Vocabulary:
Natural numbers: Ex. 1, 2, 3, 4, 5, ...
Whole numbers: Ex. 0, 1, 2, 3, 4, 5,...
Integers: Ex. ... ­4, ­3, ­2, ­1 , 0, 1, 2, 3, ...
Rational numbers: Ex. 6.27; 8.222222 where you can write it as 8.2; 3/4
Irrational numbers:
Ex. Real numbers: All rational and irrational numbers.
1
Ex 1: Circle all of the sets to which each number belongs.
a.
17
natural
whole
integer
rational
irrational
b.
0
natural
whole
integer
rational
irrational
c.
­23
natural
whole
integer
rational
irrational
d.
14
3
natural
whole
integer
rational
irrational
e.
8.16
natural
whole
integer
rational
irrational
f.
√2
natural
whole
integer
rational
irrational
2
Counterexamples prove a statement false. You only need one counterexample to prove a statement false.
Are these statements true or false? If false, prove it with a counterexample.
All whole numbers are rational numbers.
The square of a number is always greater than the number.
All whole numbers are integers.
No fractions are whole numbers.
All negative numbers are integers.
Every multiple of 3 is odd.
No positive number is less than its absolute value.
No negative number is less than its absolute value.
All integers are rational numbers
3
Comparing and Ordering Real Numbers:
is less than
is equal to is greater than
is less than or equal to is not equal to is greater than or equal to
4
Ex 2: Comparing Real Numbers
a.
­1 ____ 1
b.
0.5 ____ 5
c.
1 ____ 1
6
8
d.
­3 _____ ­4
5 5
e.
0.12 ____ 0.012
Ordering Fractions: Order these fractions from least to greatest.
­
3
1
­ 5
­
8 ,
2 , 12
5
Def: Two numbers are opposites if they are the same distance from 0 on a number line.
Ex. Def: The absolute value of a number is its distance from 0 on a number line.
You write “the absolute value of ­3” as Ex. 6
Ex 3: Finding Opposite and Absolute Values
a.
Find the opposite of 8.
b.
Find the opposite of ­4.
c.
Find |­7|
d.
Find ­|­12|
e. Compare |3| ____ |­5|
f.
Compare |9+1| ____ ­10
.
g. Simplify 41 ­ 38 6
7