Comparing, Ordering and Rounding Decimals
I. Comparing Decimals
At the beginning of this course, we we encountered the number line, a graphical device that helps
us visualize the relationships between two numbers. Just as we can place whole numbers on the
Converting Fractions to Decimals and Order of Operations
I. Converting Fractions to Decimals
To convert fractions to decimals we just divide. The only catch is when should we stop.
Sometimes we end when there is no remainder.
Example
Convert the fraction
Estimating and Solving Applied Problems Using Decimals
I. Doing Arithmetic of Decimals Using Estimation
Since arithmetic can be cumbersome when it involves complicated numbers, it is convenient to
know how to estimate to get a ball park figure. A useful m
Decimal Notation
I. Naming a Decimal
Among all fractions there is a collection of special fractions called decimal fractions. Decimal
fractions are fractions where the denominator is a power of ten. For example
3
78
,
10
91
,
142
,
100
10,000
1,000
There
Exponents and Order of Operations
I. Exponents
Recall that multiplication is defined as repeated addition, for example
4+4+4+4+4+4+4 = 4x7
What about repeated multiplication? For example, is there an easy way to write
4x4x4x4x4x4x4
Fortunately, mathematic
Division of Fractions
I. Dividing Two Proper or Improper Fractions
To divide two proper or improper fractions we turn the problem into a multiplication problem by
multiplying by the reciprocal
Example
3
2
3
5
=
4
15
x
5
=
4
2
8
Example
2
12
4
9
=
515
x
39
Division of Whole Numbers
I. Definition of Division
Example:
Suppose that we have twelve students in the class and we want to divide the class into three equal
groups. How many should be in each group?
Solution:
We can ask the alternative question, "Three
Rounding and Estimation
I. The Number Line
On of the most useful ways of displaying numbers is the number line which is defined as follows.
First draw a line. then label a number on the line (usually 0). To the left of that number represents
values below
Improper Fractions and Mixed Numbers
I. Definitions of Improper Fractions and Mixed Numbers
In your pocket, you have five quarters. Their are two ways of mentioning your cash. The first
way is five quarters or 5/4 dollars. The second way is one dollar and
Multiplication of Fractions
I. Multiplying Two Fractions
Suppose that you are making lemonade and have found a recipe that requires three-quarters of a
cup of sugar to make one pitcher of lemonade. You want to make a half pitcher of lemonade.
How much sug
Key Concepts and Ideas For Fractions
Fill in the blanks for the following. Then come up with an example that illustrates each. Hold the mouse over th
yellow box to check your answer.
1. The top number of a fraction is called the
.
2. The bottom number of