Solved Examples and Worksheet for Exploring Associative Property of Addition

Q1Name the property illustrated by the equation below.
4 + (5 + 3) = (4 + 5) + 3
A. Commutative property of multiplication
B. Associative property of addition
C. Associative property of multiplication
D. Commutative property of addition

Solutions
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Step: 1
4 + (5 + 3), (4 + 5) + 3 illustrates same sum. But grouping of addends is changed.
Step: 2
According to associative property of addition, changing the grouping of the addends does not change the sum.
Step: 3
So, 4 + (5 + 3), (4 + 5) + 3 illustrates associative property of addition.
Correct Answer is :   Associative property of addition
Q2Find the missing number.
4 + (6 + 1) = (4 + 6) + ___
A. 4
B. 6
C. 1
D. none of these

Solutions
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Step: 1
According to associative property of addition, changing the grouping of addends does not change the sum.
Step: 2
4 + (6 + 1) = (4 + 6) + 1
  [Use associative property of addition.]
Correct Answer is :   1
Q3Fill in the blank.
(4 + 7) + 7 = 4 + (7 + __ )
A. 8
B. 1
C. 4
D. 7

Solutions
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Step: 1
According to associative property of addition, changing the grouping of addends does not change the sum.
Step: 2
(4 + 7) + 7 = 4 + (7 + 7)
  [Use associative property of addition.]
Correct Answer is :   7
Q4Choose the mathematical expression that is the same as (5 + 8) + 3.
A. 3 + (5 - 8)
B. 16
C. 5 × (8 × 3)
D. 5 + (8 + 3)

Solutions
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Step: 1
The sum of the expression (5 + 8) + 3 is (13) + 3 = 16.
  [Add.]
Step: 2
The associative property of addition states that "the grouping of addends when changed in a problem does not change the sum. "
Step: 3
So, (5 + 8) + 3 = 5 + (8 + 3) = 16.
  [Use the associative property of addition.]
Correct Answer is :   5 + (8 + 3)
Q5Use the associative property of addition to find the number sentence in such a way that the answer remains the same.
(40 + 40) + 3 = _______

A. 40 + 3
B. (40 + 40)
C. (40 + 40) × 3
D. 40 + (40 + 3)

Solutions
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Step: 1
The sum of the expression (40 + 40) + 3 is (80) + 3 = 83.
  [Add.]
Step: 2
The associative property of addition states that "the grouping of addends when changed in a problem does not change the sum."
Step: 3
So, (40 + 40) + 3 = 40 + (40 + 3) = 83.
  [Use the associative property of addition.]
Correct Answer is :   40 + (40 + 3)
Q6Edward earns $90, Nathan earns $10, and Jeff earns $56 per day. Find the total amount earned per day by all three of them.
A. $156
B. $166
C. $171
D. $146

Solutions
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Step: 1
Total amount earned by them = Amount Edward earns + amount Nathan earns + amount Jeff earns
Step: 2
= $90 + $10 + $56
  [Substitute the values.]
Step: 3
= ($90 + $10) + $56
  [Use associative property of addition.]
Step: 4
= $100 + $56 = $156
  [Work inside the grouping symbols and add.]
Step: 5
So, they earn $156 per day altogether .
Correct Answer is :   $156
Q7In a library, 180 books are arranged in the first shelf, 220 books in the second shelf, and 162 books in the third shelf. Find the total number of books arranged in all the three shelves.

A. 662
B. 762
C. 562
D. 462

Solutions
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Step: 1
Total number of books arranged in all the three shelves = number of books arranged in the first shelf + number of books arranged in the second shelf + number of books arranged in the third shelf
Step: 2
= 180 + 220 + 162
  [Substitute the values.]
Step: 3
= (180 + 220) + 162
  [Use associative property of addition.]
Step: 4
= 400 + 162 = 562
  [Work inside the grouping symbols and add.]
Step: 5
So, 562 books are arranged in all the three shelves.
Correct Answer is :   562
Q8At a concert hall there were 18 chairs in the first row, 35 chairs in the second row, and 65 chairs in the third row. Find the total number of chairs in the three rows.
A. 68
B. 108
C. 218
D. 118

Solutions
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Step: 1
Total number of chairs arranged in all the three rows = number of chairs arranged in the first row + number of chairs arranged in the second row + number of chairs arranged in the third row
Step: 2
= 18 + 35 + 65
  [Substitute the values.]
Step: 3
= 18 + (35 + 65)
  [Use associative property of addition.]
Step: 4
= 18 + 100 = 118
Step: 5
So, 118 chairs are arranged in all the three rows.
Correct Answer is :   118
Q9Jeremy ate 60 chocolates, Dennis ate 40 chocolates, and Louis ate 54 chocolates in a month. How many chocolates did they eat altogether?
A. 154
B. 204
C. 254
D. 134

Solutions
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Step: 1
Total number of chocolates ate by all of them = number of chocolates ate by Jeremy + number of chocolates ate by Dennis + number of chocolates ate by Louis
Step: 2
= 60 + 40 + 54
  [Substitute the values.]
Step: 3
= (60 + 40) + 54
  [Use associative property of addition.]
Step: 4
= 100 + 54 = 154
  [Work inside the grouping symbols and add.]
Step: 5
So, they ate 154 chocolates altogether.
Correct Answer is :   154
Q10Jerald cooked 8 hamburgers, Charles cooked 4 hamburgers, and Tony cooked 4 hamburgers at a country fair. Find the total number of hamburgers they cooked altogether.

A. 18
B. 14
C. 16
D. 19

Solutions
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Step: 1
Total number of hamburgers cooked by all of them = number of hamburgers cooked by Jerald + number of hamburgers cooked by Charles + number of hamburgers cooked by Tony
Step: 2
= 8 + 4 + 4
  [Substitute the values.]
Step: 3
= (8 + 4) + 4
  [Use associative property of addition.]
Step: 4
= 12 + 4
  [Work inside the grouping symbols and add.]
Step: 5
= 16
Step: 6
So, the total number of hamburgers cooked by all of them = 16.
Correct Answer is :   16

HighSchool Math