Solutions to Odd Numbered

Introduction – Solutions to odd numbered:
An odd number is an integer number which is not a divisible by 2. Suppose if odd number is divisible by 2 the result will be fraction. 1 is the 1st odd positive number. Another four bigger odd numbers are 3, 5, 7, and 9. We can identify a decimal number is an odd number or not if the last digit is an odd number. Let us see solutions to odd numbered.

More about Odd Number – Solutions to Odd Numbered:

Any one number which is not divisible by 2 that is known as odd number.
While we divide any one number by 2 if it has remainder 1 that number will be an odd number.
The entire odd numbers last digit will be 1, 3, 5, 7 and 9. So we can find very easily that is odd number or not.
Few examples for odd numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 and 31.
Fundamental operations – Solutions to odd numbered:

Addition Operation:

Operation                    Result                         Example
even + even                  even                            4 + 14 = 18
odd + even                    odd                            3 + 4 = 7
odd + odd                      even                          9 + 9 = 18
Subtraction Operation:

Operation                   Result                         Example
even - even                even                             6 - 2 = 4
odd - even                  odd                             10 - 3 =7
odd - odd                    even                           15 - 5 = 10

Multiplication Operation:

Operation                   Result                         Example
even × even                 even                            4 × 6 = 24
odd × even                   even                           5 × 4 = 20
odd × odd                     odd                            3 × 3 = 9

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Examples – Solutions to Odd Numbered:

Problem 1:

Add: 21 + 25 = 46

Subtract: 55 – 23 = 32

Multiply: 13 * 19 = 247

Divide: `545 / 5` = 109

Problem 2:

The number 31 is odd number. Because the last digit is 1
The number 453 is odd number. Because the last digit is 3
The number 4625 is odd number. Because the last digit is 5
The number 48347 is odd number. Because the last digit is 7

The number 642879 is odd number. Because the last digit is 9

Problem 3:

List all the odd numbers from 30 to 50?

Solution:

The odd number remainder will be 1, while we divide by one.
The numbers from 30 to 50 are 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49 and 50.
From 30 to 50 odd numbers are 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.
Totally ten odd numbers from 30 to 50.

Odd Square Numbers

Introduction to odd square numbers:

Odd square numbers are one of the basis for mathematics. The odd numbers are 1,3,5,7 etc. The formula for representing the odd square numbers are 2M+1, where m value is used to represent the any type of variable function. Simply the odd number can be defined as the number which are not divisible the number two. These numbers are called as the odd number.

Explanation for Odd Square Number

Odd numbers are the alternatives of the even numbers. The number that are not divisible by the number 2, 4, 6 ,8 etc are called as the odd number. For example, the numbers 3, 5, 7, 9, 11 etc are represented as the odd numbers. The diagrammatic representation of odd numbers are shown below,

The odd square numbers are represented by using the formula, (2M+1)2 . The formula can be simplified as 2(m2 + m) +1. By using the this formula the odd square number problems are solved.

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Example Problem for Odd Square Numbers

Pro 1: Find the odd square number for the given value. M = 4.

Sol :  Step 1: The formula for finding the odd square numbers is given below,

Odd square numbers = (2M+1)2 = `4M^2 + 8M + 1` = 4M(M+2) + 1

Step 2: The value of m is given. Therefore substitute the value in the formula.

Step 3: By substituting the formula we get,

= (2(4)+1)2

= 2(42 +4)+1

= 2(20)+1

= 40+1

= 41.

This is the required odd square number.

Pro 2: Find the odd square number for the given value. M = 6.

Sol :  Step 1: The formula for finding the odd square numbers is given below,

Odd square numbers = (2M+1)2 = 4(m2 + 2m) +1.

Step 2: The value of m is given. Therefore substitute the value in the formula.

Step 3: By substituting the formula we get,

= (2(6)+1)2 

= (12+1)2 = 13x13 = 169

This is the required odd square number.

Practice Problem for Odd Square Numbers

Pro 1: Find the odd square number for the given value. M = 8.

Ans : 196

Pro 2: Find the odd square number for the given value. M = 10.

Ans : 221