1.1 Real Numbers and Number Operations
The Real Number System
Create a Venn Diagram that represents the real number system, be sure to include the following
types of numbers: real, irrational, rational, integers, wholes, and natural/counting.
Properties of Real Numbers
Let a, b and c be real numbers.
Property
Closure
Commutative
Associative
Identity
Addition
a + b is a real number
a+b=b+a
(a + b) + c = a + (b + c)
a+0=a; 0+a=a
Inverse
a + (-a) = 0
Multiplication
a · b is a real number
a·b=b·a
(ab) · c = a · (bc)
a ·1 = a , 1 · a = a
1
a ⋅ = 1 ; (a ≠ 0)
a
a(b + c) = ab + ac
Distributive Property
Identify the property illustrated.
a.) 14 + 7 = 7 + 14
1
b.) 5⋅ = 1
5
d.) 5 ( x + 2) = 5x + 10
e.)
2 ⎛ 2⎞
+ −
=0
3 ⎜⎝ 3 ⎟⎠
c.) (5 + 3) + 2 = 5 + (3 + 2)
f.) 1 · 5 = 5
About that Closure property.....
a.) The Closure property may seem a little obvious, but sometimes not. For example, is the set of irrational
numbers closed under addition? Is the set of irrational numbers closed under multiplication?
2+3 2 =
2 ⋅3 2 =
b.) What about the set of only odd integers? Is that set closed under addition? Is that set closed under
multiplication?
1.1 Real Numbers and Number Operations
Unit Analysis
1 ft = 12 in
1 mi = 5280 ft
1 lb = 16 oz
1 gal = 4 qt
1 yd = 3 ft
Conversion Reference Table
1 in = 2.54 cm
1 m = 1000 mm
1 mi = 1.61 km
1 kg = 1000 g
1 lb = 454 g
1 L = 1000 mL
1 L = 1.057 qt
1 m = 100 cm
Perform the given operation and give the answer with the appropriate unite of measure.
(
66 ft 3600 sec 1mile
)(
)(
)
1sec
1h
5280 ft
Try the following conversions.
1.) 2.45 ft =_____________ mi
2.) 36 g = _____________ kg
3.) 470 mi = _____________ km
4.) 200 mi/hr = _____________ ft/sec
5.) 526 yds/sec = _____________ mi/hr
6.) 75.0 kg = _____________ lbs.
7.) 10 gal = _____________ mL
8.) 1.43 kg/L =_____________g/mL