Basic Properties of Numbers

Question 1

divisibility rules: 2

Answer 1

if the units digit is even

Question 2

divisibility rules: 3

Answer 2

sum of digits is divisible by 3

ex. 27 , 2+7 = 9 which is divisible by 3

Question 3

divisibility rules: 4

Answer 3

final two digits are divisible by 4

ex. 316

Question 4

divisibility rules: 5

Answer 4

units digit of 5 or 0

Question 5

divisibility rules: 6

Answer 5

• units digit is even

- sum of digits is divisible by 3

Question 6

divisibility rules: 9

Answer 6

sum of digits is divisibly by 9

Question 7

divisibility rules: 10

Answer 7

units digit is 0

Question 8

is zero (0) an even or odd?

Answer 8

even

Question 9

is zero (0) an integer, yes or no?

Answer 9

yes

Question 10

is zero (0) a prime number, yes or no?

Answer 10

no

Question 11

is 1/2 or 0.5 an integer, yes or no?

Answer 11

no

Question 12

integer

Answer 12

has to be a whole number ex. 3, 4, 89

Question 13

prime number

Answer 13

• positive integer

- divisible only by itself and 1

Question 14

is one, 1, an integer? is one, 1, a prime number?

Answer 14

1 is an integer but not a prime number

Question 15

is 2 an integer, is 2 a prime number?

Answer 15

2 is an integer and 2 is also a prime number

- 2 is the only even prime number and the least prime number

Question 16

factor vs. multiple

Answer 16

think “factors few, multiples many”

Question 17

is zero (0), positive or negative?

Answer 17

0 is not positive nor negative

Question 18

remainder

Answer 18

integer left over when an integer is divided by another
a remainder is always an integer

if integer m is divided by integer n then:
m = (a)(n) + b where a and b are integers and integer b is the remainder
ex. 13/5 where 13=m and 5=n so, 13 = (a)(5) + b then you know a = 2 and b = 3 and 3 is the remainder

Question 19

divisible

Answer 19

when a number is divisible, it divides evenly

all factors of a number are its divisors

Question 20

what are the first 5 prime numbers?

Answer 20

2, 3, 5, 7, 11

Question 21

common factors

Answer 21

factors that two integers share

Question 22

what is the greatest common factor of 12 and 18?

Answer 22

6

Question 23

prime factorization

Answer 23

writing an integer as a product of its prime factors
ex. 45
/ \
3 15
/ \
3 5
so the primer factorization of 45 = 3^2 * 5

Question 24

prime factorization of 72

Answer 24

72
          /      \
         2      36 
                 /   \
                3    12
                       /  \
                     3    4 
                           /  \
                          2    2 

= 2^3 * 3^2

Question 25

multiples

Answer 25

multiples can be positive or negative and multiples of integer n are all the numbers: 0, +- 1 *n, +- 2 *n, +- 3 *n, +- 4*n ex. the positive multiples of 4? = 4, 8, 12, 16, 20, 24...

Question 26

is 21 a factor OR a multiple of 42?

Answer 26

factor

Question 27

least common multiple of 6 and 8?

Answer 27

make a list of the multiples of each number until you find a number on both lists multiples of 6: 6, 12, 18, 24, 30 multiples of 6: 8, 16, 24 least common multiple of 6 and 8 = 24

Question 28

fractions ex. there are 5 men and 7 women in a room, what fraction are men?

Answer 28

part/ whole ex. there are 5 men and 7 women in a room, what fraction are men? = 5/12

Question 29

comparing fractions to know which one is greater | ex. which is greater 4/7 or 5/9?

Answer 29

use the bow time method if neither the numerator or denominator is the same 4/7 5/9 --> 7*5 = 35 and 9*4 = 36 so 4/7 is greater

Question 30

multiplying fractions

Answer 30

multiply straight across 3/4 x 2/6 = 6/20 = 3/10

Question 31

dividing fractions 9/5 divided by 7/10 = ?

Answer 31

flip the second fraction then multiply 9/5 * 10/7 = 18/7

Question 32

what is the reciprocal of 1/ (1/4)?

Answer 32

= (1/4)/1 = 1/4

Question 33

Adding and subtracting fractions if the denominators are the same

Answer 33

just add or subtract the numerator and keep the denominator then simplify

Question 34

Adding and subtracting fractions if the denominators are not the same 7/12 + 1/3

Answer 34

use bowtie method to add or subtract! 7/12 + 1/3 = (21 + 12)/ 36 = 33/36

Question 35

how many distinct factors of 36 are there?

Answer 35

``` 36 / \ 1 36 2 18 3 12 4 9 6 6 ``` = 9 distinct factors

Question 36

How do you know when a factor list is done?

Answer 36

When there are no numbers between the last two factors that divides evenly into the number you are factoring

Question 37

How many integers between 100 and 300 are multiples of both 3 and 7?

Answer 37

answer = 10 3 and 7 are both prime numbers and 3 x 7 = 21. The only numbers that will be divisible by 3 and 7 are multiples of 21 ``` so 21: (times these numbers is between 100 - 300 x 5 x 10 x 6 x 11 x 7 x 12 x 8 x 13 x 9 x 14 ```

Question 38

QA: The number of positive integers that are both factors of 48 and multiples of 4 QB: 5 A B C D

Answer 38

Answer = A 4 is a multiple of 4 so there are six values that re factors and multiples

Question 39

The incoming class in a college can be divided up evenly into 18, 20, 24, or 36 lecture halls. Which could be the number of students in the incoming class? Select all that apply ``` 180 360 480 720 960 1080 1440 ```

Answer 39

answers = A, B , F, G PRIME FACTOR - any correct answer must be divisible by all of the prime factors also if one of the options is divisible by an answer that was correct, it will also work. Aka 1080 and 1440 are divisible by 360 which we showed to be true so they will work too

Question 40

What is the difference between the product of the distinct prime factors of 84 and the sum of the distinct prime factors of 192 ?

Answer 40

answer = 37

Question 41

How can 10^3 be rewritten?

Answer 41

5^2 x 2^3

Question 42

x, y, and z are negative integers, and -(x/y) = z QA: x^2 QB: yz

Answer 42

Answer = D cannot be determined! do not forget to try 1 as a number!!

Question 43

The remainder when 10 is divided by positive integer x is y for all values of y > 0. If the remainder when 11 is divided by x is y^2 + 1, then which of the following could be the value for x? ``` 5 6 7 8 9 ```

Answer 43

answer = 9 when 10 is divided by 9 the remainder is 1 when 11 is divided by 9 the remainder is 2 which is = 1^2 + 1