math 9

Question 0

rational numbers

Answer 0

any number that can be expressed as a fraction (any number that ends or repeats)
ex. 3, -3, 5, 1/2
closed under add., subt., and mult.
not closed under div.

Question 1

irrational numbers

Answer 1

any number that can’t be expressed as a fraction

Question 2

integers

Answer 2

.. -3, -2, -1, 0, 1, 2, 3
closed under add., subt., and mult.
not closed under div.

Question 3

whole numbers

Answer 3

0, 1, 2, 3…
closed under add., and mult.
not closed under subt., and div.

Question 4

natural numbers

Answer 4

1, 2, 3…

Question 5

communitive prop. of addition

Answer 5

a+b=b+a

1+4=4+1

Question 6

communitive prop. of multiplication

Answer 6

ab=ba

Question 7

associative prop. of addition

Answer 7

a+(b+c)=b+(a+c)

4+(5+2)=(4+5)+2

Question 8

associative prop. of multiplication

Answer 8

a(bc)=(ab)c

3(62)=(36)2

Question 9

inverse prop. of addition

Answer 9

a+(-a)=0

2+-2=0

Question 10

inverse prop. of multiplication

Answer 10

a*1/a=1

3*1/3=1

Question 11

identity prop. of addition

Answer 11

a+0=a

Question 12

identity property of multiplication

Answer 12

a*1=a

6*1=6

Question 13

distributive property

Answer 13

a(bc)= ab + ac

Question 14

finding the produvt of powers

x^a*x^b

Answer 14

x^a+b

when you multiply powers with the same base, you keep the base and add the exponents

Question 15

finding a power of a power

(x^a)^b

Answer 15

x^a*b

Question 16

dividing powers with the same base

x^a/x^b

Answer 16

x^a-b

when you divide powers with the same base, you keep the base and subtract the exponents

Question 17

zero exponent

x^0

Answer 17

x^0=1

when the exponent is 0, the answr will always be 1.

Question 18

negative exponents x^-n

Answer 18

1/x^n

if there is a negative exponent put it in the form of a fraction with a one on top.

Question 19

closure

Answer 19

if two numbers belong to the same set, it is closed or has closure if after an operation you get a number of that set.

Question 20

set notation
{} x€r
“x is a real element of the real numbers”

Answer 20

ex.) {x€r:x>1}

Question 21

interval notation

Answer 21

( ) = o or <,>,=
[ ] = closed circle or greater than or equal to, or less than or equal to
ex. (-infinity, 5]