Page 182 - Basic College Mathematics with Early Integers

CHAPTER HIGHLIGHTS 159

Definitions and Concepts Examples

Section 2.3 Adding Integers

ADDING TWO NUMBERS WITH THE SAME SIGN Add:
-3 + 1-22 =-5
Step 1. Add their absolute values.
-7 + 1-152 =-22
Step 2. Use their common sign as the sign of the sum.

ADDING TWO NUMBERS WITH DIFFERENT SIGNS -6 + 4 =-2
17 + 1-122 = 5
Step 1. Find the larger absolute value minus the
smaller absolute value.
Step 2. Use the sign of the number with the larger -32 + 1-22 + 14 = -34 + 14
absolute value as the sign of the sum. =-20

Section 2.4 Subtracting Integers

SUBTRACTING TWO NUMBERS Subtract:
If a and b are numbers, then a - b = a + 1-b2. -35 - 4 =-35 + 1-42 =-39
3 - 8 = 3 + 1-82 =-5
-10 - 1-122 =-10 + 12 = 2
7 - 20 - 18 - 1-32 = 7 + 1-202 + 1-182 + 1+32
=-13 + 1-182 + 3
=-31 + 3
=-28

Section 2.5 Multiplying and Dividing Integers

MULTIPLYING NUMBERS Multiply:
The product of two numbers having the same sign 1-721-62 = 42
is a positive number. 91-42 =-36
The product of two numbers having different signs
Evaluate:
is a negative number.
2
1-32 = 1-321-32 = 9
DIVIDING NUMBERS Divide:
The quotient of two numbers having the same sign -100 , 1-102 = 10
is a positive number. 14 0 22
The quotient of two numbers having different signs =-7, = 0, is undefined.
-2 -3 0
is a negative number.
Section 2.6 Order of Operations

ORDER OF OPERATIONS Simplify:
#
1. Perform all operations within parentheses ( ), brackets 3 + 2 1-52 = 3 + 1-102
[ ], or other grouping symbols such as fraction bars or =-7
square roots, starting with the innermost set.
-215 - 72 -21-22
2. Evaluate any expressions with exponents. =
-7 + ƒ -3ƒ -7 + 3
3. Multiply or divide in order from left to right.
4
4. Add or subtract in order from left to right. =
-4
=-1