Riley had to add this group of numbers $(56+47)+53$, but he wanted to add them as quickly and as easily as possible. Here is how he decided to add the numbers:
Original problem: $(56+47)+53$
Riley rewrote it as $56+(47+53)=56+100=156$.
Which number property allowed him to add the numbers in this way?
A. the Identity Property of Addition
B. the Associative Property of Addition
C. the Commutative Property of Addition
Answer (2)
The associative property of addition allows changing the grouping of numbers in an addition problem without changing the sum.
The expression ( 56 + 47 ) + 53 is equivalent to 56 + ( 47 + 53 ) due to the associative property.
Riley used the associative property to simplify the addition.
The correct answer is B: Ae Asiscialive Property of Adision. B
Explanation
Understanding the Problem We are asked to identify the property that allows us to change the grouping of numbers in an addition problem without changing the sum.
Explaining the Associative Property The associative property of addition states that the way in which numbers are grouped in an addition problem does not change the sum. In other words, for any numbers a , b , and c , we have ( a + b ) + c = a + ( b + c ) .
Applying the Property to the Problem In Riley's problem, we have ( 56 + 47 ) + 53 . He rewrote this as 56 + ( 47 + 53 ) . This is an example of the associative property of addition.
Identifying the Correct Option Therefore, the number property that allowed him to add the numbers in this way is the associative property of addition. The correct answer is B.
Examples
The associative property is useful in everyday situations. For example, if you are calculating the total cost of items you bought at a store, you can group the items in any order to make the calculation easier. If you bought a book for $15, a pen for $5, and a notebook for 10 , yo u c ana dd t h e ma s (15+5)+10 = 20+10 = $30 or as $15+(5+10) = 15+15 = $30. The total cost remains the same regardless of how you group the items.
Riley used the Associative Property of Addition to change the grouping of the numbers in his addition problem, simplifying it to find the sum more easily. This property states that changing the grouping of numbers does not change the sum. Therefore, the correct answer is B.
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