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5 Aug 2007

 

The Magic 1
 
By Frank Ho
 
Teacher at Ho Math and Chess Learning Centre
 
The numeral 1 in math is a magnificent number. It simplifies computational procedure when used properly and yet it becomes redundant in some cases. So while 1 is very useful it also can cause problems if not handled carefully.
 
How useful is 1? Take a look at the following examples.
 
·       1 can be used like a variable. For example in work problems, we can assume the work amount is 1 and it actually acts like a variable.
·       1 is used to turn a fraction upside down. For example one half when written in fraction, the 1 turns 2 upside down so it becomes ½. In this case 1 has the meaning of a reciprocal command. By knowing this, we then can do 1 over a fraction very quickly, for example when 1 is over 1 and one-third then we know the answer is 3.
·       1 can also be used to convert a radian to degree and vice versa.
·       1 can be used to convert any numbers to %.
·       When working on fractions, it is easier to change a whole number to a fraction by dividing 1, such as 2x = 2/3
·       We use 1 concept in fraction as “whole” or “entirety”
 
While the above list is not meant to be exhaustive, it does indicate the usefulness of 1. How useless is 1? Take a look at the following.
 
·       1x + 2, the coefficient 1 in front of x is useless.
·       How about 2x to the power of 2? Often, a wrong answer is written as 2 times power 2 of x and the correct answer of number 2 to the power of 2 is forgotten. It all is caused by the problem that 2 to the power 1 was not written originally to give us a reminder.
·       The common factor of 1 is between any numbers, so we do not consider 1 as a factor of relative prime between 2 numbers.
·       For an exponential number a to the power x, the base a should not be 1.
·       1 is not a prime number nor a composite number.
 
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Frank Ho

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