Modular Arithmetic and Remainders

The video tutorial explains how to use mod 12 arithmetic, also known as clock arithmetic, to find the sum of numbers and determine their remainders when divided by 12. It provides examples with 9 + 17, 23 + 50, and 153 + 216, demonstrating how to write these sums in mod 12 form and verify the results using a clock method. The tutorial emphasizes the concept of congruence, showing that numbers with the same remainder when divided by 12 are congruent.

What is the result of 9 + 17 in mod 12 arithmetic?

• 0

• 2

• 6

• 4

Tags

CCSS.7.NS.A.1D

How do you express that two numbers have the same remainder when divided by 12?

• They are identical

• They are similar

• They are congruent

• They are equal

Tags

CCSS.4.NBT.B.6

What is the remainder when 26 is divided by 12?

• 3

• 2

• 1

• 0

Tags

CCSS.7.NS.A.1D

What is the result of 23 + 50 in mod 12 arithmetic?

• 2

• 0

• 3

• 1

Tags

CCSS.6.NS.B.3

How many complete rotations around the clock are made when moving 73 hours ahead?

• 6

• 5

• 8

• 7

Tags

CCSS.4.NBT.B.6

What is the remainder when 73 is divided by 12?

• 0

• 3

• 2

• 1

Tags

CCSS.4.NBT.B.6

What is the result of 153 + 216 in mod 12 arithmetic?

• 8

• 7

• 9

• 10

Tags

CCSS.7.EE.B.3

How many complete rotations around the clock are made when moving 369 hours ahead?

• 28

• 29

• 30

• 31

Tags

CCSS.4.NBT.B.6

What is the remainder when 369 is divided by 12?

• 7

• 8

• 9

• 10

Tags

CCSS.4.NBT.B.6

What does it mean if a number is congruent to another number mod 12?

• They are both even

• They are both odd

• They have the same remainder when divided by 12

• They are equal