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Lecture notes Business mathematics (BMD115D)
- Institution
- Tshwane University Of Technology (TUT)
Explanation of how to complete certain questions for business mathematics, as well as a practice with answers.
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1CHAPTER 1
NUMBERS
AIM: To give a background on different
kinds of numbers and the number line.
1.1 INTEGERS
When starting to count we used the set of counting numbers, also called positive integers.
Counting numbers 7 1 ; 2 ; 3 ; 4 ; 5............?
A zero was added to the set of counting numbers and then it was called whole numbers.
Whole numbers 7 0 ; 1 ; 2 ; 3 ; 4 ; 5........?
Soon it became evident that every problem could not be solved with the above whole numbers.
EXAMPLE 1.1
Solve the following problems:
1.1.1 4+3
This is no problem. Add the whole numbers 4 and 3 to get an answer of 7.
4+3=7
1.1.2 5-8
When subtracting a larger whole number from a smaller one there is no solution in the set of
whole numbers.
The set of numbers will have to be extended to include negative integers.
Negative integers 7 ......... -6 ; -5 ; -4 ; -3 ; -2 ; -1 ?
The answer for example 1.1.2 will be -3 and that will come from the set of negative integers.
If the set of whole numbers is combined to the set of negative integers, the new set of numbers
is called the set of integers.
Integers 7 ........ -4; -3; -2; -1; 0; 1; 2; 3; 4; 5 .........?
An integer can be odd (uneven) or even.
Odd integers 7 ........ -3 ; -1 ; 1 ; 3 ; 5 .........?
Even integers 7 ........ -4 ; -2 ; 0 ; 2 ; 4..........?
, 2
1.2 NUMBER LINE FOR INTEGERS
To construct the number line we have to construct a straight line with a reference point on it. The
reference point will normally be 0 .
}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|
0
Divide the line in convenient unit lengths.
}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|
0
We shall now assign positive values to the units to the right of zero and negative values to the
left of zero.
}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|
-4 -3 -2 -1 0 1 2 3 4 5
We refer to any position on the number line as a certain number of units away from 0.
1.3 RATIONAL NUMBERS
EXAMPLE 1.2
Solve the following problems:
1.2.1 4×3
This is no problem. Multiply integer 4 by integer 3 to get an answer of 12.
4 × 3 = 12
1.2.2 4÷8
When dividing the integer 4 by the integer 8 the answer will not be an integer. The answer will
be the number 4/8. That is an example of a rational number.
In general we define rational numbers as any number of the form
where c and d are integers (d not zero).
EXAMPLE 1.3
The following are all examples of rational numbers:
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