The associative property describes how numbers can be added and multiplied regardless of how they are grouped. The numbers given inside the parentheses are referred to as grouping. If we group the numbers in addition operations like 2 + (3 + 8) or (2 + 3 + 8), the result will be the same in both cases.
Similarly, the result will be the same in the multiplication case, 2 x (3 x 8) or (2 x 3 x 8).
In layman’s terms, the associative property states that whether you add or multiply real numbers, it doesn’t matter how they’re grouped; the result will always be the same.
Table of Contents
Associative Property of Addition
The associative property of addition states that the total does not change if the addends are grouped differently. Its mathematical form is given as (x + y) + z = x + (y + z)
- (70+61)+48 = 70+(61+48)
- (10+2)+4 = 10+(2+4)
Associative Property of Multiplication
The associative property of addition states that the total does not change if the multiplicands are grouped differently. Its mathematical form is given as (xy)z = x(yz)
- (2 × 4) × 5 = 2 × (4 × 5)
- 10 × (5 × 7) = (10 × 5) × 7
Important Points
- subtraction and division are not associative.
- Three or more numbers are always involved in the associative property.
- It doesn’t matter where you put the parenthesis if you’re adding or multiplying.
Frequently Asked Questions
1. Is a circle a polygon?
A polygon is not the same as a circle. From end to end, a polygon is a closed-form on a plane made up of a finite number of linked line segments. Because a circle is curved, it cannot be made from line segments and so does not meet the conditions for becoming a polygon. Check the full topic “is circle a polygon?”
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