The Associative Property of Addition Explained

The associative property of addition shows that the total of three numbers or more will remain the same even if the numbers are grouped in various ways. In mathematics, addition properties have characteristics of not changing the sum, even if the numbers are interchanging the places. The process adds two or more numbers which can be small or high digits of numbers.  

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The associative properties of addition refer to algebraic equations in order to eliminate complex calculations. Addition properties are very helpful for learners to get deep insights into numbers. This article is going to explain all about the essential properties of addition with definitions and examples.  

Definition of Associative Property of Addition  

The associative property is a sum of two or more numbers that produce the same output even if the numbers are interchanged in their positions. It does not change its value, no matter how the numbers are grouped.  

The formula is A+(B+C) =(A+B) +C 

Examples:  

• 5+ (2+3) = (5+2) +3 

• 8+(5+2) = (8+5) +2 

• 10+ (5+6) = (10+5) +6 

Types of Addition Properties with Examples  

Addition properties are defined for the various conditions and rules. Each operation in mathematics has different properties. The four main properties of addition are commutative property, associative property, distributive property, and additive identity property.  

• Commutative property:  

This property refers to two numbers being added and the sum remains the same even when the integers change their positions.  

Formula: A + B = B + A 

Example: 2+3= 3+2 

• Associative property:  

According to this law, when adding three numbers, the various groups of numbers do not change the end results.  

Formula:  A+(B+C) =(A+B) +C 

Example: 3+(2+4) = (3+2) +4 

• Distributive property: 

It shows the sum of two numbers, multiplied by the third number is equal to the sum when each of the two numbers is multiplied by the third number. It is different from commutative and associative properties.  

Formula: A × (B + C) = (A × B) + (A × C) 

Example: 1*(2+3) = (1*2) +(1*3) 

• Additive Identity Property:  

It means that any real added to itself will produce that same number. Zero is the unique real number that helps to generate the number itself.  

Formula: A + 0 = A or 0 + A = A 

Example: 2+0= 2 or 0+2=2 

More Addition Properties 

• Property of opposites depicts that if A is a real number, then there is the true existence of a unique number.  

Formula: A + (-A) = 0 or (-A) + A = 0  

Example: if A = 2, and two numbers are added together, the output will be 0.  

2+(-2) = 2-2 = 0 

• The sum of Opposite of Numbers refers to two numbers A and B, then their opposites must be -A and -B.  

Formula: - (A + B) = (-A) + (-B) 

Example: if A=2 and B=3,  

So, -(2+3) = (-2) +(-3) 

-(2+3) =-2-3 

-5=-5 

To sum up, associative property in addition depends on two or three numbers that remain unchanged even if it interchanges the positions. It is usually based on two or more numbers. Addition properties are different, yet the associative property of addition is applied to solve the equation. As it is easy to calculate, especially for students. The properties of addition can be added to various equations to reduce complexity. To learn and grow stay connected with us on www.98thpercentile.com  

FAQs (Frequently Asked Questions) 

Q.1. What are the major properties of addition?  

Ans- Commutative property, Associative property, Distributive property, Additive identity property. 

Q.2. What is the usage of properties of addition?  

Ans- It helps to resolve difficult mathematical calculations to get more accurate results.  

Q.3. Can I use associative property in subtraction?  

Ans- No, associative property can be applied in addition and multiplication.  

Q.4. How many integers are required in associative property?  

Ans- A minimum number of 3 is required to apply in the associative property.  

Q.5. What is the formula of associative property?  

Ans- A+(B+C) =(A+B) +C. 

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