Page 764 - Basic College Mathematics with Early Integers

Bigger Picture—Study Guide Outline

I. Operations on Sets of Numbers
A. Whole Numbers
1. Add or Subtract: 14 300
+39 - 27
53 273
127 R2
2. Multiply or Divide: 238 7891
* 47 -7
1666 19
9520 -14
11,186 51
-49
2
3. Exponent: 4 factors of 3
μ
# # #
4
3 = 3 3 3 3 = 81
4. Square Root:
#
125 = 5 because 5 5 = 25 and 5 is a positive number.
5. Order of Operations:
#
#
24 , 3 2 - (2 + 8) = 24 , 3 2 - (10) Simplify within parentheses.
#
= 8 2 - 10 Multiply or divide from left to right.
= 16 - 10 Multiply or divide from left to right.
= 6 Add or subtract from left to right.
B. Integers
1. Add: -5 + (-2) =-7 Adding like signs
Add absolute value.Attach the common sign.
-5 + 2 =-3 Adding unlike signs
Subtract absolute values. Attach the sign of the number
with the larger absolute value.
2. Subtract: Add the first number to the opposite of the second number.
7 - 10 = 7 + (-10) =-3
3. Multiply or Divide: Multiply or divide as usual. If the signs of the two
numbers are the same, the answer is positive. If the signs of the two num-
bers are different, the answer is negative.
-32
#
-5 5 =-25, = 4
-8
C. Fractions
1. Simplify: Factor the numerator and denominator.Then divide out factors
of 1 by dividing out common factors in the numerator and denominator.
#
20 4 5 5
Simplify: = =
#
28 4 7 7
2. Multiply: Numerator times numerator over denominator times denomi- Copyright 2012 Pearson Education, Inc.
nator.
5 2 10
# =
9 7 63
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