Ch. 3: Properties of numbers

Even integers are represented by ?

2n

What are odd integers represented by?

2n+1 or 2n-1

All positive bases of 3 will have a units digit of ....?

3-9-7-1

All positive bases of 4 will have a units digit of ....?

4-6-4-6 odd=4 Even=6

All positive bases of 5 will have a units digit of ....?

5 ex) 5^1 = 5 5^2 = 25 5^3 = 125

All positive bases of 6 will have a units digit of ....?

6 ex) 6^1=6 6^2=36

All positive bases of 7 will have a units digit in the pattern.....?

7-9-3-1

Any number that ends in 000 will be divisible by what?

8

All positive bases of 8 will have a units digit of ....?

8-4-2-6

All positive bases of 9 will have a units digit of ....?

9-1-9-1 Odd=9 Even=1

How can you tell if a number has a terminating decimal?

A fraction will terminate if and only if the denominator of the fraction has a prime factorization of only 2's or 5's or both. ex) 1/25 --> 25= 5*5 There for it terminates

How can you tell if a number is divisible by 12?

A number is divisible by 12 IF the number is divisible by BOTH 4 and 3 ex) 24 is divisible by 12 because it is divisible by both 4 and 3

How can you tell if a number is divisible by 11?

A number will be divisible by 11 if the sum of all the odd number digits minus the sum of all the even number digits is divisible by 11. ex) 2534 is divisible by 11 becase odd-> 2+3=5 even-> 5+4=9 O-E=#/11 5-9=-4 -4 is not divisible by 11

A number that ends in 2,3,7, or 8 can never be.....?

A perfect square

Any multiplication of 5 and 2 will create what?

A product with a units digit of 0, regardless of what additional numbers are multiplied

What is absolute value?

Absolute value is the distance between 0 and a number on a number line.

How can you tell if a number is divisible by 6

Add each digit and if that is divisible by three AND it is an even number , then the whole number is divisible by 6

How can you tell if a number is divisible by 3

Add each digit and if that is divisible by three, then the whole number is divisible by 3 ex) 9,132 9+1+3+2=15. 15 is divisible by 3 so 9,132 is divisible by 3.

How can you tell if a number is divisible by 9

Add each digit and if that is divisible by three, then the whole number is divisible by 9 ex) 13,675 1+3+6+7+5=22 22 is not divisible by 9. Therefore 13,675 is not divisible by 9.

Even + Even =

Even

Even x Even =

Even

Even x Odd =

Even

Even- Even

Even

Even/Odd=

Even

Odd +Odd=

Even

Odd- Odd

Even

Zero is a(n)...

Even Number

Even/Even=

Even or Odd we cannot be sure

What is the only way to get an odd product?

If both numbers are odd Odd x Odd

How can you tell if a number is divisible by 8

If the last three numbers are divisible by 8 ex) 400,000 is divisible by 8 because 8 divides into 1000

How can you tell if a number is divisible by 4

If the last two digits are divisible by 4, the whole number is divisible by 4 ex) 544 44 is visible by 4 so 544 is divisible by 4

0/any number is?

0

How do you find the GCF?

1) Find the prime factorization of each number 2) Identify repeated prime factors 3) Of any repeated factors among the two numbers, take the smallest exponent that each have in common ex) 24 60 / \ / \ 4 6 6 10 /\ /\ /\ /\ 2 2 3 2 3 2 5 2 24=(2^3)(3) 60=(3)(5)(2^2) Therefore since 24 and 60 have 2^2 and 3 in common we multiply them to find the GCF. GCF=12

How to find the LCM?

1) Find the prime factorization of each number 2)Take the highest power of each repeated number ex) 24 60 / \ / \ 4 6 6 10 /\ /\ /\ /\ 2 2 3 2 3 2 5 2 24=(2^3)(3) 60=(3)(5)(2^2) LCM(Greatest power from each number): (2^3)(3)(5)

How many zeros are to the right of the last non-zero digit in the number 5^18 x2^20?

18 because 5^18 x 2^20 have 18 in common

All positive bases of 2 will have a units digit of ....?

2-4-8-6

When will the sum or difference be an even number?

When both numbers are Odd or both numbers are Even

Any factorial above 5! will always have

a zero as its units digit

Multiple/ Factor =

Integer

How can you tell if a number is divisible by 7

Just do the long division

Even + Odd=

Odd

Odd/Odd=

Odd ex) 21/7 or 33/11

Zero is neither..

Positive nor Negative

One is a ____

Prime Number