Addition and Subtraction of Decimals
I. Addition of Decimals
Adding decimals is very similar to adding whole numbers except with a few extra technical details
and bookkeeping. Recall that decimals are just fractions. We add fractions by adding the whole
n
Division of Decimals
I. Dividing a Decimal by a Whole Number
Dividing a decimal by a whole number is similar to dividing whole numbers. One must only be
sure to line up the decimal point of the dividend with that of the quotient.
Example
Divide
143.22 6
S
Applications
I. Strategies For Solving Application Problems
Application problems, a.k.a. word problems or story problems, traditional pose the greatest
challenge to math students. We must keep in mind, however, that other then just enjoying math as
a beau
Applied Problems Involving Fractions
We will follow the same method from 181A to solve applied problems that involve fractions.
Example
The width of a piece of paper is 8 inches. If you want the left and right margins to be 2/3 inches, what
is the width o
Addition and Subtraction of Fractions
I. Adding and Subtracting Fractions With a Common Denominator
No matter how tempting it may be, we can only perform addition and subtraction of fractions
when the denominators are the same.
When the denominators are t
Combining Mixed Numbers and Order of Operations
I. Adding Mixed Numbers
In the last section we learned how to add and subtract two fractions.
If we have two mixed numbers to add, we can just add the whole number parts and then add the
fraction parts.
Exam
The Least Common Denominator
I. The Least Common Multiple
A multiple of a number is a whole number times that number. For example, some multiples of 6
are
6, 12, 18, 24, 30, and 36
If two numbers are given then a common multiple of the two numbers is a nu
Multiplication of Decimals
I. General Multiplication of Decimals
The rules for multiplication of decimals come from the rules of multiplying fractions. Consider
the product
0.02 x 0.013
in fraction form this is
2
13
x
26
=
100
1000
= 0.00026
100000
Notice
Understanding Fractions
I. Definitions
In module A, all the numbers that we encountered were whole numbers. Although the whole
numbers are important, they only tell part of the story. Module B is the study of fractions which are
defined as parts of the wh
Simplifying Fractions
I. Writing a Number as a Product of Primes
We call a whole number greater than one prime if it cannot be divided evenly except by itself and
one. For example the number 7 is prime but the number 6 is not, because
6 = 2x3
A number tha
Square Roots
I. Definition of the Square Root
Recall how we defined exponents, especially with exponent 2. Some examples are
32 = 3 x 3 = 9
102 = 10 x 10 = 100
52 = 5 x 5 = 25
Also recall that the inverse of addition is subtraction and the inverse of mult
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