Download Adding Without a Number Line

Math 52
1.3 "Addition of Real Numbers"
Objectives:
*
Add real numbers without using a number line.
*
Find the opposite, or additive inverse, of a real number.
Preliminaries:
In this section, we consider addition of real numbers. First, to gain an understanding, we add using a number line. Then
we consider rules for addition.
Addition on a Number Line:
To do the addition a + b on a number line, we start at 0. Then we move to a and then move according to b
a) If b is positive, we move from a to the right
b) If b is negative, we move from a to the left
c) If b is zero, we stay at a
Example 1: (Adding using a number line)
Add:
a) 3
7
b)
5 1
+
2 2
Adding Without a Number Line
Rules for Addition of Real Numbers:
1: Positive numbers: Add the numbers (the answer is positive)
2: Negative numbers: Add absolute values (the answer is negative)
3: A positive and a negative number: Subtract the smaller absolute value from the larger
(the answer has the sign of the larger number).
4: One number is zero: The sum is the other number.
Note:
Rule 4 is known as the identity property of 0. (it says that for any real number a, a + 0 = a)
Example 2: (Adding without using a number line)
Add without using a number line:
a) 5 + ( 6)
b) 1:5 + ( 1:5)
c)
2:8 + 0
d)
f)
1
+
5
0:17 + 0:7
e)
36 + 21
Page: 1
3
4
Notes by Bibiana Lopez
Introductory Algebra by Marvin L. Bittinger
1.3
Example 2: (Adding without using a number line)
Add without using a number line.
a) 2:5 + ( 10) + 6 + ( 7:5) + 3:5 + ( 1:5)
b) 15 + ( 2) + 7 + 14 + ( 5) + ( 12)
Opposites or Additive Inverses
De…nition:
"Opposites or Additive Inverses"
Two numbers whose sum is 0 are called opposites, or additive inverses, of each other.
The opposite of a number a can be named
a:
Example 3: (Finding the opposite)
Find the opposite, or additive inverse, of each number.
a)
4
b) 0
c)
7:74
d)
8
9
De…nition:
"The Opposite of an Opposite"
kThe opposite of the opposite of a number is the number itself. That is, for any number a;
Example 4: (Finding the opposite and the opposite of an opposite)
Evaluate x and
( x) when:
b)
x=
a)
x = 32
The Sum of Opposites:
kFor any real number a, the opposite of a expressed as
( a) = a:k
3
a, is such that a + ( a) = ( a) + a = 0k
Page: 2
Notes by Bibiana Lopez