How To Apply the Associative Property

In mathematics, the associative property is a rule of combining numbers in any order resulting in the same answer. Sometimes people confuse the associative property with the commutative property. The commutative property applies to only two numbers. The associative property involves three or more numbers. Addition, subtraction, multiplication and division are examples of binary operations. The binary operations that are applicable to the associative property are addition and multiplication. No matter how you group the numbers by sets, it always results to the same answer. Associative property basically groups together numbers in sets of twos to make it easier for you to execute the binary operations. Here are tips on how to apply the associative property:

1.    Determine your binary operation. Are you using addition or multiplication? These two binary operations are the most common to be used for the associative property. Division and subtraction are also binary operations but the associative property does not use these binaries because if you interchange the numbers, they do not produce the same results.

2.    Group the numbers. Group the first two numbers with a parenthesis. It does not follow any particular order how you group it. If you are having more than three numbers, group them into two numbers per set. Say you have the numbers 3, 5, 4 and 6.

Group them as: (3+4) + (5 + 6).

If you have three numbers say, 5, 7 and 2.

Group them as: (5 + 7) + 2.

3.    Using the parenthesis. The parenthesis breaks down your numbers into groups. It just basically makes it easier for you to add or multiply the numbers. For example your associative equation is: 3 + 4 +1 = 8. Applying the parenthesis should be:

(3 + 4) + 1 = 8 or it can be the other order such as
(4 + 1) + 3 = 8 or (1 + 3) + 4 = 8.
Regardless how you arrange the numbers, it will still get the same result.

4.    Add the numbers. Add first the numbers grouped in a parenthesis. Then add the rest of the numbers to get the result. If you have more than one group in a parenthesis, start from the first group down to the last group and finally, the remaining numbers.

5.    Multiplication. The associative property for multiplication is basically the same as the addition associative property. Follow the same steps. Group together two numbers in a parenthesis in any order.

Adding or multiplying a lot of numbers sometimes confuses you. The use of the associative property is to basically breakdown the numbers. Remember that you cannot use the associative property in binaries like division and subtraction. In these binaries, rearranging the order of the numbers will produce different results. This property is particularly helpful and useful because it will help you to add or multiply numbers mentally. Some people attest that it is easier to add 3 to 45 than add 45 to 3. Since you can add numbers in any order, you can always go to which way it is arranged that is easier for you.


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