# ODD AND EVEN NUMBERS

● A number is called an odd number if it cannot be grouped equally in twos. 1, 3, 5, 7, …, 73, 75, …, 2009,… are
odd numbers.

● A number is called an even number if it can be grouped equally in twos. 2, 4, 6, 8, ..., 68, 70, . . , 4592,... are even numbers.

● All odd numbers end with any one of the digits 1, 3, 5, 7 or 9.

● All even numbers end with any one of the digits 0, 2, 4, 6 or 8.

●In whole numbers, odd and even numbers come alternatively.

● 1 is odd, its successor 2 is even and so its predecessor 0 is also even.

●The first natural number 1 is odd and the first whole number 0 is even.

1 + 3 = 4

5 + 11 = 16

21 + 47 = 88

From this observation, we conclude that “the sum of any two odd numbers is always an even number".

4 + 5 = 9

7 + 12 = 19

35 + 56 = 93

From this observation, we conclude that “the sum of any odd number and any even number is always an odd number".

Observe the following products :

5 x 3 = 15

7 x 9 = 63

11 x 13 = 143

From this observation, we conclude that “the product of any two odd numbers is always an odd number”

Observe the following products :

2 x 4 = 8

9 x 6 = 36

12 x 8 = 96

15 x 12 = 180

From this observation, we conclude that “the product of any number (odd or even) and an even number is always an even number”

Observe the following products :

1 x 3 x 5 = 15

7 x 9 x 11 = 693

13 x 17 x 21 = 4641

From this observation, we conclude that “the product of any three odd numbers is always an odd number.”

## Solving Problems on Odd NUmbers and Even Numbers

Problem 1 :

Find the sum of the smallest and largest two-digit even numbers?

Solution :

Smallest two-digit even number = 10

Largest two-digit even number = 98

Sum of the smallest and largest two-digit even numbers :

= 10 + 98

= 108

Problem 2 :

Find the sum of the smallest and largest two-digit odd numbers?

Solution :

Smallest two-digit odd number = 11

Largest two-digit even number = 99

Sum of the smallest and largest two-digit odd numbers :

= 11 + 99

= 110

Problem 3 :

Find the sum of the smallest two-digit even number and the largest three-digit odd number?

Solution :

Smallest two-digit even number = 10

Largest three-digit odd number = 999

Sum of the smallest two-digit even number and the largest three-digit odd number :

= 10 + 999

= 1009

Problem 4 :

What is the difference between the largest three-digit even number and the smallest three-digit odd number?

Solution :

Largest three-digit even number = 998

Smallest three-digit odd number = 101

Difference between the largest three-digit even number and the smallest three-digit odd number :

= 998 - 101

= 897

Problem 5 :

What is the difference between the largest four-digit odd number and the smallest three-digit even number?

Solution :

Largest four-digit odd number = 9999

Smallest three-digit even number = 100

Difference between the largest three-digit even number and the smallest three-digit odd number :

= 9999 - 100

= 9899

Problem 6 :

Write all the two-digit odd numbers which are multiples of 7.

Solution :

21, 35, 49, 63, 77, 91

Problem 7 :

Write all the two-digit even numbers which are multiples of 7.

Solution :

14, 28, 42, 56, 70, 84, 98

Problem 8 :

Write all the two-digit odd numbers which are multiples of 5.

Solution :

10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95

Problem 9 :

Find the sum of all two-digit even numbers which are multiples of 12.

Solution :

Sum of all two-digit even numbers which are multiples of 12 :

= 12 + 24 + 36 + 48 + 60 + 72 + 84 + 96

= 432

Problem 10 :

Find the sum of all three-digit even numbers which are multiples of 100.

Solution :

Sum of all three-digit even numbers which are multiples of 100 :

= 100 + 200 + 300 + 400 + 500 + 600 + 700 + 800 + 900

= 4500

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