number properties

Question 1

real numbers

Answer 1

all numbers in the number line

positive and negative, decimals, integers and fractions

Question 2

integers

Answer 2

all numbers that are not fractions or decimals

i.e 0, 1, 2, -15

Question 3

rational numbers

Answer 3

all the numbers that can be expresses as the ratio of two integers
- all integers and fractions

Question 4

irrational numbers

Answer 4

• square root of 3

3. 14 (pi)

Question 5

rules for even and odds

Answer 5

odd +- odd= even
even +- even= even
odd+- even= odd

oddodd= odd
eveneven=even
odd*even=even

Question 6

exponent rules for odds and even

Answer 6

odd^ any positive int= odd

even^ any positive int= even

Question 7

the reciprocal of a number between 0 and 1 is always

Answer 7

greater than the number
i.e. 2/3 an its reciprocal is 3/2
3/2>2/3

Question 8

the reciprocal of a number between -1 and 0

Answer 8

is less than the number itself

Question 9

square number between 0 and 1

Answer 9

is less than the number itself

Question 10

multiplying any positive number by a fraction between 0 and 1

Answer 10

gives the product smaller than the original number

Question 11

multiplying any negative number by a fraction between and 1

Answer 11

gives the product greater than the number itself

Question 12

multiple/factor= integer

Answer 12

i.e 36/6
36/2
36/4
36/9

Question 13

multiple

factor

Answer 13

multiple is the product of a given integer and another integer i.e 9*2=36
36 is a multiple of 9 and 2
factor or divisor is an integer that divides another integer without leaving remainder

Question 14

sum of n consecutive terms

Answer 14

mean*number of terms
mean= the average of the first number and the last
=(a1+an/2) *n

Question 15

if n is odd the sum of the consecutive integer is always divisible by n

Answer 15

9+10+11= 30
n=3
30/3=10

Question 16

if n is even the sum of the consecutive integers is never divisible by n

Answer 16

9+10+11+12=42

42 is not divisible by 4

Question 17

product of n consecutive integers is always divisible by n!

Answer 17

345*6=360 which is divisible by 4! = 24

Question 18

evenly spaced set or arithmetic progression

Answer 18

is a sequence of numbers such that the difference of any two successive members of the sequence is constant
i.e 9, 13, 17, 21

Question 19

how to calculate the nth term of the sequence

Answer 19

an=a1 +d(n-1)
a1= first term
d= common difference of the successive number

Question 20

in evenly spaced set/ arithmetic mean the average is calculated

Answer 20

mean/average = median
=a1+an/2
a1=first term
an= last term

Question 21

if evenly spaced set contains odd number of elements then median is

Answer 21

the middle number 
and the sum is middle number * number of terms
i.e 1, 7, 13, 19, 25
median= 13
sum= 13*5= 65

Question 22

comparing fractions

when the numerator is the same and de

Answer 22

bigger the denominator smaller the fraction

Question 23

average arithmetic mean

Answer 23

sum of the terms/ number of the terms

18+21+45/3

Question 24

range

Answer 24

last number - first number

Question 25

perfect squares will always have odd number of factors

Answer 25

i.e 4- 1, 2, 4

9- 1, 3, 9