Fifth GradeUnit 4

Vocabulary/RulesLesson 1

EvenDefinition Examples

Ends 0, 2, 4, 6, or 8

1,234 984561,592,342

OddDefinition Examples

Ends 1, 3, 5, 7, or 9

1,243 894651,592,423

DivisibleDefinition Examples

Can be divided by with no remainder

45 is divisible by 5

36 is divisible by2

320 is divisible by 10

Are these divisible? (Can these be divided evenly-with no remainder?) You have 10 seconds to answer!

How did I do this so fast?

8,375,895 ÷ 5 1,568,342 ÷ 5

9,853,479 ÷ 2 27,853,024 ÷ 2

4,182,010 ÷ 3 3,293,121 ÷ 3

653,890 ÷ 10 5,278,825 ÷ 10

A number is divisible by 2 if

RULE ExamplesIt is even (ends 0, 2, 4, 6, or 8)

1,234 984561,592,342

2 is the ONLY even prime #

A number is divisible by 3 if

RULE Examples

The sum of the digits is divisible by 3

234 2+3+4=99 is divisible by 3 so 234 is divisible by 3

A number is divisible by 5 if

RULE Examples

It ends with 0 or 5

9351,3402,908,675

A number is divisible by 6 if

RULE Examples

It is divisible by 2 and 3

234

Ends 4 so divisible by 2

2+3+4=99 is divisible by 3 so 234 is

divisible by 3

Divisible by 2 and 3 so divisible by 6

A number is divisible by 9 if

RULE Examples

The sum of the digits is divisible by 9

135 1+3+5=99 is divisible by 9 so 135 is divisible by 9

A number is divisible by 10 if

RULE Examples

It ends with 0

901,234,5602504,350

Sieve of Eratosthenes

PrimeDefinition Examples

Has exactly 2 factors

(1 X itself)

291 X 29971 X 97

CompositeDefinition Examples

Has more than 2 factors

121 X 122 X 63 X 4

Do I need to do a sieve each time to find prime/composite?

For numbers through 100

Is it divisible by 2 (other than the #2) – composite

Is it divisible by 3 (other than the # 3) – composite

Is it divisible by 5 (other than the #5) – composite

Magic numbers 49, 77, & 91 are composite because they are multiples of 7

FactorDefinition Examples

the integers (numbers) multiplied to get a product

3 X 4=12

fact

or

fact

or

pro

duct

ExponentDefinition ExamplesNumber written as a power that tells how many base numbers are being multiplied

103

10X10X10=1,000

Base

#

exponent

Greatest Common Factor (GCF)

Definition Examples

Largest factor 2 or more numbers have in common

61X6 2X3

91X93X3

3 is the GCF

MultipleDefinition Examples

Product of a given whole number and an integer

Multiples of 3

3,6,9,12…3X1, 3X2, 3X3,

3X4…

Least Common Multiple (LCM)

Definition Examples

Smallest multiple two or more numbers have in common

44,8,12

66,12

12 is the LCM

DecomposeDefinition Examples

Break into smaller parts

25 + 37 (2X10) + 5 + (3 X10) +

7

122 x 2 x 3