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
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
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
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 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
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
Subtracting Whole Numbers
I. No Borrowing
To subtract whole numbers we write them as in an addition problem and subtract each digit moving
from the right to the left.
Example:
789
- 34
755
Note that 9 - 4 = 5,
8 - 3 = 5, and 7 - 0 = 7
II. Borrowing is Nec
Multiplication of Real Numbers
I. Some Definitions
When multiplying two numbers such as
2x3 = 6
The numbers on the left (the 2 and the 3) are called factors and the result (the 6) is called the product.
II. Properties of Multiplication
A. The Zero Propert
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