Let’s solve this step by step.
The
Associative Property of Multiplication says that when multiplying three or more numbers, you can group them in different ways — the answer stays the same.
For example:
> 2 × (3 × 4) = (2 × 3) × 4
Both sides equal 24.
We’ll use this idea to find the missing numbers in each equation.
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Part 1: Find the missing number
We look at how the grouping changes and match the numbers accordingly.
1.
3 × (5 × 2) = (3 × 5) × ___
Left side: groups 5 and 2 first → then multiplies by 3
Right side: groups 3 and 5 first → then multiplies by ?
To keep it the same, the last number must be
2
✔ Answer:
2
2.
8 × (1 × 6) = (___ × 1) × 6
Left: 1 and 6 grouped → multiplied by 8
Right: ? and 1 grouped → multiplied by 6
So the missing number must be
8
✔ Answer:
8
3.
7 × (5 × 3) = (7 × ___) × 3
Left: 5 and 3 grouped → multiplied by 7
Right: 7 and ? grouped → multiplied by 3
Missing number is
5
✔ Answer:
5
4.
2 × (4 × 1) = (2 × ___) × 1
Left: 4 and 1 grouped → multiplied by 2
Right: 2 and ? grouped → multiplied by 1
Missing number is
4
✔ Answer:
4
5.
7 × (3 × 5) = (___ × 3) × 5
Left: 3 and 5 grouped → multiplied by 7
Right: ? and 3 grouped → multiplied by 5
Missing number is
7
✔ Answer:
7
6.
6 × (3 × 2) = (6 × 3) × ___
Left: 3 and 2 grouped → multiplied by 6
Right: 6 and 3 grouped → multiplied by ?
Missing number is
2
✔ Answer:
2
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Part 2: Match according to the associative property
We need to pair expressions that are equivalent due to regrouping.
Left column:
- A: 5 × (7 × 6)
- B: (7 × 3) × 2
- C: 3 × (9 × 1)
- D: (4 × 3) × 2
- E: (3 × 4) × 6
Right column:
- F: 3 × (4 × 6)
- G: (3 × 9) × 1
- H: 4 × (3 × 2)
- I: 7 × (3 × 2)
- J: (5 × 7) × 6
Now match:
- A: 5 × (7 × 6) → same as (5 × 7) × 6 → matches
J
- B: (7 × 3) × 2 → same as 7 × (3 × 2) → matches
I
- C: 3 × (9 × 1) → same as (3 × 9) × 1 → matches
G
- D: (4 × 3) × 2 → same as 4 × (3 × 2) → matches
H
- E: (3 × 4) × 6 → same as 3 × (4 × 6) → matches
F
✔ All matched!
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Final Answer:
Part 1 Missing Numbers (in order):
2, 8, 5, 4, 7, 2
Part 2 Matches:
A ↔ J
B ↔ I
C ↔ G
D ↔ H
E ↔ F
Parent Tip: Review the logic above to help your child master the concept of associative property of multiplication worksheet.
