# Number Sense: Basic Conceptual Number Properties

Whether it is advanced math like algebra, calculus or it is basic/standard math, number sense and the basic number properties is an important concept for all types. The number forms the basis of the number system, and it forms the base of mathematics. That’s the understanding of the basic properties of numbers, i.e., commutative property, associative property, distributive property, identity property and inverse property.

Here we will be learning short and precise explanations of the same with a few tips and to the point words that will make the concept simple and easy. These hints will also help a child clear any doubts regarding the topic. Let’s get started.

Given below are the best possible hints to memorize the properties applicable to all sets of numbers..

• Commutative property-In general terms: swapping of numbers. Commutativity means swapping numbers or changing the position with no effect on results. In simple words, the term reflects the interchanging nature of the numbers under the same operation as commuting means traveling from the initial location to the other one or physical shift of location. Generally, it can be explained like, if X and Y are to be added, the property says

Similarly, if X and Y are to be multiplied, then the property describes the application as

• Associative Property- In general terms: pairing of the terms, i.e.,

The term highlights the concept of associations. Any number associated with any of the other terms of

numbers give the same result in different combinations of a single operation. Mostly under associative property, the associations vary and not the sequence.

• Distributive Property- In general terms: sharing the common number mutually across the

The term highlights the identical distribution of the numbers outside the brackets when it is multiplied

with all the quantities inside the same bracket.

• Identity Property – In general words, the result remains unchanged, i.e., the input retains its identity as for addition 0 serves as an identity and is called the additive identity while in the case of multiplication 1 is the multiplicative identity as any number multiplied to 1 remains the same. The same can be represented as X+0= 0+X=X……. for addition and X*1= 1*X= X……for multiplication.
• Inverse Property – The property can also be called an inverse of identity property. Here, in general terms for additive inverse, we investigate which number is to be added to a certain number so that the result is 0 and in the case of multiplicative inverse we find out how we can obtain the multiplicative identity (which is 1) from a certain number.

Expression for addition can be X+(-X) = 0.

The precise and accurate information about the topic enhances a child’s understanding of numbers in relation to sets like whole numbers, real numbers, integers, real and natural numbers, etc.

Note*: It should be remembered that all the above-mentioned properties are applicable only for the operations of addition and multiplication but not to the basic concepts of division, exponents and subtraction as these do not hold good under the same. The above-mentioned hints may result in easy understanding and clarity of the topic. The parents may also find it useful to understand how to explain the basic concept to the kids.

Cuemath efficiently creates content and provides live classes for a better understanding of the topic with relatable and easy access to practical knowledge. The experts and teachers are experienced and well trained to clarify the topic as and when required.

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