How to read correctly this statement (associative law)

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In summary, The statement "a + (b + c) = (a + b) + c" is read as "a plus the sum of b and c is equal to the sum of a and b plus c". The second option of "a plus b plus c is equal to a plus b plus c" is not as accurate as it doesn't mention the associative law. However, once the operation is associative, the parentheses can be dropped for simplicity. This clarification was helpful for the person asking the question.
  • #1
tomas_xc
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I'm not a native speaker of English and I was reading a Calculus's book and I didn't know the correct way to read a statement about real numbers. This is the statement:

"a + (b + c) = (a + b) + c"

Is it "a plus the sum of b and c is equal to the sum of a and b plus c"?
Or is it just "a plus b plus c is equal to a plus b plus c"?

I just think the second one inappropriate because it doesn't tell the associative law at all.

So, can anybody tell me the correct way?
Thanks!
 
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  • #2
The first one is exactly what it's saying.
 
  • #3
Office_Shredder said:
The first one is exactly what it's saying.

Thank you! You really helped me.
 
  • #4
the first implies the second. once you have an associative operation, you always drop such parentheses to save effort.
 

1. What is the associative law?

The associative law is a mathematical property that states that when adding or multiplying three or more numbers, the grouping of the numbers does not affect the result. This means that you can group the numbers in any way you want and still get the same final answer.

2. How do I read and interpret a statement involving the associative law?

To read and interpret a statement involving the associative law, you need to understand the order of operations and the meaning of the symbols used. The associative law applies to addition and multiplication, and the statement will typically involve several numbers and parentheses to indicate the grouping of the numbers.

3. Can you give an example of a statement involving the associative law?

One example of a statement involving the associative law is (2+3)+4=2+(3+4). This statement shows that no matter how you group the numbers, the result will always be the same: 9.

4. Why is the associative law important?

The associative law is important because it allows us to simplify and solve complex mathematical expressions by changing the grouping of the numbers without changing the final result. This can save time and make calculations easier.

5. Are there any exceptions to the associative law?

Yes, there are some operations that do not follow the associative law, such as subtraction and division. This means that changing the grouping of the numbers in these operations can change the final result. It is important to pay attention to the type of operation being used when applying the associative law.

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