Problem: Solve the worksheet on the Associative Property of Addition
The
Associative Property of Addition states that when adding three or more numbers, the way in which the numbers are grouped does not affect the sum. Mathematically, it is expressed as:
\[
(a + b) + c = a + (b + c)
\]
####
Part A: Fill in the missing numbers
1.
(2 + 5) + 4 = 2 + (___ + 4)
- Simplify the left side: \( (2 + 5) + 4 = 7 + 4 = 11 \).
- To match the right side, we need \( 2 + (\text{something} + 4) = 11 \).
- The "something" must be 5 because \( 2 + (5 + 4) = 2 + 9 = 11 \).
-
Answer: \( 5 \)
2.
6 + (10 + 3) = (6 + ___) + 3
- Simplify the left side: \( 6 + (10 + 3) = 6 + 13 = 19 \).
- To match the right side, we need \( (6 + \text{something}) + 3 = 19 \).
- The "something" must be 10 because \( (6 + 10) + 3 = 16 + 3 = 19 \).
-
Answer: \( 10 \)
3.
(__ + 8) + 3 = 7 + (8 + 3)
- Simplify the right side: \( 7 + (8 + 3) = 7 + 11 = 18 \).
- To match the left side, we need \( (\text{something} + 8) + 3 = 18 \).
- The "something" must be 7 because \( (7 + 8) + 3 = 15 + 3 = 18 \).
-
Answer: \( 7 \)
4.
2 + (9 + 5) = (2 + ___) + 5
- Simplify the left side: \( 2 + (9 + 5) = 2 + 14 = 16 \).
- To match the right side, we need \( (2 + \text{something}) + 5 = 16 \).
- The "something" must be 9 because \( (2 + 9) + 5 = 11 + 5 = 16 \).
-
Answer: \( 9 \)
5.
7 + (6 + 2) = (___ + 6) + 2
- Simplify the left side: \( 7 + (6 + 2) = 7 + 8 = 15 \).
- To match the right side, we need \( (\text{something} + 6) + 2 = 15 \).
- The "something" must be 7 because \( (7 + 6) + 2 = 13 + 2 = 15 \).
-
Answer: \( 7 \)
6.
9 + (10 + 12) = (9 + 10) + ___
- Simplify the left side: \( 9 + (10 + 12) = 9 + 22 = 31 \).
- To match the right side, we need \( (9 + 10) + \text{something} = 31 \).
- The "something" must be 12 because \( (9 + 10) + 12 = 19 + 12 = 31 \).
-
Answer: \( 12 \)
####
Part B: Complete the following using the associative property of addition
1.
(5 + 6) + 7 = ___
- Using the associative property: \( (5 + 6) + 7 = 5 + (6 + 7) \).
-
Answer: \( 5 + (6 + 7) \)
2.
8 + (9 + 3) = ___
- Using the associative property: \( 8 + (9 + 3) = (8 + 9) + 3 \).
-
Answer: \( (8 + 9) + 3 \)
3.
(10 + 2) + 5 = ___
- Using the associative property: \( (10 + 2) + 5 = 10 + (2 + 5) \).
-
Answer: \( 10 + (2 + 5) \)
4.
11 + (3 + 4) = ___
- Using the associative property: \( 11 + (3 + 4) = (11 + 3) + 4 \).
-
Answer: \( (11 + 3) + 4 \)
Final Answers:
#### Part A:
1. \( 5 \)
2. \( 10 \)
3. \( 7 \)
4. \( 9 \)
5. \( 7 \)
6. \( 12 \)
#### Part B:
1. \( 5 + (6 + 7) \)
2. \( (8 + 9) + 3 \)
3. \( 10 + (2 + 5) \)
4. \( (11 + 3) + 4 \)
Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Part A: } 5, 10, 7, 9, 7, 12 \\
\text{Part B: } 5 + (6 + 7), (8 + 9) + 3, 10 + (2 + 5), (11 + 3) + 4
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of properties of addition worksheet for grade 2.
