Associative Property of Multiplication - Formula, Examples, FAQs (2024)

The associative property of multiplication states that the way in which the numbers are grouped in a multiplication problem does not affect or change the product of those numbers. In other words, the product of three or more numbers remains the same irrespective of the way they are grouped. Let us study 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 three or more numbers are multiplied, we get the same result irrespective of how the three numbers are grouped. Here, grouping means the way in which the brackets are placed in the given multiplication expression. Observe the following example to understand the concept of the associative property of multiplication. The expression on the left-hand side shows that 6 and 5 are grouped together, whereas, the expression on the right-hand side groups 5 and 7 together. However, when we finally multiply all the numbers, the resultant product is the same.

Associative Property of Multiplication - Formula, Examples, FAQs (1)

Associative Property of Multiplication Formula

The formula for the associative property of multiplication is (a × b) × c = a × (b × c). This formula tells us that no matter how the brackets are placed in a multiplication expression, the product 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 property of multiplication.

Associative Property of Multiplication - Formula, Examples, FAQs (2)

Let us understand the formula using numbers. For example, let us multiply 2 × 3 × 4 and see how the formula of associative property of multiplication is proved with the help of the following steps:

  • Step 1: Let us group 2 and 3 together making it (2 × 3) × 4. If we find the product of this expression, we get 6 × 4, which is 24.
  • Step 2: Now, let us group 3 and 4 together making it 2 × (3 × 4). If we multiply this expression, it comes to 2 × 12, which again gives the product as 24.
  • Step 3: This means that no matter how we group the numbers in a multiplication expression, the product remains the same.

Associative Property of Multiplication and Addition

The associative property states that multiplication and addition of numbers can be done irrespective of how they are grouped. For example, to add 7, 6, and 3, if we group them as 7 + (6 + 3), the sum that we get is 16. Now, let us group it as (7 + 6) + 3 and we see that the sum is 16 again. This is the associative property of addition which applies to multiplication as well. For example, let us multiply 7, 6, and 3 and group the numbers as 7 × (6 × 3). The product of these numbers is 126. Now, if we group the numbers as (7 × 6) × 3, we get the same product, that is, 126. Observe the following figure which shows the associative property of multiplication and addition.

Associative Property of Multiplication - Formula, Examples, FAQs (3)

Tips on the Associative Property of Multiplication:

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

  • The associative property always applies to 3 or more numbers.
  • The associative property exists in addition and multiplication and cannot be applied to subtraction and division.

☛ Related Articles

  • Commutative Property of Multiplication
  • Multiplicative Identity Property
  • Distributive Property of Multiplication
  • Zero Property of Multiplication
  • Associative Property of Addition
  • Distributive Property
  • Additive Identity Property

Examples on Associative Property of Multiplication

  1. Example 1: Which of the two expressions are equivalent to 8 × 3 × 4?

    a.) (8 × 3) × 4

    b.) 24 × 4

    c.) 11 × 4

    Solution:

    The product of the given expression is 8 × 3 × 4 = 96. Now, let us check the product of the following expressions.

    a.) The product of (8 × 3) × 4 is 96.

    b.) The product of 24 × 4 is 96.

    c.) The product of 11 × 4 is 44.

    Therefore, the first two expressions are equivalent to 8 × 3 × 4. For the first expression, we used the associative property of multiplication to group together 8 and 3, and the second option is the simplified form of the first option. So, both are correct.

  2. Example 2: Choose the correct number to fill the blank in the expression: 5 × (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, after substituting the given equation in this formula, we get 4 as the answer. The correct option is (b) 4 which means that the product of both the sides will be equal to 60 if we place 4 in the blank.

  3. Example 3: Fill the missing number in the blank.
    10 × (8 × 7) = (10 × 8) × ___
    Solution:

    According to the associative property of multiplication: a × (b × c) = (a × b) × c. Substituting the values in the formula: 10 × (8 × 7) = (10 × 8) × 7

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

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Associative Property of Multiplication - Formula, Examples, FAQs (4)

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FAQs on the Associative Property of Multiplication

What is the Associative Property 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 example, 3 × (5 × 6) = (3 × 5) × 6. Here, no matter 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 three or more numbers does not 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 be 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 any three or more numbers does not change even if the grouping of the numbers is changed. Similarly, the associative property of multiplication is written as: a × (b × c) = (a × b) × c, which means that the product of any three or more numbers remains the same even after they have 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) × 10, we get the product as 8 × 10 = 80. Now, if we group these numbers as 4 × (2 × 10), we still get the product as 4 × 20 = 80. This proves the associative property of multiplication.

What is the Associative Property of Multiplication of Whole Numbers?

The associative property of multiplication of whole numbers says that the product of three or more whole numbers does not change even if the numbers are grouped in a different way. For example, 11 × (5 × 2) = (11 × 5) × 2. Here, the product of both the expressions is 110.

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

The commutative property of multiplication states that changing the order of numbers does not change the product of the given numbers. For example, 6 × 8 = 8 × 6 = 48. The associative property of multiplication states that changing the grouping of numbers does not change the product of the given numbers. For example, 7 ×(2 × 3) = (7 × 2) × 3 = 42.

Associative Property of Multiplication - Formula, Examples, FAQs (2024)

FAQs

Associative Property of Multiplication - Formula, Examples, FAQs? ›

For example, 7 × 20 = 20 × 7 = 140. The Associative property of multiplication states that if the grouping of a set of numbers is changed, the product still remains the same. For example, 22 × (4 × 10) = (22 × 4) × 10 = 880.

Why would you use the associative property of multiplication? ›

The associative property of multiplication helps you multiply numbers faster. Instead of multiplying a list of numbers in the order in which they're written, group them differently to multiply in an order convenient to you.

How does the associative property of multiplication help to calculate products mentally? ›

The associative property lets us regroup and create friendlier numbers. 7 × 30 7 \times 30 7×30 is easier to solve mentally than. (7 \times 5) \times 6=35 \times 6. (7×5)×6=35×6.

What is the associative property of multiplication easy? ›

The associative property of multiplication states that when performing a multiplication problem with more than two numbers, it does not matter which numbers you multiply first. In other words, (a x b) x c = a x (b x c). So, no matter where we put our set of parentheses, we will still get the same answer.

What is the proof of the associative property of multiplication? ›

An example of associative property is 3 × (5 × 6) = (3 × 5) × 6. This is because the law states that with the multiplication of numbers, you can change the grouping of the numbers in the problem and it will not affect the answer.

What is the difference between associative property of multiplication? ›

The associative property states numbers can be regrouped with addition or multiplication, and the answer will not change. The commutative property states the numbers can change positions with addition or multiplication, and the answer will not change.

What is the purpose of associative property? ›

Associative property states that when three or more numbers are added (or multiplied), the sum (or the product) is the same regardless of the grouping of the addends (or the multiplicands).

What best describes the associative property of multiplication? ›

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 example, 3 × (5 × 6) = (3 × 5) × 6. Here, no matter how the numbers are grouped, the product of both the expressions remains 90.

Which equation best demonstrates the associative property of multiplication? ›

Expert-Verified Answer

The best example that shows the associative property of multiplication is equal to (4 x 3) x 6 = 4 x (3 x 6). This property states that the grouping of factors in a multiplication expression does not affect the final result.

What is the associative property of multiplication over addition? ›

The associative property states that when adding or multiplying, the grouping symbols can be relocated without affecting the result. The formula for addition states (a+b)+c=a+(b+c) and the formula for multiplication states (a×b)×c=a×(b×c).

What is the associative property of multiplication real numbers? ›

Associative Property When adding or multiplying, changing the grouping gives the same result. of AdditionIf a,b, and c are real numbers, then(a+b)+c=a+(b+c). of MultiplicationIf a,b, and c are real numbers, then(a·b)·c=a·(b·c).

What is the associative property of multiplication identity? ›

Associative property of multiplication: Changing the grouping of factors does not change the product. For example, ( 2 × 3 ) × 4 = 2 × ( 3 × 4 ) ‍ . Identity property of multiplication: The product of ‍ and any number is that number. For example, 7 × 1 = 7 ‍ .

What is an example of associative property of multiplication with complex numbers? ›

Properties of Multiplication And Addition

The Closure law or the closure property: (z1 × z2) is always a complex number. The Associative Law: If z1, z2, z3 are any three complex numbers then we have (z1 × z2) × z3 = z1 × (z2×z3).

How do you verify the associative property of multiplication? ›

For Multiplication: The associative law for multiplication is given as (A × B) × C = A × (B × C). For example, (1 × 4) × 2 = 1 × (4 × 2) = 8. Therefore, we can say that the associative property is applicable to multiplication.

What is the associative property of multiplication of whole numbers? ›

The associative property of addition and multiplication states that the regrouping of three whole numbers does not change the result of their sum and product. Let A, B and C are three whole numbers, then as per associativity, A + (B + C) = (A + B) + C. A x (B x C) = (A x B) x C.

Is associative property true for matrix multiplication? ›

Matrix multiplication is associative. Al- though it's not commutative, it is associative. That's because it corresponds to composition of functions, and that's associative.

What is the main idea of associative property? ›

In mathematics, the associative property of addition (or multiplication) states that when adding (multiplying) three or more numbers, the sum (product) remains the same regardless of how the numbers are grouped to be added (multiplied). This definition can also be stated algebraically.

Why would you use the associative property of multiplication to solve 10 4 2? ›

The correct answer is: You would use the associative property to regroup the numbers so that you have easily recognizable products to multiply together. We can regroup these factors as 10 × (4 × 2). This gives us the product in parentheses, 4×2 = 8.

What is the benefit of using associative property of addition? ›

What is the benefit of using the associative property of addition? The associative property of addition helps you add numbers faster. Instead of adding a list of numbers in the order that they're written, add them in any order convenient to you.

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