Maths - Operations on Numbers

Face Value: The face value of a digit in a numeral is its own value, at  whatever place it may be. eg. in 6872 the face value of 7 is 7.

Place Value: The Place value of a digit in a numeral is its value as per position, at  whatever place it may be. eg. in 6872 the Place value of 7 is 70.

Natural Numbers:Counting no. are called natural numbers. eg. 1, 2, 3, 4, .......

Whole Numbers: All counting no. including zero are called Whole numbers. eg. 0, 1, 2, 3, 4, .......

Integers: All counting numbers, zero and negative numbers are called integers. eg. ..., -3, -2, -1, 0, 1, 2, 3, .....

Even Numbers: All numbers divisible by 2 are called even no. eg. 2, 4, 6, .....

Odd Numbers: All numbers not divisible by 2 are called odd no. eg. 1, 3, 5, .....

Prime Number: A no which is divisible by 1 or itself is called Prime number. eg. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53....

Co-Prime: Two natural no are said to be co-prime if their HCF is 1. eg. (2, 3), (7, 9), (23,24), etc

Divisibility:

Divisibility by 2: A no is divisibile by 2 if its unit digit is 0, 2, 4, 6, 8. eg. 58888

Divisibility by 3: A no is divisible by 3 if the sum of all its numeral is divisible by 3. eg. 111111 total is 6 which is multiple of 3.

Divisibility by 4: A no is divisible by 4 if its last two numerals are divisible by 4. eg. 111116, here 16 is divisible by4.

Divisibility by 5: A no is divisible by 5 if its unit digit is 0 or 5. eg. 22225 or 11110.

Divisibility by 6: A no is divisible by 6 if it is divisible by 2 and 3.

Divisibility by 8: A no is divisible by 8 if its last three no are divisible by 8. 123123352 .

Divisiblity by 9: A no is divisible by 9 if the sum of its numerals is divisible by 9. eg 111111111 here total of numerals is 9 so it is divisible by 9.

Divisibility by 10: A no is divisible by 10 if its unit digit is zero. eg 1230.

Divisibility by 11: A no is divisible by 11 if the difference between the sum of its digits at odd places and the sum of digits at even places is either 0 or a no divisible by 11. eg. 29435417. now (7+4+3+9)-(1+5+4+2)=11 which is divisible by 11.

                                                  EXERCISE

1.  The diffrence between the place value and the face value of 6 in the numeral 856973 is : 

     a. 973 b. 6973 c. 5994 d. None 

2.   The unit digit in (784 x 618 x 917 x 463 ) is: 

      a. 2 b. 3 c. 4 d. 5,   

3.    If the no 481*673 is fully divisible by 9, than smallest whole no in place of * is: 

.      a. 2 b. 5 c. 6 d. 7 e. None 

4.    If the no 97215*6 is fully divisible by 11, than smallest whole no in place of * is: 

       a. 3 b. 2 c. 1 d. 5. e. None 

5      Which one of the following no is completely divisible by 45:  

        a. 181560 b. 331145 c. 202860 d. 1033550 e. None. 

6.     The smallest prime no is:  

       a. 0 b. 1 c. 2 d. 3 e. None 

7.     Which one of the following cannot be square of a natural no.: 

      a. 32761 b. 81225 c. 42437 d. 20164 e. None 

 8.     Which one of the following is divisible by 11 : 

      a. 235641 b. 245642 c. 315624 d. 415624 e. None

ANSWER: 1  C, 2 A, 3 D, 4 A, 5 C, 6 C, 7 C, 8 D