Does associative property work on whole numbers and integers with an example

When we multiply three or more whole numbers, the value of the product remains the same when they are grouped in any manner. The associative property of multiplication holds for whole numbers. Thus, if 'a', 'b', and 'c' are three whole numbers, then a × (b × c) = (a × b) × c = (a × c) × b.

Step-by-step explanation:

This property of the whole numbers tells that the order of addition does not change the value of the sum. Let a and b are two whole numbers, then a + b = b + a. Suppose a = 10 and b = 18 ⇒ 10 + 18 = 28 = 18 + 10.

Associative Property

When we add three or more whole numbers, the value of the sum remains the same. The order of addition of numbers is not important. Or, in other words, the numbers can be grouped in any manner. The sum remains the same. This is the associative property of addition.

If a, b, and c are three whole numbers, then a + (b + c) = (a + b) + c = (a + c) + b. For example, 10 + (5 + 12) = (10 + 5) + 12 = (10 + 12) + 5 = 27

Additive Identity

This is the property of zero by which the value of the whole number remains the same when added to any whole number. Zero is the additive identity of whole numbers. If w is a whole number, then w + 0 = w = 0 + w. For example, 0 + 7 = 7 = 7 + 0.

Properties of Subtraction

Closure Property

When one whole number is subtracted from another, the difference is not always a whole number. This means that the whole numbers are not closed under subtraction. If a and b are two whole numbers and a − b = c, then c is not always a whole number. Take a = 7 and b = 5, a − b = 7 − 5 = 2 and b − a = 5 − 7 = −2 (not a whole number).

Commutative Property

Subtraction of two whole numbers is not commutative. This means we cannot subtract two whole numbers in any order and get the same result. Let a and b be two whole numbers, then a − b ≠ b − a. Take a = 7 and b = 5, 7 − 5 = 2 ≠ 5 − 7 = −2.

Associative Property

An associative property does not hold for the subtraction of whole numbers. This means that we cannot group any two whole numbers and subtract them first. Order of subtraction is an important factor. If ‘a’, ‘b’, and ‘c’ are the three whole numbers then, a − (b − c) ≠ (a − b) − c. Consider the case when a = 8, b = 5 and c = 2, 8 − (5 − 2) = 5 ≠ (8 − 5) − 2 = 1.

Subtractive Property of Zero

When we subtract zero from a whole number, the value of the whole number remains the same. Take an example, a = 98, a − 0 = 98 − 0 = 98.

Properties of Multiplication

Closure Property

Multiplication of two whole numbers will result in a whole number. Suppose, a and b are the two whole numbers and a × b = c, then c is also a whole number. Let a = 10, b = 5, 10 × 5 = 50 (whole number). The whole number is closed under multiplication.