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## 6η Δημοτικού

### Ενότητα 1: Μάθημα 3

Εισαγωγή στους ρυθμούς μεταβολής

# Comparing rates example

Sal puts three fish tanks in order by volume of water per fish.

## Απομαγνητοφώνηση βίντεο

- [Voiceover] Let's get some practice comparing and computing rates. So they tell us the pet store has three fish tanks, each holding a different volume of water and a different number of fish. So Tank A has five fish, and it has 40 liters of water, Tank B, 12 fish, 100 liters of water, and Tank C, 23 fish, and it has 180 liters of water. Order the tanks by volume per fish from least to greatest. So let's think about what volume per fish, and we could think about this as volume divided by fish. Volume per fish. All right, so here for Tank A, it's going to be 40 liters for every five fish. 40 for every five fish, and let's see, 40 over five is eight, so you have eight liters per fish, is the rate at which they have to add water per fish for Tank A. Now, Tank B, you have 100 liters for 12 fish, so what is this going to be? This is going to be, 12 goes into 100 eight times, so eight times 12 is 96, and then you have four left over. So this is going to be eight and 4/12, or eight and 1/3 liters per fish. And all I did is I converted this improper fraction, 100 over 12, to a mixed number, and I simplified it. 12 goes into 100 eight times with a remainder of four, so it's eight and 4/12, which is the same thing as eight and 1/3. And then finally in Tank C, I have 180 liters for 23 fish. So what is this going to be? 23 goes into 180. Let me try to calculate this. 23 goes into 180, it looks like it's going to be less than nine times. Is it eight times? Eight times, no, not eight times. Let's see, seven times. Seven times three is 21, seven times two is 14, plus two is 16. When you subtract you get a remainder of 19. So this is going to be seven with a remainder of 19, or you could say this is seven and 19/23 liters per fish. So which one has, we're going to order the tanks by volume per fish, from least to greatest, so Tank B has the largest volume per fish, has eight and 1/3 liters per fish, so this is in first place. And then Tank A is in second place. Tank A is in second place. And then Tank C is in third place. Oh, actually we wanna go from least to greatest, so this is, let me write it this way. This is Tank C is the least, and Tank A is the greatest. So we really have to swap this order around. Now, I just copied and pasted this from the Khan Academy exercises. Let me actually bring the actual exercise up, and I can rearrange it. C was the least, and B was the most, and we check our answer and we got it right.