Associative Law for Addition

Associative Law or Associateve Property for addition in mathematics is either of the laws relating numbers to the operation of addition. It is stated symbolically as: (A + B) + C = A + (B + C) where A, B and C are numbers.

In this article, we will explore associative law for addition, along with the associative law for addition formula and associative law for addition examples. We will also solve some examples related to associative law for addition. Let’s start our learning on the topic “Associative law for Addition.”

Associative Law is a fundamental principle in mathematics that is related to the way operands are grouped in expressions involving addition or multiplication. The law states that the way in which the operands are grouped does not change the result of the expression. This is applicable to both addition and multiplication, but not to subtraction and division.

• Associative Law of Addition
• Associative Law of Multiplication

Read More about Associative Law.

In this article, we will be learning about the “Associative Law of Addition.”

The associative law is referred to as the law where the grouping order of the operands does not affect the result of the expression if there are three or more operands and an addition operator.

In other words, the associative law for addition is the law in which the association of multiple operands does not reflect in the result of the expression.

Associative Law for Addition Formula

The formula for the associative law for addition for three numbers p, q, r is given by:

(p + q) + r = p + (q + r)

This means that adding a and b together first, and then adding c yields the same result as adding b and c together first, and then adding a.

Some examples of associative law for addition are listed below.

• (9 + 2) + 3 = 9 + (2 + 3)
• (4 + 1) + 10 = 4 + (1 + 10)
• (−7 + 4) + 3 = −7 + (4 + 3)
• (1.5 + 2.5) + 6.0 = 1.5 + (2.5 + 6.0)
• (100 + 200) + 300 = 100 + (200 + 300)

Read More,

• Closure Property
• Commutative Property
• Distributive Property

Example 1: Prove the associative law; given the three numbers x, y, z as 1, 15 and 2 respectively.

Solution:

Associative law for addition: (x + y) + z = x + (y + z)

LHS = (x + y) + z

(x + y) + z = (1 + 15) + 2 = 16 + 2 = 18

RHS = x + (y + z)

⇒ x + (y + z) = 1 + (15 + 2) = 1 + 17 = 18

⇒ (x + y) + z = x + (y + z)

Thus, LHS = RHS

Example 2: Find the value of 2 + (8 + 4) given that (2 + 8) + 4 = 14.

Solution:

By associative law for addition i.e., a + (b + c) = (a + b) + c.

2 + (8 + 4) = (2 + 8) + 4

Since, (2 + 8) + 4 = 14

2 + (8 + 4) = 14

Example 3: Determine the value of (10 + 7) + 5 given that 10 + (7 + 5) = 22.

Solution:

By associative law for addition i.e., a + (b + c) = (a + b) + c.

(10 + 7) + 5 = 10 + (7 + 5)

Since, 10 + (7 + 5) = 22

(10 + 7) + 5 = 22

Q1: Prove the associative law; given the three numbers p, q, r as 10, 5 and 13 respectively.

Q2: Find the value of 29 + (98 + 124) given that (29 + 98) + 124 = 251.

Q3: Determine the value of (32 + 12) + 15 given that 32 + (12 + 15) = 59.

Define Associative Property of Addition.

The associative law of addition states that if there are three or more numbers as operand and addition as operator then, grouping any numbers does not affect the result of the expression.

Write on example for associative Property of addition.

Example of Associative Law for Addition: (3 + 2) + 9 = 3 + (2 + 9)

What is the Formula for Associativity?

The formula for associativity of addition for three numbers a, b, c is given by:

(a + b) + c = a + (b + c)

Is Addition Always Associative?

Yes, addition is always associative.