Math Division and Hashing Concepts

What is the quotient when you divide 37 by 6 using the division algorithm?

What is the remainder when 89 is divided by 8 using the division algorithm?

When dividing 54 by 9 using the division algorithm, what is the remainder?

How many total boxes are needed if 52 books are packed into boxes of 9 books each?

In the scenario of distributing 83 laptops to 7 schools, how many laptops does each school receive?

What is the hash value in terms of data?

What does the division algorithm primarily determine when dividing two numbers?

What is the result when 102 is divided by 7 using the division algorithm?

What is the primary benefit of using a hash table for data storage?

When typing 'Hello' into a hashing algorithm, what would be the result if you changed it to 'hello'?

How many baskets are needed to pack 128 apples if each basket holds 12 apples, and how many apples will be left in the partially filled basket?

How does a hash function contribute to the efficiency of a hash table?

If you have 95 tablets to distribute evenly among 8 classrooms, how many tablets does each classroom receive, and how many tablets are left over?

When distributing 123 chairs among 9 offices, how many chairs does each office get, and how many are left?

What characteristic of hashing algorithms allows for a different hash value when the input is slightly altered?

Division with Remainders

The division algorithm allows determination of the quotient and remainder in division problems.
Example 1: For 23 ÷ 5, the quotient is 4, resulting in 23 = 5×4 + 3, where the remainder is 3.
Example 2: For 102 ÷ 7, the quotient is 14, yielding 102 = 7×14 + 4, with the remainder being 4.

Practice Problems

Exercises include divisions such as:
- 37 ÷ 6
- 89 ÷ 8
- 54 ÷ 9
- 94 ÷ 7
- 65 ÷ 2

Real-Life Applications

Scenario 1: Packing 52 books into boxes of 9.
- Calculation shows 5 full boxes and 1 partially filled box with 7 books.
Scenario 2: Distributing 83 laptops among 7 schools.
- Each school receives 11 laptops with 6 remaining.

Hashing Algorithms

A hash value is a unique fingerprint for data, generated by a hashing algorithm.
Changes in input, like capitalization, produce entirely different hash values.
Example: "Hello" could generate the hash 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c.

Hash Tables

A hash table utilizes keys to store data efficiently using a hash function.
Benefits include:
- Fast lookups allowing direct access to stored data rather than searching through lists.
- Efficient storage handling large datasets effectively without slowing down.

Application of Hashing Algorithms

Division and remainders are used to compute keys in hashing.
Example: In a hash table with 10 slots, a key value of 123 is stored in slot 3 (the remainder of 123 ÷ 10).

Additional Practice Problems

Pack 128 apples into baskets of 12: find out how many baskets and leftover apples.
Calculate the hash value for the key 37 in a hash table of size 10.
Distribute 95 tablets across 8 classrooms and determine the leftovers.
Distribute 123 chairs among 9 offices and establish how many are left over.

This quiz covers division with remainders, including examples and practical applications. It also introduces basic hashing algorithms and their uses. Test your understanding of these key mathematical and computer science concepts!