Modular Arithmetic and Congruences

The video tutorial explains how to use mod 12 arithmetic, also known as clock arithmetic, to find products and remainders. It provides two examples: calculating 4 * 27 mod 12 and 23 * 15 mod 12. The tutorial demonstrates the process of finding the remainder when a product is divided by 12 and explains the concept of congruence. It also shows how to verify results using a clock analogy, where each full rotation represents 12 hours.

What is the first step in solving 4 * 27 using mod 12 arithmetic?

• Subtract 12 from 27.

• Divide 27 by 12.

• Multiply 4 and 27 directly.

• Write it as 4 * 27 mod 12.

What is the result of 108 mod 12?

• 0

• 9

• 1

• 12

What does the symbol that looks like an equal sign with an extra bar represent?

• Equality

• Congruence

• Inequality

• Approximation

How many complete rotations does the hour hand make for 108 hours on a clock?

• 8

• 11

• 9

• 10

What is the product of 23 and 15?

• 345

• 315

• 360

• 330

What is the remainder when 345 is divided by 12?

• 7

• 10

• 8

• 9

How many complete rotations does the hour hand make for 345 hours on a clock?

• 30

• 28

• 27

• 29

What is the result of 345 mod 12?

• 7

• 10

• 8

• 9

What is the congruence statement for 345 mod 12?

• 345 is congruent to 9 mod 12

• 345 is congruent to 10 mod 12

• 345 is congruent to 8 mod 12

• 345 is congruent to 7 mod 12

What is the significance of replacing 12 with zero on the clock?

• It is used for subtraction.

• It simplifies the multiplication.

• It indicates the start of a new cycle.

• It helps in calculating the remainder.