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Historical Beginnings |
The Place Value System | The Branches of Mathematics |
Numerical and Literal Numbers |
Signs and Symbols in Mathematics |
Expressing More Relationships Between Numbers
The Place
Value System
CA GR7 AF 1.4
In the Hindu-Arabic number system that we
use, the digits have a place value, depending on their
(horizontal) position in the number. The position of the digit
determines its place value. And since our number system has the
base 10, the digit in each place is multiplied by a power of 10
(10, 100, 1000, 10,000, 100,000, 1,000,000 etc.) except the
furthest right digit, which is multiplied by one (1).
- The digit furthest to the right is
multiplied by one (1).
- The next one to the left is multiplied by
ten (10).
- The next one to the left is multiplied by
one hundred (100).
- The next one to the left is multiplied by
one thousand (1000).
- Etc.
For example: in the number 4782
- The 2 is multiplied by 1 and 2 x l =2
- The 8 is multiplied by 10 and 10 x 8 = 80
- The 7 is multiplied by 100 and 100 x 7 =
700
- The 4 is multiplied by 1000 and 1000 x 4
= 4000
And the value of these numbers is four
thousand, seven hundred eighty two (4,782). Here is a graphic
picture of the place values in the number 4,782:
- thousands (4)
- | hundreds (7)
- | | tens
(8)
- | | |
ones (2)
- | | |
|
- 4 7 8 2
The Branches of
Mathematics (top)
CA GR7 AF 1.4
There are several branches of mathematics
that students are involved in through high school. Each of them
deals with different topics. Here is a short summary:
ARITHMETIC - is involved with
addition, subtraction, multiplication and division. These are the
fundamental operations in mathematics. Everyone begins learning
these fundamental operations in the earliest grades. We also learn
about raising numbers to powers (squaring, cubing, etc.) and
finding roots (square roots, etc.). Arithmetic also includes
computation which involves solving problems by applying the
fundamental operations.
ALGEBRA - In algebra, we use a letter
of the alphabet to represent an unknown number, and place it in an
equation that we formulate, in order to solve a problem. For
example, we will use the letter x to represent an unknown, and
formulate an equation to solve a problem:
The problem: How many eggs do we need to
make a dozen if we already have five? We will use the letter x to
stand for the number of eggs that we need (x = how many eggs we
need).
- We formulate the equation: x
+ 5 = 12
- By inspection you can see
that x =
7, because 7
+ 5 = 12
When letters of the alphabet are used to
represent numbers, they are called literal numbers, which
means "letter numbers." In algebra, you will learn how
to carry out fundamental operations (adding, subtracting,
multiplying and dividing) when you are dealing with literal
numbers and equations. Algebra also includes working with
formulas, which are specific mathematical equations used to solve
specific problems. For example, the formula D=
RT is used to find distance traveled
(D)
when you know the rate of speed (R)
and the time of the trip (T).
In algebra, you will learn how to substitute values into formulas
to solve a variety of problems.
GEOMETRY - In geometry, you will be
dealing with lines, angles, surfaces and volumes of a variety of
figures including rectangles, circles and triangles. Often, you
will be using proven formulas to calculate areas, volumes, etc.
TRIGONOMETRY - The field of
trigonometry is involved with computing solutions to distance
problems instead of using direct measurement. This includes
calculation of distances of the sides of right triangles, and a
variety of calculations involving circular figures.
In addition to the above branches of
mathematics, there are a number of advanced subjects such as
analytic geometry, calculus and other offshoots of these that can
be taken by students who want to specialize in mathematics or
science.
Next Page: Signs
and Symbols in Mathematics
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