Problem Overview:
The task involves solving addition problems and identifying which property of addition is used in each case. The two properties mentioned are:
1.
Commutative Property of Addition: This property states that the order of numbers being added does not affect the sum. Mathematically, \( a + b = b + a \).
2.
Associative Property of Addition: This property states that the grouping of numbers being added does not affect the sum. Mathematically, \( (a + b) + c = a + (b + c) \).
Step-by-Step Solution:
####
Problem 1:
\[ 874 + 235 = \]
\[ 235 + 874 = \]
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Solution:
\[ 874 + 235 = 1109 \]
\[ 235 + 874 = 1109 \]
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Property Used: Commutative Property of Addition, because the order of the numbers being added is changed but the sum remains the same.
####
Problem 2:
\[ 549 + (605 + 777) = \]
\[ (549 + 605) + 777 = \]
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Solution:
\[ 549 + (605 + 777) = 549 + 1382 = 1931 \]
\[ (549 + 605) + 777 = 1154 + 777 = 1931 \]
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Property Used: Associative Property of Addition, because the grouping of the numbers being added is changed but the sum remains the same.
####
Problem 3:
\[ (2.23 + 5.35) + 9.57 = \]
\[ 2.23 + (5.35 + 9.57) = \]
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Solution:
\[ (2.23 + 5.35) + 9.57 = 7.58 + 9.57 = 17.15 \]
\[ 2.23 + (5.35 + 9.57) = 2.23 + 14.92 = 17.15 \]
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Property Used: Associative Property of Addition, because the grouping of the numbers being added is changed but the sum remains the same.
####
Problem 4:
\[ 999 + 693 = \]
\[ 693 + 999 = \]
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Solution:
\[ 999 + 693 = 1692 \]
\[ 693 + 999 = 1692 \]
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Property Used: Commutative Property of Addition, because the order of the numbers being added is changed but the sum remains the same.
####
Problem 5:
\[ 1,077 + 1,770 + 797 = \]
\[ 797 + 1,077 + 1,770 = \]
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Solution:
\[ 1,077 + 1,770 + 797 = 3,644 \]
\[ 797 + 1,077 + 1,770 = 3,644 \]
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Property Used: Commutative Property of Addition, because the order of the numbers being added is changed but the sum remains the same.
####
Problem 6:
\[ 8,765 + (5,411 + 203) = \]
\[ (8,765 + 5,411) + 203 = \]
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Solution:
\[ 8,765 + (5,411 + 203) = 8,765 + 5,614 = 14,379 \]
\[ (8,765 + 5,411) + 203 = 14,176 + 203 = 14,379 \]
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Property Used: Associative Property of Addition, because the grouping of the numbers being added is changed but the sum remains the same.
Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & \text{Commutative Property} \\
2. & \text{Associative Property} \\
3. & \text{Associative Property} \\
4. & \text{Commutative Property} \\
5. & \text{Commutative Property} \\
6. & \text{Associative Property} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of associative property addition worksheet 4th grade.
