ix
Contents
SECTION
1
Whole Numbers
UNIT
1
Number Systems
. . . . . . . . . . . . . . . . . . . . . . .
2
Positive and Negative Numbers . . . . . . . . . . . 2
Arabic Number System . . . . . . . . . . . . . . . . . . . 3
Abstract, Concrete, and Denominate
Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
UNIT
2
Adding Whole Numbers
. . . . . . . . . . . . . . .
.7
Adding Numbers of Less Than 10 . . . . . . . . . 7
Adding Numbers Greater Than 10 . . . . . . . . . 9
UNIT
3
Subtracting Whole Numbers.
. . . . . . . . .
15
Subtracting Numbers of Less Than 10 . . . . . 15
Borrowing When the Bottom Numeral
Is Greater Than the Upper Numeral . . . . 15
Subtracting More Than One Amount . . . . . . 16
Checking Subtraction . . . . . . . . . . . . . . . . . . . 17
Checking Addition . . . . . . . . . . . . . . . . . . . . . 17
UNIT
4
Multiplying Whole Numbers.
. . . . . . . . .
23
Multiplication Symbols . . . . . . . . . . . . . . . . . . 23
Multiplication Table . . . . . . . . . . . . . . . . . . . . . 23
Multiplication by Less Than 10 . . . . . . . . . . . 25
Multiplication by 10 or More . . . . . . . . . . . . . 25
UNIT
5
Dividing Whole Numbers
. . . . . . . . . . . . .
33
The Language of Division . . . . . . . . . . . . . . . 33
Division of Whole Numbers . . . . . . . . . . . . . 34
Division with a Remainder . . . . . . . . . . . . . . 35
Checking Division with Multiplication . . . . 35
UNIT
6
Combined Operations.
. . . . . . . . . . . . . . . .
43
Problems Involving More Than One Type
of Operation . . . . . . . . . . . . . . . . . . . . . . . . 43
SECTION
2
Common Fractions
UNIT
7
Parts of a Fraction.
. . . . . . . . . . . . . . . . . . . .
52
Parts of a Fraction . . . . . . . . . . . . . . . . . . . . . . 52
Equivalent Fractions . . . . . . . . . . . . . . . . . . . . 52
UNIT
8
Proper Fractions, Improper Fractions,
and Mixed Numbers
. . . . . . . . . . . . . . . .
61
Proper and Improper Fractions . . . . . . . . . . . 61
Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . 62
Changing Mixed Numbers to Improper
Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
UNIT
9
Least Common Denominator
. . . . . . . . .
67
Least Common Denominators . . . . . . . . . . . . 67
UNIT
10
Adding Fractions
. . . . . . . . . . . . . . . . . . . . . .
73
Learning the Principles. . . . . . . . . . . . . . . . . . 73
UNIT
11
Subtracting Fractions
. . . . . . . . . . . . . . . . .
85
Learning the Principles. . . . . . . . . . . . . . . . . . 85
UNIT
12
Multiplying Fractions
. . . . . . . . . . . . . . . . .
93
Multiplying Proper Fractions . . . . . . . . . . . . . 93
Multiplying Mixed Numbers . . . . . . . . . . . . . 94