Quicker Maths » Vedic Mathematics

Why is 1 not a Prime Number?

admin — Thu, 14 Jan 2010 13:59:51 +0000

Is 1 a Prime Number?

Friends, in one of the post where I have described ‘Prime’ and ‘Composite’ Numbers, one of the curious visitor have asked me a very logical question. I will quote that question for your reference –
Text from Previous post-

“Prime and Composite : Any integer which is divisible by 1 and itself only is called a prime number.
unquote

quote
N.B.: 1 is not a prime number.”

Question

Could you explaine what is the creteria thar excludes 1 from the list of prime numbers?
a) 1 is integer
b) 1 is divisible by 1 and itself (1)
Since anybody in the past has declared that 1 is not prime number, why we should follow this without thinking and contravene the general rule for prime numbers?
Is 1 as a figure is something which has come from the thin air. It is and always will be an integer. The criteria for 2 are the same – divisible by 1 and itself. And for all prime numbers.
Most probably the 1 is “guilty” because with 1 starts the series on numbers (natural, odd or prime). Suppose 2 was the beginning of the series. Should we ignore 2, because series starts with 2?

My Explanation-

1 can be rejected being a prime number because of the given reasons-

The "real" definition of a prime number is "a natural number that has exactly two distinct natural number divisors." This definition can be considered little confusing for general masses. This in essence means " Any integer which is divisible by 1 and itself only is called a prime number.", which is easier to digest. The only problem is that if one uses that phrasing, the number 1 is a little grey zone case. "Well, it is divisible by 1, and it is divisible by itself," you could think. "Isn't it also a prime number then?"

No, not by the official definition, because it only has a single natural number divisor: 1. This is why the "exception" had to be made, that 1 is not a prime number.

In short: the definition as we know it is a simplification that doesn't work completely - except if we specify that 1 is not included.

Is it really important whether 1 is or not a prime number?

It is indeed very crucial to make the distinction. If we consider 1 not to be a prime number, then any composite number (such as 20) can be written as a product of primes in only one way (here, 2*2*5), not counting different orders. However, if 1 were a prime number, there would be infinitely many ways! We could write 20 for example, as 2*2*5, or 1*2*2*5, or 1*1*1*1*1*2*2*5. Having only one way to write a number as a product of primes is very useful when doing math.

Friends if you have similar questions or doubts hunting you, please feel free to write us@ info@fireup.co.in or leave a comment on any post. "We will be Happy to Help You"

Comparison of Fractions

admin — Mon, 04 Jan 2010 11:03:43 +0000

Comparison of fractions: Suppose, some fractions are to be arranged in ascending or descending order of magnitude.

Fractions can be compared in many ways. Find below 4 different ways of doing it. If denominators are same, like 56/98 and 57/98, then just compare the numerators,

So the rule is:

a b

--- > ---, if a > b

n n

Since 56 < 57,

56/98 < 57/98.

They are in the same order as their numerators.

Second, suppose the numerators are the same, as in your problem, 5/9

and 5/6. Then it works the opposite way: The bigger the denominator, the smaller the fraction. So the rule

is:

n n

--- > --- if a < b

a b

Since 9 > 6, 5/9 < 5/6. They are in the reverse order of their

denominators.

Thirdly, in general cases, you simply convert the fractions to the first case, by giving them a common denominator.

You do not really have to worry about finding the least common denominator, though sometimes that will save a lot of work. Let us compare 5/9 and 4/7. Since we do not see any common factors immediately (and in fact there are not any), we can just multiply the denominators to get a common denominator, 63. To convert 5/9 to 63rds, we multiply

by 7; to convert 4/7 to 63rds, we multiply by 9:

5 4

--- ? ---

9 7

5*7 4*9

--- ? ---

9*7 7*9

35 < 36,

5 4

--- < ---

9 7

You may not calculate the value of denominator because it will be same in both cases.

5*7=35 4*9=36; since this is bigger, 4/7 is bigger

\ /

5 4

--- ? ---

9 7

If there is a common multiple in denominators, for instance, which is bigger, 5/9 or 44/81? I see that

81 is a multiple of 9, so I do not have to go to the trouble of

multiplying 5 by 81 and 44 by 9; I just multiply 5 by 9 and compare to

44:

5 44

--- ? --

9 81

5*9 44

--- ? --

9*9 81

45 > 44 so

5 44

--- > --

9 81

Fractions can be compared in many ways. Find below 3 differnet ways of doing it.
If denominators are same, like 56/98 and 57/98, then just compare the numerators,
So the rule is:
a b --- > --- if a > b n n
Since 56 < 57, 56/98 < 57/98. They are in the same order as their numerators.
Second, suppose the numerators are the same, as in your problem, 5/9 and 5/6. Then it works the opposite way: The bigger the denominator, the smaller the fraction. So the rule is: n n --- > --- if a < b a b
Since 9 > 6, 5/9 < 5/6. They are in the reverse order of their denominators.

Thirdly, in general cases, you simply convert the fractions to the first case, by giving them a common denominator. You do not really have to worry about finding the least common denominator, though sometimes that will save a lot of work. Let us compare 5/9 and 4/7. Since we do not see any common factors immediately (and in fact there are not any), we can just multiply the denominators to get a common denominator, 63. To convert 5/9 to 63rds, we multiply by 7; to convert 4/7 to 63rds, we multiply by 9:
5 4   --- ? ---   9 7
5*7 4*9   --- ? ---   9*7 7*9
35 < 36, so
5 4   --- < ---   9 7
You may not calculate the value of denominator because it will be same in both cases.

5*7=35 4*9=36; since this is bigger, 4/7 is bigger   \ /   5 4   --- ? ---   9 7
If there is a common multiple in denominators, for instance, which is bigger, 5/9 or 44/81? I see that 81 is a multiple of 9, so I do not have to go to the trouble of multiplying 5 by 81 and 44 by 9; I just multiply 5 by 9 and compare to 44:   5 44   --- ? --   9 81
5*9 44   --- ? --   9*9 81
45 > 44 so
5 44   --- > --   9 81
Finally, convert each one of the given fractions in the decimal form. Now, arrange them in ascending order

as per requirements.

Recurring Decimal: - If, in a decimal fraction, a figure or a set of figures is repeated continuously, then such a number is called a recurring decimal. In a recurring decimal, if a single figure is repeated, then it is expressed by putting a dot on it. If a set of figures is repeated, it is expressed by putting a bar on the set.

Pure Recurring Decimal: A decimal fraction, in which all the figures after the decimal point are repeated, is called a pure recurring decimal e.g. 2/3 = 0.666…=0.6.

Converting a Pure Recurring Decimal into Vulgar Fraction:-Rule: - Write the repeated figures only once in the numerator and take as many nines in the denominator as is the number of repeating figures.

Decimal: - a decimal fraction in which some figures do not repeat and some of them are repeated is called a mixed recurring decimal, e.g. 0.173333…= 0.173.

Decimal Fraction Rules

admin — Mon, 04 Jan 2010 05:45:23 +0000

Multiplication of a decimal Fraction by a Power of 10: Rule: Shift the decimal point to the right by as many places of decimal as is the power of 10.

Multiplication of Decimal fractions:- Rule :- Multiply the given numbers considering them without the decimal point. Now, in the product, the decimal point is marked off to obtain as many places of decimal as is the sum of the number of decimal in the given numbers.

Dividing a Decimal fraction By a Counting Number

Rule: - Divide the given number without considering the decimal point by the given counting number. Now, in the quotient, put the decimal point to give as many places of decimal as are there in the dividend.

Dividing a Decimal fraction By a Decimal Fraction

Rule: - Multiply both the dividend and the divisor by a suitable power of 10 to make divisor a whole number. Now, proceed as above.

H. C. F. & L. C. M. of Decimal fractions:- Rule :- In given numbers, make the same number of decimal places by annexing zeros in some numbers, if necessary. Considering these numbers as without decimal point, find H. C. F. or, L.C.M., as the case may be. Now, in the result, make off as many decimal places as are there in each of the given numbers.

There are 9 coins.

admin — Mon, 26 Oct 2009 12:49:46 +0000

There are 9 coins. 8 are of 1 gm and 1 is of 2 grams. How will you find out the heavier coin in minimum number of weighing and how many weighing it will need?

Solve a Dilemma

admin — Thu, 22 Oct 2009 13:07:06 +0000

What is wrong with this proof?

2 = 1

a = b

a² = ab

a² – b² = ab – b²

(a + b) (a – b) = b (a – b)

a + b = b

2b = b

2 = 1

A Puzzle Of Cultural Groups

admin — Thu, 22 Oct 2009 12:59:49 +0000

My club has five cultural groups. They are literary, dramatic, musical, dancing and painting groups. The literary group meets every other day, the dramatic every third day, the musical every fourth day, the dancing every fifth day and the painting every sixth day. The five groups met, for the first time on the New Year’s day of 1975 and starting from that day they met regularly according to schedule.

Now, can you tell how many times did all the five meet on one and the same day in the first quarter? Of course the New Year’s day is excluded.

One more question-were there any days when none of the groups met in the first quarter and if so how many were there?

Entrance Test

admin — Tue, 20 Oct 2009 05:32:39 +0000

As an entrance test for a particular university, you are given a corked bottle with a very small coin in it. Your task is to remove the coin without taking the cork out of the bottle or breaking the glass, or boring a hole in the cork or glass.

How do you pass the test and get the coin out?

Vedic Multiplication by 9, 99, 999 and so on

admin — Mon, 19 Oct 2009 07:22:35 +0000

When any number has to be multiplied by a series of 9s, like 9, 99, 999, 9999 and so on than we can apply this very simple vedic maths technique to increase your speed of calculation.

Multiplication with 9/ 99 / 999 and so on.

we know, 789 × 999 = 788,211

You will get the answers in two parts,

The left hand side of the answer: subtract 1 from 789, which is 788
The right hand side of the answer subtract 789 from 1000 = 1000-789= 211

Thus, 999 x 789 = 789-1 | 1000-789 = 788, 211 (answer)

{for the right hand side of the answer, 789 should be subtracted from (999+1)}

or, 99999 x 78 = 78-1 | 100000 - 78

= 7799922

{78 should be subtracted from (99999+1)}

Another example:

1203579 × 9999999 = 1203579-1 | 10000000- 1203579

=120357887964 21

Number in red is 1 less than 1203579. Number in blue is (10000000-1203579). Hence the answer.

This method has to be altered a little bit when number of 9s are lessers than the number of digit in the divisor.

1432 x 9 = 1432 (10 – 1) = 14320 – 1432 = 12888

So for multiplication with 9, put a zero after that number and subtract the number itself from that.

Likewise for 99 put two zeroes after that number .

3256 x 99 = 325600 – 3256 = 322344

Eye Spy

admin — Thu, 15 Oct 2009 13:15:22 +0000

Which is Wrong?

Click on image to enlarge

Astral Maths

admin — Tue, 13 Oct 2009 13:41:42 +0000

Look at the shape below and answer the following questions on it.

1. How many triangles are there in the diagram?
2. How many rectangles are there in the diagram?
3. How many hexagons can you find?
4. Deduct the sum of the numbers in the rectangles from the sum of the numbers in the triangles.