Associative Property of Addition Worksheets with Answer Key - Free Printable
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Step-by-step solution for: Associative Property of Addition Worksheets with Answer Key
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Step-by-step solution for: Associative Property of Addition Worksheets with Answer Key
Let’s go through each problem step by step. The key idea here is the Associative Property of Addition, which means that when adding three or more numbers, you can group them in any way — the sum stays the same.
For example:
5 + (4 + 3) = (5 + 4) + 3 → both equal 12.
We’ll use this to fill in the blanks and find the missing sums.
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Problem ①:
8 + (__ + 3) = (__ + 4) + 3 = □
Look at the right side: (__ + 4) + 3
The left side has 8 + (__ + 3). Since it’s associative, the first blank on the left must be 4 (to match the 4 inside the parentheses on the right), and the first blank on the right must be 8 (to match the 8 outside on the left).
So:
8 + (4 + 3) = (8 + 4) + 3
Now calculate: 4 + 3 = 7 → 8 + 7 = 15
Or: 8 + 4 = 12 → 12 + 3 = 15
✔ Sum is 15.
Answer for ①: 8 + (4 + 3) = (8 + 4) + 3 = 15
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Problem ②:
10 + (__ + 2) = (__ + 5) + 2 = □
Left side: 10 + (__ + 2)
Right side: (__ + 5) + 2
To make them equal using associativity, the number added to 5 on the right should be 10, so the blank there is 10. Then on the left, the blank inside the parentheses should be 5 (since 5+2 matches the structure).
So:
10 + (5 + 2) = (10 + 5) + 2
Calculate: 5 + 2 = 7 → 10 + 7 = 17
Or: 10 + 5 = 15 → 15 + 2 = 17
✔ Sum is 17.
Answer for ②: 10 + (5 + 2) = (10 + 5) + 2 = 17
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Problem ③:
(3 + 7) + __ = 3 + (__ + 6) = 16
We know the total is 16.
Left side: (3 + 7) + __ → 10 + __ = 16 → so blank = 6
Check right side: 3 + (__ + 6) = 16
If blank is 7, then 3 + (7 + 6) = 3 + 13 = 16 ✔
Also, check if it matches associative property:
(3 + 7) + 6 = 3 + (7 + 6) → yes! Both are 16.
Answer for ③: (3 + 7) + 6 = 3 + (7 + 6) = 16
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Problem ④:
4 + (__ + 2) = (4 + 6) + __ = □
Right side: (4 + 6) + __ → 10 + __
Left side: 4 + (__ + 2)
From right side, we see 6 is used inside, so on left, the blank inside should be 6? Wait — let’s think differently.
Actually, look:
Left: 4 + (__ + 2)
Right: (4 + 6) + __
For these to be equal via association, the “__” on the left inside must be 6, and the “__” on the right after the parenthesis must be 2.
So:
4 + (6 + 2) = (4 + 6) + 2
Calculate: 6 + 2 = 8 → 4 + 8 = 12
Or: 4 + 6 = 10 → 10 + 2 = 12
✔ Sum is 12.
Answer for ④: 4 + (6 + 2) = (4 + 6) + 2 = 12
---
Problem ⑤:
(__ + 2) + 5 = 6 + (__ + 5) = 13
Total is 13.
Left side: (__ + 2) + 5 = 13 → (__ + 2) = 8 → blank = 6
Right side: 6 + (__ + 5) = 13 → (__ + 5) = 7 → blank = 2
Check: (6 + 2) + 5 = 8 + 5 = 13
6 + (2 + 5) = 6 + 7 = 13 ✔
And it fits associative property: (6 + 2) + 5 = 6 + (2 + 5)
Answer for ⑤: (6 + 2) + 5 = 6 + (2 + 5) = 13
---
Problem ⑥:
7 + (8 + __) = (7 + __) + 2 = □
We need to find the blanks and the sum.
Notice the last term on the right is +2, but on the left it’s + (8 + __). For the groups to match, the blank inside on the left should be 2, and the blank after 7 on the right should be 8.
Try:
7 + (8 + 2) = (7 + 8) + 2
Calculate: 8 + 2 = 10 → 7 + 10 = 17
Or: 7 + 8 = 15 → 15 + 2 = 17
✔ Sum is 17.
Answer for ⑥: 7 + (8 + 2) = (7 + 8) + 2 = 17
---
Problem ⑦:
9 + (__ + 3) = (__ + 1) + 3 = □
Similar pattern.
Left: 9 + (__ + 3)
Right: (__ + 1) + 3
To match, the blank on the left inside should be 1, and the blank on the right before +1 should be 9.
So:
9 + (1 + 3) = (9 + 1) + 3
Calculate: 1 + 3 = 4 → 9 + 4 = 13
Or: 9 + 1 = 10 → 10 + 3 = 13
✔ Sum is 13.
Answer for ⑦: 9 + (1 + 3) = (9 + 1) + 3 = 13
---
Problem ⑧:
__ + (16 + 3) = (2 + __) + 3 = 21
Total is 21.
Left side: __ + (16 + 3) = __ + 19 = 21 → blank = 2
Right side: (2 + __) + 3 = 21 → (2 + __) = 18 → blank = 16
Check: 2 + (16 + 3) = 2 + 19 = 21
(2 + 16) + 3 = 18 + 3 = 21 ✔
Perfect.
Answer for ⑧: 2 + (16 + 3) = (2 + 16) + 3 = 21
---
Problem ⑨:
(4 + 6) + __ = 4 + (__ + 8) = □
Left: (4 + 6) + __ → 10 + __
Right: 4 + (__ + 8)
For them to be equal, the blank on the left should be 8, and the blank inside on the right should be 6.
Try:
(4 + 6) + 8 = 4 + (6 + 8)
Calculate: 10 + 8 = 18
Or: 6 + 8 = 14 → 4 + 14 = 18
✔ Sum is 18.
Answer for ⑨: (4 + 6) + 8 = 4 + (6 + 8) = 18
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Final Answers:
① 8 + (4 + 3) = (8 + 4) + 3 = 15
② 10 + (5 + 2) = (10 + 5) + 2 = 17
③ (3 + 7) + 6 = 3 + (7 + 6) = 16
④ 4 + (6 + 2) = (4 + 6) + 2 = 12
⑤ (6 + 2) + 5 = 6 + (2 + 5) = 13
⑥ 7 + (8 + 2) = (7 + 8) + 2 = 17
⑦ 9 + (1 + 3) = (9 + 1) + 3 = 13
⑧ 2 + (16 + 3) = (2 + 16) + 3 = 21
⑨ (4 + 6) + 8 = 4 + (6 + 8) = 18
Final Answer:
① 15
② 17
③ 16
④ 12
⑤ 13
⑥ 17
⑦ 13
⑧ 21
⑨ 18
For example:
5 + (4 + 3) = (5 + 4) + 3 → both equal 12.
We’ll use this to fill in the blanks and find the missing sums.
---
Problem ①:
8 + (__ + 3) = (__ + 4) + 3 = □
Look at the right side: (__ + 4) + 3
The left side has 8 + (__ + 3). Since it’s associative, the first blank on the left must be 4 (to match the 4 inside the parentheses on the right), and the first blank on the right must be 8 (to match the 8 outside on the left).
So:
8 + (4 + 3) = (8 + 4) + 3
Now calculate: 4 + 3 = 7 → 8 + 7 = 15
Or: 8 + 4 = 12 → 12 + 3 = 15
✔ Sum is 15.
Answer for ①: 8 + (4 + 3) = (8 + 4) + 3 = 15
---
Problem ②:
10 + (__ + 2) = (__ + 5) + 2 = □
Left side: 10 + (__ + 2)
Right side: (__ + 5) + 2
To make them equal using associativity, the number added to 5 on the right should be 10, so the blank there is 10. Then on the left, the blank inside the parentheses should be 5 (since 5+2 matches the structure).
So:
10 + (5 + 2) = (10 + 5) + 2
Calculate: 5 + 2 = 7 → 10 + 7 = 17
Or: 10 + 5 = 15 → 15 + 2 = 17
✔ Sum is 17.
Answer for ②: 10 + (5 + 2) = (10 + 5) + 2 = 17
---
Problem ③:
(3 + 7) + __ = 3 + (__ + 6) = 16
We know the total is 16.
Left side: (3 + 7) + __ → 10 + __ = 16 → so blank = 6
Check right side: 3 + (__ + 6) = 16
If blank is 7, then 3 + (7 + 6) = 3 + 13 = 16 ✔
Also, check if it matches associative property:
(3 + 7) + 6 = 3 + (7 + 6) → yes! Both are 16.
Answer for ③: (3 + 7) + 6 = 3 + (7 + 6) = 16
---
Problem ④:
4 + (__ + 2) = (4 + 6) + __ = □
Right side: (4 + 6) + __ → 10 + __
Left side: 4 + (__ + 2)
From right side, we see 6 is used inside, so on left, the blank inside should be 6? Wait — let’s think differently.
Actually, look:
Left: 4 + (__ + 2)
Right: (4 + 6) + __
For these to be equal via association, the “__” on the left inside must be 6, and the “__” on the right after the parenthesis must be 2.
So:
4 + (6 + 2) = (4 + 6) + 2
Calculate: 6 + 2 = 8 → 4 + 8 = 12
Or: 4 + 6 = 10 → 10 + 2 = 12
✔ Sum is 12.
Answer for ④: 4 + (6 + 2) = (4 + 6) + 2 = 12
---
Problem ⑤:
(__ + 2) + 5 = 6 + (__ + 5) = 13
Total is 13.
Left side: (__ + 2) + 5 = 13 → (__ + 2) = 8 → blank = 6
Right side: 6 + (__ + 5) = 13 → (__ + 5) = 7 → blank = 2
Check: (6 + 2) + 5 = 8 + 5 = 13
6 + (2 + 5) = 6 + 7 = 13 ✔
And it fits associative property: (6 + 2) + 5 = 6 + (2 + 5)
Answer for ⑤: (6 + 2) + 5 = 6 + (2 + 5) = 13
---
Problem ⑥:
7 + (8 + __) = (7 + __) + 2 = □
We need to find the blanks and the sum.
Notice the last term on the right is +2, but on the left it’s + (8 + __). For the groups to match, the blank inside on the left should be 2, and the blank after 7 on the right should be 8.
Try:
7 + (8 + 2) = (7 + 8) + 2
Calculate: 8 + 2 = 10 → 7 + 10 = 17
Or: 7 + 8 = 15 → 15 + 2 = 17
✔ Sum is 17.
Answer for ⑥: 7 + (8 + 2) = (7 + 8) + 2 = 17
---
Problem ⑦:
9 + (__ + 3) = (__ + 1) + 3 = □
Similar pattern.
Left: 9 + (__ + 3)
Right: (__ + 1) + 3
To match, the blank on the left inside should be 1, and the blank on the right before +1 should be 9.
So:
9 + (1 + 3) = (9 + 1) + 3
Calculate: 1 + 3 = 4 → 9 + 4 = 13
Or: 9 + 1 = 10 → 10 + 3 = 13
✔ Sum is 13.
Answer for ⑦: 9 + (1 + 3) = (9 + 1) + 3 = 13
---
Problem ⑧:
__ + (16 + 3) = (2 + __) + 3 = 21
Total is 21.
Left side: __ + (16 + 3) = __ + 19 = 21 → blank = 2
Right side: (2 + __) + 3 = 21 → (2 + __) = 18 → blank = 16
Check: 2 + (16 + 3) = 2 + 19 = 21
(2 + 16) + 3 = 18 + 3 = 21 ✔
Perfect.
Answer for ⑧: 2 + (16 + 3) = (2 + 16) + 3 = 21
---
Problem ⑨:
(4 + 6) + __ = 4 + (__ + 8) = □
Left: (4 + 6) + __ → 10 + __
Right: 4 + (__ + 8)
For them to be equal, the blank on the left should be 8, and the blank inside on the right should be 6.
Try:
(4 + 6) + 8 = 4 + (6 + 8)
Calculate: 10 + 8 = 18
Or: 6 + 8 = 14 → 4 + 14 = 18
✔ Sum is 18.
Answer for ⑨: (4 + 6) + 8 = 4 + (6 + 8) = 18
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Final Answers:
① 8 + (4 + 3) = (8 + 4) + 3 = 15
② 10 + (5 + 2) = (10 + 5) + 2 = 17
③ (3 + 7) + 6 = 3 + (7 + 6) = 16
④ 4 + (6 + 2) = (4 + 6) + 2 = 12
⑤ (6 + 2) + 5 = 6 + (2 + 5) = 13
⑥ 7 + (8 + 2) = (7 + 8) + 2 = 17
⑦ 9 + (1 + 3) = (9 + 1) + 3 = 13
⑧ 2 + (16 + 3) = (2 + 16) + 3 = 21
⑨ (4 + 6) + 8 = 4 + (6 + 8) = 18
Final Answer:
① 15
② 17
③ 16
④ 12
⑤ 13
⑥ 17
⑦ 13
⑧ 21
⑨ 18
Parent Tip: Review the logic above to help your child master the concept of commutative property of addition worksheet.
