The following was written in the book I am reading.
Suppose you’re organizing an outing for $100$ people, and you're renting minibuses that can hold $15$ people each. How many minibuses do you need? Basically you need to calculate$$100 \,÷\,15 \approx 6.7$$But then you have to take the context into account: you can’t book $0.7$ of a minibus, so you have to round up to $7$ minibuses.
Now consider a different context. You want to send a friend some chocolates in the mail, and a first-class stamp is valid for up to $100$ g. The chocolates weigh $15$ g each, so how many chocolates can you send? You still need to start with the same calculation$$100 \,÷\,15 \approx 6.7$$But this time the context gives a different answer: since you can’t send $0.7$ of a chocolate, you'll need to round down to $6$ chocolates.
I can't help but sense that there's a deeper underlying phenomenon going on here. So I have a few questions.
- What is actually the deeper thing going on here?
- What might be some exercises worth thinking about (i.e. struggling with) to better grasp what is actually going on here, for someone who has virtually zero proof experience in math?