Wednesday, Aug 20 Review Lesson 1 Divisibility Patterns.

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Presentation transcript:

Wednesday, Aug 20 Review Lesson 1 Divisibility Patterns

Objective: To understand divisibility patterns.

Divisibility Patterns Divisibility patterns or rules enable one to determine if two whole numbers are evenly divisible.

Divisibility Patterns Is 4578 divisible by 2?

Divisibility Patterns Is 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 Patterns Is 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 Patterns Is 4578 divisible by 3?

Divisibility Patterns Is 4578 divisible by 3? 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 Patterns Is 4578 divisible by 3? 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 = 24, and = 6 Since 6 is divisible by 3, then 4578 is also.

Divisibility Patterns Is 4578 divisible by 4?

Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4.

Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by is not divisible by 4, since 4 x 20 = 80 and 78 is 2 less than 80.

Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4. Are all numbers divisible by 4 divisible by 2?

Divisibility Patterns Is 4578 divisible by 4? Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4. Can an odd number by divisible by 4?

Divisibility Patterns Is 4578 divisible by 5?

Divisibility Patterns Is 4578 divisible by 5? Divisibility Rule of 5: If the last digit is a 5 or 0 the entire number is divisible by 5.

Divisibility Patterns Is 4578 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 Patterns Is 4578 divisible by 6?

Divisibility Patterns Is 4578 divisible by 6? Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6.

Divisibility Patterns Is 4578 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 Patterns Is 4578 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 Patterns Is 4578 divisible by 9?

Divisibility Patterns Is 4578 divisible by 9? 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 Patterns Is 4578 divisible by 9? 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 = 24, = 6 ≠ 9.

Divisibility Patterns Is 4578 divisible by 10?

Divisibility Patterns Is 4578 divisible by 10? Divisibility Rule of 10: If the last digit is a zero, then the number is divisible by 10.

Divisibility Patterns Is 4578 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 Patterns Can an odd number ever be divisible by an even number?

Divisibility Patterns Can an odd number ever be divisible by an even number? NO! An odd number can never be divisible by an even number.

Divisibility Patterns 89 Is this number divisible by 2,3,4,5,6,9,10?

Divisibility Patterns 89 Is this number divisible by 2,3,4,5,6,9,10? No!

Divisibility Patterns 89 Is this number divisible by 2,3,4,5,6,9,10? If a number is only divisible by 1 and itself, it is called what?

Divisibility Patterns 89 Is this number divisible by 2,3,4,5,6,9,10? If a number is only divisible by 1 and itself, it is called what? Prime Number

Divisibility Patterns 478 Is this number divisible by 2,3,4,5,6,9,10?

Divisibility Patterns 478 Is this number divisible by 2,3,4,5,6,9,10? 478 is divisible by 2.

Divisibility Patterns 3135 Is this number divisible by 2,3,4,5,6,9,10?

Divisibility Patterns 3135 Is this number divisible by 2,3,4,5,6,9,10? 3135 is divisible by 3 and 5.

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

Divisibility Patterns Is this number divisible by 2,3,4,5,6,9,10? is divisible by 2, 4, 5, and 10.

Divisibility Patterns The 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 Patterns The 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? = 8 Since 8 is not divisible by 3 the answer is no.

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

Divisibility Patterns You and three of your friends just won $4,567. Can you divide the money evenly? = 4 Since $4,567 is an odd number it can not be divisible by an even number.

Divisibility Patterns Was the year 1776 a leap year?

Divisibility Patterns Was 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 was a leap year.

Divisibility Patterns Was the year 1922 a leap year?

Divisibility Patterns Was the year 1922 a leap year? Since a leap (mostly) occurs every 4 years, is 1922 divisible by 4? Since 22 is not divisible by 4, then 1922 is not was not a leap year.

Divisibility Patterns Will the year 2054 be a leap year?

Divisibility Patterns Will the year 2054 be a leap year? Since a leap (mostly) occurs every 4 years, is 2054 divisible by 4? Since 54 is not divisible by 4, then 2054 is not will not be a leap year.

Divisibility Patterns Agenda Notes Homework – Homework Practice R.1 Due Thursday, Aug 21