Divisibility by Nine Concepts

The video tutorial explains the rule for determining if a number is divisible by nine by summing its digits. It uses the example of 2943 to demonstrate the process and confirms the rule's validity through mathematical proof. The tutorial also hints at future discussions on why this rule works for nine and three but not for other numbers.

What is the first step to determine if a number is divisible by nine?

• Multiply the number by nine

• Divide the number by nine

• Subtract nine from the number

• Add up the digits of the number

What is the sum of the digits of 2943?

• 15

• 18

• 20

• 21

What is the result of adding the digits of 18?

• 10

• 9

• 8

• 7

Why does the rule of adding digits work specifically for nine?

• Because nine is a prime number

• Because nine is a factor of ten

• Because nine is a multiple of three

• Because nine is a factor of 999

How is the number 2943 broken down into its place values?

• As 200, 900, 40, and 3

• As 2000, 900, 40, and 3

• As 294, 30, and 3

• As 2900, 40, and 3

What is the rewritten form of 1000 in terms of divisibility by nine?

• 1000 is rewritten as 900 + 100

• 1000 is rewritten as 100 + 900

• 1000 is rewritten as 999 + 1

• 1000 is rewritten as 1000

What happens when you distribute the terms in the expression?

• You divide all terms by nine

• You separate terms into multiples of nine and others

• You add all terms together

• You multiply all terms by nine

What is the rewritten form of 10 in terms of divisibility by nine?

• 10 is rewritten as 6 + 4

• 10 is rewritten as 7 + 3

• 10 is rewritten as 8 + 2

• 10 is rewritten as 9 + 1

Why must the sum of the digits be divisible by nine for the whole number to be divisible?

• Because the sum is greater than the original number

• Because the sum is the only part not already divisible by nine

• Because the sum is always a multiple of nine

• Because the sum represents the original number

Which of the following numbers is not divisible by nine?

• 27

• 18

• 36

• 45