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ASSOCIATIVE PROPERTY

Associative Property

Definition Of Associative Property

Associative Property of Addition The problem (3 + 6) + 8 = 3 + (6 + 8) demonstrates the associative property of addition.
Observe that the addends are the same on either side of the equal sign: 3 plus 6 plus 8

The associative property of addition says that when we add more than two numbers the grouping of the addends does not change the sum.
In the example above, we can easily observe that:
(3 + 6) + 8 = 3 + (6 + 8)
9 + 8 = 3 + 14
17 = 17

Notice that the SUM is the same no matter what way you group the addends. In general, the associative property of addition can be written as:
(a + b) + c = a + (b + c)

More about Associative Property

Associative property holds good for both addition and multiplication, but not for subtraction and division.

Associative Property of Multiplication
The problem (2 x 4) x 3 = 2 x(4 x 3) demonstrates the associative property of multiplication. Observe that the factors are the same on either side of the equal sign: 
2 times 4 times 3

Video Examples: Associative Property

The associative property of multiplication says that when we multiply more than two numbers the grouping of the factors does not change the product.
In the example above, we can easily observe that:
(2 x 4) x 3 = 2 x (4 x 3)
8 x 3 = 2 x 12
24 = 24
Notice that the PRODUCT is the same no matter what way you group the factors. In general, the associative property of multiplication can be written as: (a x b) x c = a x (b x c)

Quick Summary

  • Changing the grouping of addends does not change the sum.
  • Changing the grouping of factors does not change the product.
  • Applies to addition and multiplication, not subtraction or division.
\[ (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c) \]

⚠️ Common Mistakes

  • Applying the associative property to subtraction or division.
  • Incorrectly changing the order of the numbers instead of just the grouping.

🌍 Real-World Uses

  • Calculating total travel distance: If you drive 100 miles, then 150 miles, then 50 miles, the total distance is the same whether you calculate (100+150)+50 or 100+(150+50).
  • Stacking boxes: When stacking boxes of different weights, the order in which you group them to calculate the total weight doesn't change the total weight.
  • Inventory management: Counting the total number of items in a warehouse can be done in different groupings (aisles, shelves) without changing the final count.

📋 Standards Alignment

  • CCSS.MATH.CONTENT.3.OA.B.5

🔗 Related Links

🍎 Teacher Insights

Use real-world examples to illustrate the concept. For instance, grouping items in different ways but having the same total.

🎓 Prerequisites

  • Addition
  • Multiplication
  • Understanding of parentheses

Check Your Knowledge

Q1: Which equation demonstrates the associative property of addition?

Q2: Which equation demonstrates the associative property of multiplication?

Frequently Asked Questions

Q: Does the associative property work for subtraction?
A: No, the associative property does not hold for subtraction.

Q: Does the associative property work for division?
A: No, the associative property does not hold for division.

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