About Associative Property Formula
The associative feature of multiplication/addition asserts that the order in which the numbers in a multiplication/addition issue are grouped has no bearing on or changes the product/sum of those numbers. In other words, regardless matter how three or more integers are organised, the product/sum remains the same. In this post, we'll learn more about the associative property of multiplication/addition
What is the Associative Property of Multiplication?
When three or more numbers are multiplied/added, the outcome is the same regardless of how the 3 numbers are arranged, according to the associative feature of multiplication/addition. The way brackets are put in the provided multiplication/addition phrase is referred to as grouping. To learn the concept of the associative property of addition/multiplication.
(6 × 5)× 7 = 6 × (5 × 7)
(30) × 7 = 6 × (35)
210 = 210
Associative Property of Multiplication Formula
(a x b) x c = a x (b x c) is the formula for the associative property of multiplication. This formula states that product of the integers remains the same regardless of how the brackets are put in a multiplication statement. Use of brackets to group numbers helps to produce smaller components, which makes multiplication calculations easier. Consider the following formula for multiplication's associative property.
a ×(b × c) = (a × b) × c
Let us understand the formula using numbers. For example, let us multiply 3 × 4 × 5 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 (3 × 4) × 5. If we find the product of this expression, we get which is 60.
- Step 2: Now, let us group 3 and 4 together making it 3 × (4 × 5). If we multiply this expression, it comes to, which again gives the product as 60.
- 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
Multiplication and addition of numbers can be done regardless of how they are grouped, according to the associative property. To add 7, 6, and 3, for example, group them as 7 + (6 + 3), and result is 16. Let group it as (7 + 6) + 3 and observe that the total is 16 once more. This is addition's associative property, which also applies to multiplication. Multiplying 7, 6, and 3 grouping the integers as 7 (6 x 3) is an example. The sum of these numbers equals 126. Now, if we group the numbers together as (7 x 6) 3, we get the same result. 126.
Associative Property of Multiplication
(a × b ) × c = c × (b × c)
Associative Property of Addition
(a + b ) + c = c × (b + c)
Tips on the Associative Property of Multiplication:
Here are some key aspects to remember about multiplication's associative property:
- When there are three or more numbers, the associative property is always true.
- Subtraction and division are not affected by the associative property, which only applies to addition and multiplication.
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