| Fundamentally, force is applied energy. So how does this concept of
force apply to the number line which is essentially an abstract representation of quantities? The type of mapping that established the occupants of the
number line also established the forces of the number line. Consider two baskets, x and y , containing oranges. Basket x contains 7 oranges while basket y contains 5 oranges. If we remove 1 orange from basket y and put it in basket x , we have applied energy, mental and physical energy. In other words, we have applied force. This force is an incremental force because the number of oranges in basket x increased from 7 to 8. Incremental force is popularly known as addition . When addition is mapped onto the number line, it becomes a force on the number line. Here is how our example of addition is mapped on the number line. The number of oranges in basket x ( 7 in our example) is mapped onto the number line. The amount by which the oranges in basket x is increased ( 1 in our example), is counted rightwards on the number line relative to the number 7. The occupant of the number line that is at the position that marks the end of the counting, is the result of the addition. In our example, this number is 8. The formal representation of the mapping of our addition is as follows: 7 + 1 = 8. The plus symbol ( + ) is called the addition operator. |
| Now if we return to our example and focus on basket y , we observe that the number of oranges it contained (5), decreased by 1 orange. The force applied
in this scenario is the decremental force which is popularly known as subtraction. The mapping of subtraction onto the number line
is similar to the mapping of addition onto the number line except that the movement of counting is leftwards relative to the number being decreased. The formal representation of the mapping
of our subtraction is as follows: 5 - 1 = 4. The minus symbol (-) is called the subtraction operator . addition and subtraction are the two fundamental forces of the number line. Two other important forces of the number line are: multiplication and division. We can use addititon mapping to map multiplication onto the number line. Let us suppose we want to map 4 x 2 (the symbol "x" is the multiplication operator). We establish the number 0 as the point of origin of our counting and then count two 4- units or four 2-units rightwards on the number line relative to 0. The occupant of the number line that is at the position that marks the end of the counting is the result of the multiplication . We can use subtraction mapping to map division onto the number line. Division simply wants to know the number of times one number (the denominator) is contained in another number (the numerator). Let us suppose we want to map 12/3 (the forward slash "/" is a division operator). We |
| establish the numerator as the point of origin of our counting and then subtract leftwards, the number of units equal to the denominator until the remainder is zero or less than the denominator. The number of
the denominator subtracted is the result of the division. If the remainder is zero, the division is perfect. An imperfect division has a remainder greater than zero but less than the denominator.
Essentially, multiplication is a type of addition and division is a type of subtraction.
There are several rules governing addition, subtraction, multiplication and division. Some of the important rules are as follows: (1) All participants in the operations are members of the number line (2)The number 0 is neutral with respect to addition . In other words, adding 0 to a number neither increases nor decreases the value of the number. (3)The number 1 is neutral with respect to multiplication . In other words, multiplying a number by 1 neither increases nor decreases the value of the number. (4) The division of a number by 0 is not allowed. (5) The operations are slightly adjusted when the operands are negative numbers All Computational analysis are essentially based on these Forces Of The Number Line. Peter O. Sagay |
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| Let us use our environment respectfully so that future generations would not label us"prodigal ancestors" |
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