Examples Of The Associative Property

Associative Property of Multiplication

The associative property of multiplication states that the manner in which the numbers are grouped in a multiplication problem does not affect or change the product of those numbers. In other words, the production of 3 or more numbers remains the same irrespective of the way they are grouped. Let us written report more about the associative property of multiplication in this article.

1.	What is the Associative Property of Multiplication?
2.	Associative Property of Multiplication Formula
3.	Associative Property of Multiplication and Addition
4.	FAQs on the Associative Property of Multiplication

What is the Associative Property of Multiplication?

According to the associative property of multiplication, if iii or more than numbers are multiplied, nosotros get the aforementioned result irrespective of how the three numbers are grouped. Here, group means the manner in which the brackets are placed in the given multiplication expression. Discover the following example to sympathise the concept of the associative property of multiplication. The expression on the left-mitt side shows that half dozen and 5 are grouped together, whereas, the expression on the right-paw side groups v and vii together. Nevertheless, when nosotros finally multiply all the numbers, the resultant product is the aforementioned.

Associative Property of Multiplication

Associative Property of Multiplication Formula

The formula for the associative property of multiplication is (a × b) × c = a × (b × c). This formula tells usa that no matter how the brackets are placed in a multiplication expression, the production of the numbers remains the same. The grouping of numbers with the help of brackets helps to create smaller components which makes the calculation of multiplication easier. Observe the following formula for the associative belongings of multiplication.

Associative Property of Multiplication Formula

Allow u.s.a. sympathize the formula using numbers. For case, let united states of america multiply 2 × 3 × iv and meet how the formula of associative holding of multiplication is proved with the assistance of the post-obit steps:

Step ane: Let u.s.a. group 2 and 3 together making it (two × 3) × 4. If we find the production of this expression, we get 6 × 4, which is 24.
Step two: At present, let us group iii and 4 together making it 2 × (iii × 4). If we multiply this expression, it comes to 2 × 12, which once more gives the production as 24.
Step 3: This means that no matter how nosotros grouping the numbers in a multiplication expression, the product remains the same.

Associative Property of Multiplication and Addition

The associative property states that multiplication and improver of numbers can be done irrespective of how they are grouped. For example, to add 7, half dozen, and 3, if we group them as 7 + (vi + three), the sum that nosotros get is 16. Now, let the states grouping it as (seven + vi) + 3 and nosotros encounter that the sum is sixteen once more. This is the associative belongings of addition which applies to multiplication as well. For example, let united states of america multiply vii, 6, and 3 and group the numbers as 7 × (6 × 3). The product of these numbers is 126. At present, if nosotros grouping the numbers every bit (7 × 6) × 3, we get the aforementioned product, that is, 126. Discover the following effigy which shows the associative holding of multiplication and addition.

Associative Property of Multiplication and Addition

Tips on the Associative Belongings of Multiplication:

Here are a few important points related to the associative property of multiplication:

The associative belongings always applies to three or more numbers.
The associative property exists in addition and multiplication and cannot be applied to subtraction and partition.

☛ Related Articles

Commutative Property of Multiplication
Multiplicative Identity Holding
Distributive Property of Multiplication
Zero Holding of Multiplication
Associative Belongings of Addition
Distributive Property
Condiment Identity Property

Examples on Associative Belongings of Multiplication

Example 1: Which of the two expressions are equivalent to eight × 3 × iv?

a.) (8 × 3) × 4

b.) 24 × four

c.) 11 × 4

Solution:

The product of the given expression is 8 × 3 × iv = 96. Now, permit us check the product of the following expressions.

a.) The product of (viii × 3) × 4 is 96.

b.) The production of 24 × 4 is 96.

c.) The product of 11 × 4 is 44.

Therefore, the kickoff two expressions are equivalent to 8 × 3 × iv. For the beginning expression, we used the associative holding of multiplication to group together 8 and 3, and the second option is the simplified form of the first choice. So, both are correct.
Example 2: Choose the right number to fill the blank in the expression: five × (4 × 3) = (5 ×___) × 3
a.) 3
b.) 4
c.) 5

Solution:

The associative property of multiplication states that a × (b × c) = (a × b) × c. So, afterwards substituting the given equation in this formula, we get iv as the answer. The correct choice is (b) iv which ways that the product of both the sides will be equal to lx if nosotros place four in the blank.
Example 3: Fill the missing number in the bare.
10 × (8 × vii) = (10 × 8) × ___
Solution:

Co-ordinate to the associative belongings of multiplication: a × (b × c) = (a × b) × c. Substituting the values in the formula: 10 × (8 × seven) = (10 × 8) × seven

Hence, the missing number volition be 7 because the product of both the expressions is equal to 560.

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Practice Questions on Associative Belongings of Multiplication

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FAQs on the Associative Belongings of Multiplication

What is the Associative Holding of Multiplication in Math?

The associative property of multiplication states that the product of three or more numbers remains the same regardless of how the numbers are grouped. For instance, 3 × (5 × 6) = (3 × 5) × 6. Here, no thing how the numbers are grouped, the product of both the expressions remains 90.

What is the Associative Property of Multiplication Formula?

The formula for the associative property of multiplication is written as a × (b × c) = (a × b) × c. This means that the grouping of any 3 or more than numbers does non affect their product.

What is the Associative Property of Multiplication and Addition?

The associative property applies to addition and multiplication which means that the addition and multiplication of numbers can exist done irrespective of the way they are grouped. The associative property of addition is written as: a + (b + c) = (a + b) + c, which means that the sum of whatever 3 or more than numbers does not change fifty-fifty if the grouping of the numbers is changed. Similarly, the associative property of multiplication is written as: a × (b × c) = (a × b) × c, which ways that the product of any three or more numbers remains the same even after they accept been grouped in a different way.

Give an Example of the Associative Property of Multiplication.

The associative property of multiplication can be understood with the help of an example of any three numbers. If we multiply (4 × 2) × x, nosotros go the product equally 8 × 10 = 80. Now, if we group these numbers every bit 4 × (two × 10), we still become the product every bit 4 × 20 = lxxx. This proves the associative property of multiplication.

What is the Associative Holding of Multiplication of Whole Numbers?

The associative property of multiplication of whole numbers says that the product of three or more whole numbers does non alter even if the numbers are grouped in a dissimilar fashion. For example, 11 × (5 × 2) = (xi × 5) × two. Hither, the production of both the expressions is 110.

What is the Departure Between the Commutative and the Associative Property of Multiplication?

The commutative belongings of multiplication states that changing the gild of numbers does non change the production of the given numbers. For example, six × 8 = 8 × 6 = 48. The associative holding of multiplication states that changing the grouping of numbers does not alter the product of the given numbers. For example, 7 ×(2 × 3) = (seven × 2) × 3 = 42.