Monday, October 5, 2009


May we should check out some more important points related to numbers before jumping in to problems

Number line

So what is LCM ?

HCF means ....:

Absolutes and opposites

About Zero and one

Face value and place value

"Just as our face never changes, similarly the face value of the number remains same. wherever the number is " .

But the place value of the number changes depending upon their position. (Eg : For the number, 6780, the place value of 7 is 700, while the face value is 7 but for the no. 67800, the place value becomes 7000).

For any two numbers

If for two numbers x+y=k(=constant), then their PRODUCT is MAXIMUM if x=y(=k/2). The maximum product is then (k^2)/4 .

If for two numbers x*y=k(=constant), then their SUM is MINIMUM if x=y(=root(k)). The minimum sum is then 2*root(k) .

|x| + |y| >= |x+y| (|| stands for absolute value or modulus )

Product of any two numbers = Product of their HCF and LCM .

Hence product of two numbers = LCM of the numbers if they are prime to each other

For any consecutive numbers:

Average of consecutive numbers=(smallest number+largest_number)/2

Number of terms in series = (largest number - samallest number + 1 )

Sum of consecutive numbers= Average X number of terms =(smallest number+largest_number) X (largest number - samallest number + 1 )/2

Reminder Theorem:

Divident=(Divisor*Quotient) + Reminder

Sum of first n Natural Numbers = n(n+1)/2

Sum of squares of first n Natural Numbers=n(n+1)(2n+1)/6

Sum of cubes of first n Natural Numbers = ( n(n+1)/2 )^2