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### Course: Operations and Algebraic Thinking 222-226>Unit 1

Lesson 4: Identifying proportional relationships

# Proportional relationships: bananas

A proportionality problem about eating bananas.

## Want to join the conversation?

• I have four questions:
.When a problem is not proportional, do we just say it's not proportional and go on to the next question?
.What kind of relationship is it if it's not proportional?

.Could we still solve it even if it's not proportional?
. And why would he waste money on 100 bananas? :)
• 1. Since there's a way to solve nonproportional relationships, you would still solve it (in a graph or a table).
2. Non-proportional :)
3. Yes, assuming the problem still makes sense.
4. Maybe he really likes bananas and they were on sale if you got 100 of them? idk
• guys the math is not mathing
• then you maybe have to go to class 1

i have some questions for class one

1. what comes after 6__
2. 2+3=_
3. 1-1=_

4.what comes before 10____

hope the math maths now
😂😂😂
• Why does Nate have 100 bananas
• because bananas are delicious and i guess he wants to eat rotten bananas because they will go bad before he can eat them all.
• Nate is a monkey
• When doing the ratios, does it matter which number is the numerator and which is the denominator? For example, is Y always over X?
• It depends on the ratio.

For example if we say the ratio of A to B, then it is A : B, which is A / B.
• Why is it not proportional i don't understand this gibberish
• It's because it asks the number of days that pass, not the number of bananas Nate has eaten. If it was the latter, then the relationship would be proportional.

Here is an example:

imagine you have 5 apples. You eat one each day. Then, the equation would be like this.

`amount of apples left (x) (-1 per day) = number of days that pass (y) (+1 per day)`

So, it would be proportional.

I hope this helps!
• I don't understand how you would find the constant of proportionality. My teacher says that its easy but its not.
• Yes, it really is easy. Assuming that you are given a proportional relationship and some ordered pairs, choose any ordered pair with nonzero x-value, and divide the y-value by the x-value in that ordered pair to get the constant of proportionality.

Then check to see if you get the same answer if you do the same thing with another ordered pair. If you don't get the same answer, then either you made a mistake or you were not given a proportional relationship.
• i dont understand
cant you just divide without ratios?
• well sure but if you use ratios then youre doing it right and if you dont you will be executed so its kinda a lose lose
• Had it been "Number of days left", it would have been a proportional relationship.
• I have a question. Can x in a ratio be 0?
I know it's usually impossible in math, but what if a real world problem could do it?
For example, an elevator rises at the rate of 1 second per floor, so when the elevator stops at the first floor, it will be rising 0 floors and 0 meters. Is it also proportionality? I just saw this in a practice question.

## Video transcript

- [Voiceover] Today, Nate has 100 bananas. He will eat two of them every day. Is the number of bananas Nate has left proportional to the number of days that pass? And I encourage you to pause this video and think about this. And what's interesting here, they're not saying, is the number of bananas eaten, they're saying the number of bananas Nate has left, proportional to the number of days that pass. So let's draw a little table here to think about this a little bit more. So I'm gonna make three columns. I'm gonna make three columns. So in the first column, this is gonna be the number of days that pass. So number of days... that pass. So that's this right over here, the number of days that pass. And this middle column, I'm gonna write the number of bananas Nate has left. Number of bananas... bananas left. And over here, I'm gonna make the ratio between the two. In order for this to be a proportional relationship, the ratio between these two has to be constant. So bananas left. So I'm gonna divide the second column by the first column. Bananas left... left, divided by days passed. Days passed. All right, so let's think about it a little bit. When one day has passed, how many bananas will he have left? Well, in that one day he will have eaten two bananas, so you're going to have 98 bananas left. And so what's the ratio of bananas left to days passed? Well, it's 98 over one, which is going to be equal to 98. All right. When two days have passed, how many bananas is he gonna have left? Well, he's going to consume two more bananas, so he's going to have 96 left, and so what's the ratio? It's going to be 96 to two, which is equal to 48. So clearly this ratio is not constant. It changed just from going to one day to the next day. So we don't have a constant ratio of bananas left to days passed, so this is not, this is not a proportional, proportional relationship. Now, things might've been a little bit different if they said the number of bananas Nate has eaten, is that proportional to the number of days that passed? Well, yeah, sure, because then, if this was the number of bananas eaten, if this was the number of bananas eaten, then it would always be two times the number of days that pass, so that would be two, and then that would be four, and then these ratios would always be two. But that's not what they asked for. They wanted us to compare number of bananas left to number of days that pass.