brown dogs, two white dogs and 12 multi-color dogs. For every one brown dog, there are two blank dogs. Pause the video and figure out what goes in this blank. Alright, so let's see. There's five brown dogs for every 10 black dogs, five brown dogs for every two white dogs and five brown dogs for every 12 multi-color dogs but here you're saying for every one brown dog, there are two blank dogs. So what type of dog is there a ratio? So for every brown dog, there's twice as many of that type of dog. Well, here, we see for every five brown dogs, there are 10 black dogs. So one way to think about it, the number of black dogs is always gonna be twice the number of brown dogs. So for every one brown dog, there would be two, two black, two black dogs. One way to think about it, the ratio between brown dogs and black dogs and it's kinda counterintuitive. I used the wrong colors here. I should have used brown and black. So let me do that. So the ratio of brown to black is five brown dogs for every 10, 10 black dogs or if you divide both of these numbers by five, you would get one, one brown dog for every two, for every two black dogs and that's exactly what this statement is saying.