PrerequisitePrerequisiteto chapter 5to chapter 5

Divisibility Rules:Divisibility Rules:

To determine the rules of To determine the rules of divisibilitydivisibility

DivisibleDivisibleWhen one number can be divided by When one number can be divided by

another and the result is an exact another and the result is an exact whole number.whole number.

Example: 15 is divisible by 3, Example: 15 is divisible by 3, because 15 ÷ 3 = 5 exactlybecause 15 ÷ 3 = 5 exactly

But 9 is not divisible by 2 because 9 ÷ But 9 is not divisible by 2 because 9 ÷ 2 is 4 with 1 left over. 2 is 4 with 1 left over.

Divisibility RulesDivisibility Rules

A method that can be used to A method that can be used to determine whether a number is determine whether a number is evenly divisible by other numbers. evenly divisible by other numbers.

They are a shortcut for testing a They are a shortcut for testing a number's factors without resorting to number's factors without resorting to division calculations. division calculations.

Here are the Divisibility Here are the Divisibility Rules!Rules!

A number is divisible by…A number is divisible by… 2 if the ones digit is even2 if the ones digit is even

ex. 542ex. 542 12641264 234,567234,567 236,794236,794 3 if the sum of the digits is divisible by 3 if the sum of the digits is divisible by

33ex. 447ex. 447 135135 240240 4,4084,408

4 if the number formed by the last two 4 if the number formed by the last two digits is divisible by 4digits is divisible by 4ex.ex. 240 240 4,4084,408 234234 624624

A number is divisible by…A number is divisible by…

5 if the ones digit ends in a 5 or 05 if the ones digit ends in a 5 or 0

ex. 45ex. 45 3,4903,490 546546 235235 6 if the number is divisible by BOTH 6 if the number is divisible by BOTH

2 and 32 and 3

ex. 7,026ex. 7,026 34983498 8,9038,9038,4408,440

Here are the Divisibility Here are the Divisibility Rules!Rules!

9 if the sum of the digits is divisible 9 if the sum of the digits is divisible by 9by 9

ex. 1,287ex. 1,287 8,9018,901 2,9842,98450,31950,319

10 if the ones digit ends in 010 if the ones digit ends in 0

ex. 1,450ex. 1,450 570570 3,4563,456 5,4905,490

Here are the Divisibility Here are the Divisibility Rules!Rules!

Lets try a few!Lets try a few!

Is the first number divisible by the Is the first number divisible by the second number?second number?

1.1. 447;3447;3YesYes

2.2. 419;2419;2NoNo

3.3. 7,026;67,026;6YesYes

A few more…A few more…

4.4. 1,287;91,287;9yesyes

5. 1,260;105. 1,260;10yesyes

6.6. 4,480;44,480;4yesyes

7.7. 8,9308,930nono

Determine whether each Determine whether each number is divisible by number is divisible by

2,3,4,5,6,9, or 10.2,3,4,5,6,9, or 10.7127122,42,4462462

2,3,62,3,650,31950,319

3,93,98,3408,340

2,3,4,5,6,102,3,4,5,6,10

You try these!You try these!

8,9018,9013,93,9

1,0051,0053,53,5920920

2,4,5,102,4,5,103,4983,4982,3,62,3,6

On your ownOn your own

Page 554 Page 554

Numbers 1-23 oddNumbers 1-23 odd

Chapter 5Chapter 5FRACTIONS, FRACTIONS,

DECIMALS AND DECIMALS AND PERCENTSPERCENTS

Lesson 1Lesson 1Prime FactorizationPrime Factorization

Objective: Objective:

find the prime factorization find the prime factorization of a composite numberof a composite number

Refresh your memories!Refresh your memories!Factor:Factor:

Number to a multiplication Number to a multiplication problemproblem

3 x 6 = 18 2 x 4 x 3 = 24

Product:

the answer to a multiplication problem

Prime NumberPrime Number

Whole number greater than Whole number greater than 1 that has exactly two 1 that has exactly two factors: 1 and itself.factors: 1 and itself.

2 (1 x 2)2 (1 x 2)3 (1 x 3)3 (1 x 3)5 (1 x 5)5 (1 x 5)

Composite NumberComposite Number

Whole number greater than Whole number greater than 1 that has more than 2 1 that has more than 2

factors.factors.

4 (1x44 (1x4 2 x 2)2 x 2)

6 (1x6 6 (1x6 2x3)2x3)

12 (1x1212 (1x12 2x62x6 3x4)3x4)

Determine whether each Determine whether each number is prime or composite.number is prime or composite.

1717Prime (1 x 17)Prime (1 x 17)

1212CompositeComposite

(1x12(1x12 2 x 62 x 6 3 x 4)3 x 4)1111

PrimePrime(1 x 11)(1 x 11)

1515

CompositeComposite

(1 x 15 (1 x 15 3 x 15)3 x 15)

2424

Composite Composite

(1x24 (1x24 2x122x12 3x83x8 4x6)4x6)

Determine whether each Determine whether each number is prime or composite.number is prime or composite.

Every composite Every composite number can be number can be

written as a product written as a product of prime numbers in of prime numbers in

exactly one way.exactly one way.

Prime FactorizationPrime Factorization

Expressing a composite Expressing a composite number as a product of number as a product of

prime numbers.prime numbers.

Factor treeFactor tree

A diagram showing the prime A diagram showing the prime factorization of a number. factorization of a number.

The factors branch out from The factors branch out from the previous factors until all the previous factors until all

of the factors are of the factors are prime prime numbersnumbers..

Here is a model!Here is a model!

9696

6 166 16

22 33 2 82 8

2 42 4

2 22 2

2 x 32 x 35

96

12 8

3 4 4 2

2 2 2 2

2 x 35

Lets try moreLets try more

1818 2828

You try these!You try these!

1616 3030

Here are two more!Here are two more!

2222 4343

Do NowDo Now

Find the prime factorization of…Find the prime factorization of…

46 46 AndAnd 108108

Factor each expressionFactor each expression

10ac10ac 16x16x2

You try these expressions!You try these expressions!

52gh52gh 48a b48a b2 22

You try some on your own!You try some on your own!

Page 199 numbers 13-35 oddPage 199 numbers 13-35 odd

HomeworkHomework Page 199 numbers 12-34 evenPage 199 numbers 12-34 even Page 554 numbers 2-24 evenPage 554 numbers 2-24 even

You have a quiz on these 2 lessons You have a quiz on these 2 lessons Wednesday!Wednesday!