Let’s solve each problem step by step.
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Part 1: Which property is shown?
We are given three equations and need to name the multiplication property used in each.
Remember:
-
Commutative Property: Order doesn’t matter → a × b = b × a
-
Associative Property: Grouping doesn’t matter → (a × b) × c = a × (b × c)
-
Distributive Property: Multiply over addition → a × (b + c) = (a × b) + (a × c)
Now let’s look at each:
1.
4 × 6 = (4 × 5) + (4 × 1)
This breaks 6 into 5 + 1, then multiplies 4 by each part and adds. That’s the
Distributive Property.
2.
5 × 7 = 7 × 5
The order of numbers switched — that’s the
Commutative Property.
3.
4 × (2 × 5) = (4 × 2) × 5
The grouping changed — parentheses moved — but the order stayed same. That’s the
Associative Property.
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Part 2: Fill in the missing numbers using properties
We’ll go row by row, left and right columns.
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Row 1:
Left:
6 × 8 = (6 × 4) + (6 × __ )
Think: 8 = 4 + ? → 4 + 4 = 8 → so blank is
4
Check: (6×4)+(6×4)=24+24=48, and 6×8=48 ✔️
Right:
3 × 7 = 7 × __
Commutative property → just swap → blank is
3
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Row 2:
Left:
9 × 2 = __ × 9
Commutative → swap → blank is
2
Right:
4 × (2 × 6) = (__ × 2) × 6
Associative → group differently → first number stays 4 → blank is
4
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Row 3:
Left:
3 × (5 × 4) = (3 × 5) × __
Associative → last number stays 4 → blank is
4
Right:
9 × 7 = (9 × 5) + (__ × 2)
Break 7 into 5 + 2 → so it’s (9×5)+(9×2) → blank is
9
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Row 4:
Left:
2 × (6 × 5) = (__ × 6) × 5
Associative → first number is 2 → blank is
2
Right:
3 × 9 = (3 × 5) + (3 × __)
Break 9 into 5 + 4 → so blank is
4
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Row 5:
Left:
6 × 3 = 3 × __
Commutative → swap → blank is
6
Right:
3 × 8 = (3 × 5) + (3 × __)
Break 8 into 5 + 3 → so blank is
3
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✔ All answers checked!
Final Answer:
Which property is shown?
- 4 × 6 = (4 × 5) + (4 × 1) → Distributive
- 5 × 7 = 7 × 5 → Commutative
- 4 × (2 × 5) = (4 × 2) × 5 → Associative
Missing numbers:
- 6 × 8 = (6 × 4) + (6 ×
4)
- 3 × 7 = 7 ×
3
- 9 × 2 =
2 × 9
- 4 × (2 × 6) = (
4 × 2) × 6
- 3 × (5 × 4) = (3 × 5) ×
4
- 9 × 7 = (9 × 5) + (
9 × 2)
- 2 × (6 × 5) = (
2 × 6) × 5
- 3 × 9 = (3 × 5) + (3 ×
4)
- 6 × 3 = 3 ×
6
- 3 × 8 = (3 × 5) + (3 ×
3)
Parent Tip: Review the logic above to help your child master the concept of printable distributive property of multiplication.
