The associative property of addition is the property of numbers which states that the way in which three or more numbers are grouped does not change the sum of these numbers. This means that the sum of three or more numbers remains the same irrespective of the way in which they are grouped. Let us learn more about the associative property of addition along with some examples related to the associative law of addition in this article.
| 1. | What is the Associative Property of Addition? |
| 2. | Associative Property of Addition Formula |
| 3. | Associative Property of Addition and Multiplication |
| 4. | FAQs on Associative Property of Addition |
The associative property of addition is a rule which states that while adding three or more numbers, we can group them in any combination, and the sum that we get remains the same irrespective of the manner in which they are grouped. In this case, grouping refers to the placement of brackets. For example, the figure given below shows that the sum of the numbers does not change regardless of how the addends are grouped.
The formula for the associative property of addition shows that grouping of numbers in a different way does not affect the sum. The brackets that group the numbers help to make the process of addition simpler. Observe the following formula for the associative property of addition.
Let us take an example to understand and prove the formula. Let us group 13 + 7 + 3 in three ways.
The associative property is applicable to addition and multiplication, but it does not exist in subtraction and division. We know that the associative property of addition says that the grouping of numbers does not change the sum of a given set of numbers. This means, (7 + 4) + 2 = 7 + (4 + 2) = 13. Similarly, the associative property of multiplication says that the grouping of numbers does not change the product of the given set of numbers. This formula is expressed as (a × b) × c = a × (b × c). For example, (2 × 3) × 4 = 2 × (3 × 4) = 24.
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Example 1: Which equation shows an example of the associative property of addition? a.) (25 + 2) + 8 = 25 + (2 + 8) b.) 7 × (20 - 3) = (7 × 20) - (7 × 3) Solution: a.) Let us take this equation, (25 + 2) + 8 = 25 + (2 + 8) This equation shows an example of the associative property of addition. b.) Let us take this equation, 7 × (20 - 3) = (7 × 20) - (7 × 3) We can see that this equation shows the distributive property of addition.
Example 2: Fill in the missing number and then write the sum: 7 + (10 + 6) = (7 + 10) + ___ = ___ Solution: According to the associative property of addition formula, a + (b + c) = (a + b) + c. If we substitute the values in this formula we get 6 as the missing number, that is, 7 + (10 + 6) = (7 + 10) + 6, and the sum is 23.
Example 3: Choose the correct option for the missing number. 8 + (4 + 2) = (8 + ___) + 2 a) 4 b) 7 c) 6 Solution: According to the associative property of addition: a + (b + c) = (a + b) + c. Substituting the values in the formula: 8 + (4 + 2) = (8 + 4) + 2. Hence, the missing number is 4 because the sum of both the expressions is 14. Therefore, the correct option is (a).
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