module 2 lesson 17

Module 2 Lesson 17 Divisibility Tests for 3 and 9.notebook

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Lesson 16 Homework Review1. 346 + 721 Odd, because the sum of an even and an odd number is odd.

2. 4,690 x 141Even, because the product of an even and an odd number is even.

3. 1,462,891 x 745, 629Odd, because the product of two odd numbers is odd

4. 425, 922 + 32,481,064Even, because the sum of two even numbers is even.

Adding:§ The sum of two even numbers is even.§ The sum of two odd numbers is even.§ The sum of an even number and an odd number is odd.

Mulplying:§ The product of two even numbers is even.§ The product of two odd numbers is odd.§ The product of an even number and an odd number is even.


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5. 32 + 45 + 67 + 91 + 34 + 56• The first two addends will be odd, because even and an odd is odd.• Odd number + 67 will be even because the sum of two odd numbers

is even.• Even number + 91 will be odd because the sum of an even and an

odd number is odd.• Odd number + 34 will be odd because the sum of an odd and an even

number is odd.• Odd number + 56 will be odd because the sum of an odd and an

even number is odd.• Therefore, the final sum will be odd. Adding:

§ The sum of two even numbers is even.§ The sum of two odd numbers is even.§ The sum of an even number and an odd number is odd.

Mulplying:§ The product of two even numbers is even.§ The product of two odd numbers is odd.§ The product of an even number and an odd number is even.


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MODULE 2 Arithmec Operaons Including Division of Fracons

Topic D: Number Theory‐ Thinking Logically About Mulplicave Arithmec

Lesson 17: Divisibility Tests for 3 and 9Student Outcomes§ Students apply divisibility rules, specifically for 3 and 9, to understand factors and mulples.


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Discussion• Divisibility rule for 2: last digit is 0, 2, 4, 6 or 8. (even #)

• Divisibility rule for 4: last two digits are divisible by 4.

• Divisibility rules for 5: last digit is 0 or 5.

• Divisibility rule for 8: last three digits are divisible by 8.

• Divisibility rule for 10: last digit is 0.


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What do the numbers 12, 18, 30, 66, and 93 all have in common?

Calculate the sum of the digits for each given number. For example, the sum of the digits in number 12 is 3 because 1 + 2 = 3

12:

18:

30:

66:

93:

What do you notice about all the sums of the digits?

Let's make a claim or theorem....

The divisibility rule for 3: When the sum of the digits is divisible by 3, the entire number is divisible by 3.


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What do the numbers 27, 36, 54, 72, and 99 all have in common?

Calculate the sum of the digits for each given number. For example, the sum of the digits in number 12 is 3 because 1 + 2 = 3

27:

36:

54:

72:

99:What do you notice about all the sums of the digits?

Let's make a claim or theorem....

The divisibility rule for 9: When the sum of the digits is divisible by 3 and 9, the entire number is divisible by 9.


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When the sum of the digits is divisible by 3 and 9 , the entire number is divisible by 9. Let’s try to use this knowledge to determine if a large number is divisible by 3,9 or both. Is the number 765 is divisible by both 3 and 9? Find the sum of the digits.

Are 3 and 9 both factors of 18?

Calculating the sum of a number’s digits helps us to determine if the number is divisible by 3 or 9 or both.


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§ Divisibility rule for 3: If the sum of the digits is divisible by 3, then the number is divisible by 3.

§ Divisibility rule for 9: If the sum of the digits is divisible by 9, then the number is divisible by 9.


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Example 1

a. What are the three digits in the number 378?

b. What is the sum of the three digits?

Is 378 divisible by 3 or 9? Why or why not?

c. Is 18 divisible by 9?

d. Is the enre number 378 divisible by 9? Why or why not?

e. Is the enre number 378 divisible by 3? Why or why not?

Three is a factor of 378 because if 9 is a factor of 378, then 3 will also be a factor. OR

The number 378 is divisible by 3 because the sum of the digits is divisible by 3.

The number 378 is divisible by 9 because the sum of the digits is divisible by 9.


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Example 2 Is 3,822 divisible by 3 or 9? Why or why not?

Find the sum

Is sum divisible by 3?

Is sum divisible by 9?

Answer: The number 3,822 is divisible by 3, but not by 9 because the sum of the digits 3 + 8 + 2 + 2= 15 and 15 is divisible by 3 but not by 9.


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Divisibility rule for 2: last digit is 0, 2, 4, 6 or 8.

Divisibility rule for 3: if the sum of the digits is divisible by 3

Divisibility rule for 4: last two digits are a number divisible by 4.

Divisibility rules for 5: last digit is 0 or 5.

Divisibility rule for 8: last three digits are a number divisible by 8.

Divisibility rule for 9: If the sum of the digits is divisible by 9

Divisibility rule for 10: last digit is 0.

Divisibility Rules


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Exercises page s.71Circle ALL the numbers that are factors of the given number. Complete any necessary work in the space provided.

1. Is 2,838 divisible by

3

9

4

Explain your reasoning for your choices.

Divisibility rule for 2: last digit is 0, 2, 4, 6 or 8.Divisibility rule for 3: if the sum of the digits is divisible by 3Divisibility rule for 4: last two digits are a number divisible by 4.Divisibility rules for 5: last digit is 0 or 5.Divisibility rule for 8: last three digits are a number divisible by 8.Divisibility rule for 9: If the sum of the digits is divisible by 9Divisibility rule for 10: last digit is 0.


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3

9

5




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3. Is 10, 534,341 divisible by

3

9

2




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3

9

10




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3

9

8




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Closing

Please take out your exit ticket for Lesson 17, close your binder, and complete the exit ticket. This will be collected.

module 2 lesson 17

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