How best to teach the division algorithm?

[matqkks]

What is the best way to introduce the division algorithm? Are there real life examples of an application of this algorithm. At present I state and prove the division algorithm and then do some numerical examples but most of the students find this approach pretty dry and boring. I would like to bring this topic to live but how?
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[I like Serena]

What is the best way to introduce the division algorithm? Are there real life examples of an application of this algorithm. At present I state and prove the division algorithm and then do some numerical examples but most of the students find this approach pretty dry and boring. I would like to bring this topic to live but how?
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Let's organize a party for 31 people (adjust the numbers to the desired difficulty level).
We have a supply of 18 liters of punch and we can get 5 drinks out of each liter.
How many drinks can we fairly serve each person?