1.1 Real Numbers and Number Operations (Day 2)
Real Number Line – all real numbers can be represented as point on a number line.
–4 –3 –2 –1
0 1
2 3 4
5 6
0 is the origin.
Coordinate is the number.
Ex: Try graphing the coordinates for –½, 4, √2, and π.
Ordering Numbers – You can use the number line to order numbers from smallest to
greatest.
Ex:
Ex: – 4 and 1
–5 and –7
Ex:
Ex: Order the record low temperatures for 5 states from smallest to greatest:
CT = –32 ºF
ME = – 48 ºF
MD = – 40 ºF
Operations with Real Numbers
Ex:
Ex:
Write an expression and simplify.
The difference of –3 and –15 is:
The quotient of –7 and ½ is:
The sum of –2 and 5 is:
The product of –3 and –12 is:
NJ = –34 ºF VT = –50 ºF
Properties of Real Numbers
Let a, b, and c be real numbers…
Property
Addition
Multiplication
Closure
a + b is a real number
a · b is a real number
Commutative
a+b=b+a
a·b=b·a
Associative
(a + b) + c = a + (b + c)
(ab) · c = a · (bc)
Identity
a+0=a; 0+a=a
a ·1 = 1 · a = a
Inverse
a + (−a) = 0
a⋅
1
a
= 1 ; (a ≠ 0)
a(b + c) = ab + ac
Distributive
***NOTE: Additive inverses are also called “opposites.” Multiplicative inverses are also
called “reciprocals.”
Ex:
Ex: Identify the property illustrated.
a.) 14 + 7 = 7 + 14
b.) 5 ⋅
1
=1
5
c.) (5 + 3) + 2 = 5 + (3 + 2)
d.) 5(x + 2) = 5x + 10
e.)
2  2
+ −  = 0
3  3
f.) 1 · 5 = 5