Wednesday, Aug 20

Tuesday, Oct 30

Wednesday, Aug 20Review Lesson 1

Divisibility Patterns

Divisibility PatternsObjective: To understand divisibility patterns.

Divisibility PatternsDivisibility patterns or rules enable one to determine if two whole numbers are evenly divisible. Divisibility PatternsIs 4578 divisible by 2? Divisibility PatternsIs 4578 divisible by 2?

Divisibility Rule of 2: If the last digit is even (0, 2, 4, 6, 8) the entire number is divisible by 2.

Divisibility PatternsIs 4578 divisible by 2?

Divisibility Rule of 2: If the last digit is even (0, 2, 4, 6, 8) the entire number is divisible by 2.

Multiply any number by 2 and the product will always be an even number.



Divisibility Rule of 3: If the sum of the digits is divisible by 3, the entire number is divisible by 3. If the sum is more than one digit, add again.


Divisibility Rule of 3: If the sum of the digits is divisible by 3, the entire number is divisible by 3. If the sum is more than one digit, add again.

4 + 5 + 7 + 8 = 24, and 2 + 4 = 6Since 6 is divisible by 3, then 4578 is also. Divisibility PatternsIs 4578 divisible by 4?


Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4.



78 is not divisible by 4, since 4 x 20 = 80 and 78 is 2 less than 80.



Are all numbers divisible by 4 divisible by 2?



Can an odd number by divisible by 4?



Divisibility Rule of 5: If the last digit is a 5 or 0 the entire number is divisible by 5.


Divisibility Rule of 5: If the last digit is a 5 or 0 the entire number is divisible by 5.

Since the last digit is neither a 5 or 0, the number is not divisible by 5.



Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6.


Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6. The number is even it is divisible by 2 and the sum of the digits is 6, which is divisible by 3. Since both rules work, the number is divisible by 6.


Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6.

Why rules for 2 and 3? Why not 3 and 4? Or 2 and 5?



Divisibility Rule of 9: If the sum of the digits is 9, then the original number is divisible by 9. If the sum is more than one digit, add again.


Divisibility Rule of 9: If the sum of the digits is 9, then the original number is divisible by 9. If the sum is more than one digit, add again.

4 + 5 + 7 + 8 = 24, 2 + 4 = 6 9.



Divisibility Rule of 10: If the last digit is a zero, then the number is divisible by 10.


Divisibility Rule of 10: If the last digit is a zero, then the number is divisible by 10.

Since 8 0, the number is not divisible by 10.

Divisibility PatternsCan an odd number ever be divisible by an even number?

Divisibility PatternsCan an odd number ever be divisible by an even number?

NO! An odd number can never be divisible by an even number.

Divisibility Patterns89Is this number divisible by 2,3,4,5,6,9,10?


No!


If a number is only divisible by 1 and itself, it is called what?


If a number is only divisible by 1 and itself, it is called what? Prime Number



478 is divisible by 2.



3135 is divisible by 3 and 5.



14980 is divisible by 2, 4, 5, and 10.

Divisibility PatternsThe number of tickets needed to ride the Ferris wheel at the county fair is three. If Alicia has 53 tickets, can she use all of the tickets by riding only the Ferris wheel?

Divisibility PatternsThe number of tickets needed to ride the Ferris wheel at the county fair is three. If Alicia has 53 tickets, can she use all of the tickets by riding only the Ferris wheel?

5 + 3 = 8Since 8 is not divisible by 3 the answer is no.

Divisibility PatternsYou and three of your friends just won $4,567. Can you divide the money evenly?

Divisibility PatternsYou and three of your friends just won $4,567. Can you divide the money evenly?

1 + 3 = 4Since $4,567 is an odd number it can not be divisible by an even number.

Divisibility PatternsWas the year 1776 a leap year?


Since a leap (mostly) occurs every 4 years, is 1776 divisible by 4?

Since 76 is divisible by 4, then 1776 is also. 1776 was a leap year.




Since 22 is not divisible by 4, then 1922 is not. 1922 was not a leap year.

Divisibility PatternsWill the year 2054 be a leap year?

Divisibility PatternsWill the year 2054 be a leap year?


Since 54 is not divisible by 4, then 2054 is not. 2054 will not be a leap year.

Divisibility PatternsAgenda NotesHomework Homework Practice R.1 Due Thursday, Aug 21

Wednesday, Aug 20

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