Ho Math Chess Research and Articles > The Magic 1
 Vancouver math tutor, Richmond math tutor, Burnaby math tutor 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.   More details on other math related articles, please visit www.mathandchess.com. Frank Ho

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