Let’s solve each line step by step.
We’re using the
Associative Property of Addition, which means:
When adding three numbers, it doesn’t matter how you group them — the sum stays the same.
Example: (a + b) + c = a + (b + c)
Also, we can rearrange the order too — that’s the commutative property — but here we’re focusing on grouping and filling in missing numbers so both sides equal the same total.
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Line 1:
7 + (5 + 2) = ___ = 5 + (2 + 7)
First, calculate inside parentheses: 5 + 2 = 7 → then 7 + 7 = 14
Right side: 2 + 7 = 9 → 5 + 9 = 14
So middle box =
14
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Line 2:
8 + (__ + 6) = ___ = 3 + (6 + 8)
Right side: 6 + 8 = 14 → 3 + 14 = 17
So left side must also be 17 → 8 + (__ + 6) = 17
→ __ + 6 = 9 → so blank is
3
Middle box =
17
---
Line 3:
10 + (4 + __) = 19 = 4 + (5 + __)
Left side: 10 + (4 + __) = 19 → 4 + __ = 9 → __ =
5
Right side: 4 + (5 + __) = 19 → 5 + __ = 15 → __ =
10
Check: 4 + (5 + 10) = 4 + 15 = 19
✔
So blanks are
5 and
10
---
Line 4:
11 + (6 + __) = 21 = 4 + (11 + __)
Left: 11 + (6 + __) = 21 → 6 + __ = 10 → __ =
4
Right: 4 + (11 + __) = 21 → 11 + __ = 17 → __ =
6
Check: 4 + (11 + 6) = 4 + 17 = 21
✔
Blanks:
4 and
6
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Line 5:
8 + (12 + 3) = ___ = 3 + (__ + 12)
Left: 12 + 3 = 15 → 8 + 15 = 23
Right: must equal 23 → 3 + (__ + 12) = 23 → __ + 12 = 20 → __ =
8
Middle box =
23
---
Line 6:
9 + (14 + 4) = ___ = 14 + (__ + __)
Left: 14 + 4 = 18 → 9 + 18 = 27
Right: 14 + (__ + __) = 27 → __ + __ = 13
We need two numbers that add to 13 — could be 9 and 4 (since original was 9 + 14 + 4)
So blanks:
9 and
4 (order doesn’t matter, but let’s keep original order)
Middle box =
27
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Line 7:
12 + (8 + 6) = ___ = 6 + (__ + __)
Left: 8 + 6 = 14 → 12 + 14 = 26
Right: 6 + (__ + __) = 26 → __ + __ = 20
Original numbers were 12, 8, 6 — so 12 + 8 = 20 → blanks:
12 and
8
Middle box =
26
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Final Answer:
14, 3 and 17, 5 and 10, 4 and 6, 23 and 8, 27 and 9 and 4, 26 and 12 and 8
Parent Tip: Review the logic above to help your child master the concept of associative property multiplication worksheet.
