Associative Property of Multiplication: Definition with Solved Examples.

Multiplication is one of the four basic operations in mathematics. The other three operations are addition, subtraction, and division. Multiplication is the process of repeated addition. So, 5 x 3 = 5 + 5 + 5 = 15. It can also be thought of as groups of a number. For example, if there are five girls in a group and each girl has three apples, then there are fifteen apples in total. This is called the “associative property of multiplication”.

What is the associative property of multiplication?

The associative property of multiplication is when the order of the factors in a multiplication problem does not change the product. In other words, it doesn’t matter where you put the parentheses when multiplying, as long as all the factors are inside them. You will still get the same answer. For example, in the multiplication problem 3 x (4 x 5), it doesn’t matter if you multiply 3 by 4 first, or 4 by 5 first and then multiply that answer by 3. You will get the same answer either way: 60.

Associative property of multiplication definition

The associative property of multiplication is a mathematical property that states that the order of factors in a multiplication problem does not affect the answer. In other words, it doesn’t matter whether you multiply the 2 first and then multiply by 3, or whether you multiply 3 first and then multiply by 2. The answer will be the same either way: 6.

This property is helpful because it allows us to regroup factors in a multiplication problem in order to make the problem easier to solve. For instance, if we have a multiplication problem with three factors, such as 2 x 3 x 4, we can use the associative property of multiplication to regroup the factors so that we are multiplying 2 x 4 first, and then multiplying that answer by 3. This gives us the equation (2 x 4) x 3, which is easier to solve than 2 x 3 x 4.

The associative property of multiplication also applies to division problems. For instance, if we want to divide 10 by 5, we can first divide 10 by 2 and then divide that answer by 2.5. Or we could divide 10 by 5 and then divide that answer by 2. Either way, we would get the same answer: 2.

The formula for the associative property of multiplication

The associative property of multiplication states that when three or more numbers are multiplied, the order in which they are multiplied does not affect the product. In other words, for all real numbers a, b, and c, we have:

a * (b * c) = (a * b) * c

This is simply a matter of convenience; it allows us to multiply numbers in any order we please without having to worry about changing the answer. For example, consider the following multiplication problem:

2 * 3 * 4

We could compute this in two different ways. First, we could multiply 2 by 3 to get 6, and then multiply 6 by 4 to get 24. Or, we could first multiply 3 by 4 to get 12, and then multiply 2 by 12 to get 24. Either way, we would get the same answer of 24.

Generalized Associative Law

In mathematics, the associative property is a property of some binary operations. In particular, it says that the order of operation does not affect the result. The associative property is a fundamental property of addition and multiplication, and many algebraic structures are defined to be associative.

The formal definition of the associative property is as follows: let a, b, and c be elements of a set with a binary operation * . Then * is said to be associative if a * (b * c) = (a * b) * c .

In other words, the associative property states that the result of an operation does not depend on the order in which the operands are arranged. This is best demonstrated with examples.

Here are some examples of situations in which the associative property applies:

Adding real numbers: For any real numbers a , b , and c , we have a + (b + c) = (a + b) + c . This is because addition is an associative operation.

Multiplying real numbers: For any real numbers a , b , and c , we have a(bc) = (ab)c . This is because multiplication is an associative operation.

String concatenation: For any strings s , t , and u , we have s(tu) = (st)u . That is, string concatenation is an associative operation.

Why is it Important?

In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.

The associative property of multiplication states that when three or more numbers are multiplied, the order in which they are multiplied does not affect the product. More formally, the associative property of multiplication is stated as follows:

For any real numbers a, b, and c, we have:

a * (b * c) = (a * b) * c.

What are some Examples of the Associative Property of Multiplication?

The associative property of multiplication is one of the basic properties of arithmetic. It states that when multiplying three or more numbers, the order in which the numbers are multiplied does not affect the product. In other words,

For any real numbers a, b, and c:

a * (b * c) = (a * b) * c

This property is called “associative” because it associates or groups the factors in different ways while still yielding the same product.

Here are some examples of the associative property of multiplication at work:

2 * (3 * 4) = (2 * 3) * 4 24 = 12 * 4 24
4 * (5 * 6) = (4 * 5) * 6 120 = 20 * 6 120
10 * (2 * 3) = (10* 2) * 3 60 = 20* 3 60

How can the Associative Property of Multiplication be Used in Everyday Life?

If you’ve ever done any sort of shopping, then you’ve likely used the associative property of multiplication without even realizing it. This property states that when multiplying three or more numbers, the order in which the numbers are multiplied does not affect the outcome of the equation. In other words, a×b×c is equal to c×a×b.

You can use the associative property of multiplication when comparing prices at different stores, or when determining how much money you’ll need to spend on an item if tax is included. Let’s say you want to buy a new shirt that costs $20, and the sales tax in your state is 6%. To find out how much the total cost of the shirt will be, you can multiply $20 by 1.06 (which is equal to $21.20), or you can multiply $20 by 0.06 and then add that result to $20 (which is also equal to $21.20).

The associative property of multiplication can also be helpful when solving word problems. For example, if a farmer has 15 cows and each cow produces 4 gallons of milk per day, then the farmer has 60 gallons of milk in total. But what if we want to know how many cows the farmer has for every gallon of milk? In other words, we want to solve for “cows per gallon” instead of “gallons per cow”.

Conclusion

We hope that this article helped you understand the associative property of multiplication and how it can be used to simplify calculations. As we saw in the examples, this property can be very useful when multiplying large numbers or performing complex operations. So next time you’re stuck on a math problem, remember to use the associative property to make things easier. Thanks for reading!