Some Interesting Trends in Odd Number Operations

In mathematics and reasoning, odd and even numbers are an important part of understanding the number system. When certain numbers are divided by two or in equal parts, one will always be the remainder or left out. Observing and understanding trends and patterns in the operations involving odd and even numbers are an integral part of quantitative aptitude and dealing with quick maths. This section will look at the odd numbers’ definition and various patterns or trends in operations such as addition, subtraction, multiplication, and division, followed by the odd numbers.  

WHAT ARE ODD NUMBERS?

Odd numbers are integers that cannot be divided into equal parts and leave a remainder of 1 when divided by 2. You can easily tell apart the odd and even numbers by looking at their unit place digits. Therefore, the odd numbers’ definition can simply be stated as the integers that have 1, 3, 5, 7, and 9 in their unit place, whereas even numbers have 0, 2, 4, 6, and 8 in their unit place. They can be either positive or negative and always fall in-between even numbers, the same way even numbers fall in-between odd numbers. 

OPERATIONS INVOLVING ODD NUMBERS

Odd and even numbers also differ in trends shown in operations with these numbers.

• Addition property of odd numbers

1. Odd numbers are only formed when you add another odd number with an even number: 

For example, take 23 as the odd number and four as the even number. Their addition will give another odd number, 27.

This can also be tried with negative integers. The sum of -23 and 4 will also give an odd number, 

-23 + 4 = 19

You can confirm this with an odd number. Take the number 205 for an example. You can derive the number from a set of additions involving an even and an odd number.

201 + 4 = 205

200 + 5 = 205

150 + 55 = 205

You can express this as:

ODD + EVEN = ODD

2. An odd number, when added to another odd number, gives an even number:

For example, if you take 57 and 9 as the odd numbers, their addition will give you an even number, 66.

You can try this with any odd numbers, including negative integers. Take -1 and -95, for example. You will end up with -96, which is again an even number.

You can express this as:

 ODD + ODD = EVEN

Even numbers can be derived from adding odd integers or even integers.

To confirm this, let’s take an even number 10. You can only get this number by adding two even numbers or two odd numbers. For example, 

5 + 5 = 10 and 2 + 8 = 10.

• Subtraction property of odd numbers

1. Subtracting an odd number from an odd number gives an even number.

For example, if you subtract seven from 17, the answer is 10.

17 – 7 = 10

Therefore, ODD – ODD = EVEN

2. Subtracting an even number from an odd number gives an odd number.

For example, if you subtract eight from 17, you will get 9.

17 – 8 = 9.

Therefore, ODD – EVEN = ODD

• Multiplication property of odd numbers:

1. When you multiply an odd number with another odd number, it results in another odd number.

For example, if you multiply 5 and 7, the answer is 35.

This can be simply stated as ODD x ODD = ODD.

2. You will get an even number if you multiply an odd number with an even number.

For example, if you multiply 7 and 10, the answer is 70.

Therefore, ODD x EVEN = EVEN.

• Divisional property of odd numbers:

1.      Dividing an odd number with another one gives an odd number.

For example, if you divide 45 by 9, the answer will be 5.

You can state this rule as ODD / ODD = ODD.

2.      Dividing an even number with an odd number yields an even number.

For example, if you divide 40 by 5, the answer will be 8

You can state this rule as EVEN / ODD = EVEN.

3.      An odd number divided by an even number would always leave a remainder.

For example, if you divide 99 by 4, you will be left with the remainder of 3.

CONCLUSION

The numerical system consists of odd and even numbers arranged alternatively in increasing order. Understanding the definition of odd numbers and the patterns in the operations of these odd and even numbers are given in this section is a great way of learning to do quick maths in your head. Odd numbers are whole numbers that cannot be halved without leaving a remainder. Understanding simple operations such as addition, subtraction, multiplication, division and patterns can help reduce factors or multiples of a number and the probability of these being odd or even in nature.