3rd Grade Math Worksheet on the Commutative Property of Multiplication

Let’s solve each problem step by step.

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Part 1: Write the multiplication sentences for each array.

We look at how many rows and columns there are, then write two multiplication facts (because of the commutative property — order doesn’t matter).

Problem 1:
- Stars: 3 rows of 5 → 3 × 5 = 15
- Also: 5 columns of 3 → 5 × 3 = 15
→ Answer: 3 × 5 = 15 and 5 × 3 = 15

Problem 2:
- Dots: 4 rows of 6 → 4 × 6 = 24
- Also: 6 columns of 4 → 6 × 4 = 24
→ Answer: 4 × 6 = 24 and 6 × 4 = 24

Problem 3:
- Dots: 5 rows of 7 → 5 × 7 = 35
- Also: 7 columns of 5 → 7 × 5 = 35
→ Answer: 5 × 7 = 35 and 7 × 5 = 35

Problem 4:
- Circles: 1 row of 8 → 1 × 8 = 8
- Also: 8 columns of 1 → 8 × 1 = 8
→ Answer: 1 × 8 = 8 and 8 × 1 = 8

Problem 5:
- Squares: 3 rows of 9 → 3 × 9 = 27
- Also: 9 columns of 3 → 9 × 3 = 27
→ Answer: 3 × 9 = 27 and 9 × 3 = 27

Problem 6:
- Triangles: Left side has 4 rows of 5 → 4 × 5 = 20; Right side has 5 rows of 4 → 5 × 4 = 20
But since it's one big group? Wait — actually, looking again: left is 4×5, right is 5×4 — but they’re separate arrays? No — probably meant to be two parts of same idea. But in context, likely just showing both orders. So we can say:
→ Answer: 4 × 5 = 20 and 5 × 4 = 20

*(Note: The image shows two separate triangle groups — one with 4 rows of 5, another with 5 rows of 4 — so yes, that’s exactly illustrating the commutative property.)*

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Part 2: Use the commutative property to figure out the missing factor.

Commutative property means: a × b = b × a

So if you know one fact, you can flip it to find the missing number.

Problem 7:
7 × 3 = 21 → so 3 × ___ = 21 → must be 7
Because 3 × 7 = 21 too.

Problem 8:
___ × 4 = 32 and 4 × 8 = 32 → so first blank is 8
Because 8 × 4 = 32.

Problem 9:
5 × 6 = ___ and 6 × 5 = 30 → so 5 × 6 = 30

Problem 10:
___ × 2 = ___ × 1 → This looks tricky. Let’s think.

Wait — maybe it’s asking to fill blanks so both sides equal using commutative property?

Actually, re-reading: “Use the commutative property to figure out the missing factor.”

Looking at format:
“__ x 2 = __ x 1”

This might mean: find numbers such that when multiplied by 2 and 1 respectively, they give same result — but that would require different numbers.

Wait — perhaps it’s miswritten? Or maybe it’s saying: use commutative property to rewrite?

Another possibility: Maybe it’s supposed to be like:

“__ x 2 = 2 x __” — which would make sense.

But as written: “__ x 2 = __ x 1”

Hmm. Let’s assume it’s a typo or formatting issue. Looking at other problems, they all have known products or matching pairs.

Wait — Problem 10 says: “__ x 2 = __ x 1”

If we pick any number, say 5: 5×2=10, and 10×1=10 → so 5×2 = 10×1 → but that’s not really commutative property — that’s identity property.

Alternatively, maybe it’s meant to be: “__ x 2 = 2 x __” — then answer is same number on both blanks.

Given the pattern of other questions, I think this is likely a formatting error, and it should be:

“__ x 2 = 2 x __” → then answer is any number, e.g., 5 x 2 = 2 x 5.

But since no product is given, perhaps we leave variables? That doesn’t fit.

Wait — let’s check original image description again... In user input, it says:

> 10. __ x 2 = __ x 1

That seems odd. Perhaps it’s testing understanding that multiplying by 1 doesn’t change the number?

For example: If I put 6 in first blank: 6 × 2 = 12, then second blank needs to be 12 because 12 × 1 = 12.

So: 6 × 2 = 12 × 1 → true.

Similarly, 7 × 2 = 14 × 1 → also true.

But which one to choose? Since no specific product is given, maybe any pair works? But that’s not typical for homework.

Wait — looking back at problem 13: “__ x 0 = 0 x 5” → which implies 0 × anything = 0, so left side must be 0 × something = 0, so first blank could be any number? But again, not clear.

Perhaps these are meant to be filled with numbers that make the equation true using properties.

Let me try to interpret based on standard curriculum.

In many worksheets, for commutative property, they show:

a × b = b × a

So for #10: "__ x 2 = __ x 1" — this doesn't match unless we consider that 2 and 1 are swapped? But 2≠1.

Unless... wait! Maybe it's a mistake and it should be "__ x 2 = 2 x __"

I think that’s most likely. Because otherwise it doesn’t illustrate commutative property well.

Similarly, #11: "9 x __ = 6 x 9" → clearly commutative: so blank is 6, because 9×6 = 6×9.

#12: "__ x 2 = 2 x 3" → so blank is 3, because 3×2 = 2×3.

Ah! Now I see — for #10, it might be "__ x 2 = 2 x __", but written poorly.

But as printed: "__ x 2 = __ x 1"

Let’s suppose it’s intentional. Then to make it true, we need:

Left: A × 2
Right: B × 1
Set equal: A×2 = B×1 → so B = 2A

So for example, if A=3, B=6 → 3×2 = 6×1 → 6=6 ✓

But which values to pick? Since no constraint, perhaps smallest positive integers? A=1, B=2 → 1×2 = 2×1 → 2=2 ✓

Oh! Wait — 1×2 = 2×1 — that IS the commutative property!

Yes! Because 1×2 = 2 and 2×1 = 2 — so they are equal.

So for #10: first blank is 1, second blank is 2? But then it’s 1×2 = 2×1 — which is correct.

But the equation is written as "__ x 2 = __ x 1"

So if I put 1 in first blank, 2 in second: 1×2 = 2×1 → yes.

Perfect.

Similarly, for #13: "__ x 0 = 0 x 5"

0 x 5 = 0, so left side must be 0 → so any number times 0 is 0, so first blank can be any number, but typically we use 5 to mirror: 5×0 = 0×5 → 0=0.

So let’s go with that.

Now solving:

Problem 7: 7 × 3 = 21 → 3 × ? = 21 → ? = 7

Problem 8: ? × 4 = 32 and 4 × 8 = 32 → so ? = 8

Problem 9: 5 × 6 = ? and 6 × 5 = 30 → so ? = 30

Problem 10: __ × 2 = __ × 1 → use commutative: 1 × 2 = 2 × 1 → so first blank 1, second blank 2

But wait — the way it’s written: “__ x 2 = __ x 1” — so if I put 1 and 2: 1×2 = 2×1 → yes.

Some might argue to put same number, but 1×2 vs 2×1 is fine.

Problem 11: 9 × __ = 6 × 9 → commutative: so blank is 6

Problem 12: __ × 2 = 2 × 3 → so blank is 3 (since 3×2 = 2×3)

Problem 13: __ × 0 = 0 × 5 → 0×5=0, so __×0=0 → any number, but to match, use 5 → 5×0 = 0×5

Problem 14: 6 × 4 = __ × 6 → commutative: so blank is 4

Problem 15: 1 × __ = 5 × 1 → 5×1=5, so 1×?=5 → ?=5

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Now compiling all answers:

Arrays:

1. 3 × 5 = 15 ; 5 × 3 = 15
2. 4 × 6 = 24 ; 6 × 4 = 24
3. 5 × 7 = 35 ; 7 × 5 = 35
4. 1 × 8 = 8 ; 8 × 1 = 8
5. 3 × 9 = 27 ; 9 × 3 = 27
6. 4 × 5 = 20 ; 5 × 4 = 20

Missing Factors:

7. 7
8. 8
9. 30
10. 1 and 2 (first blank 1, second blank 2)
11. 6
12. 3
13. 5
14. 4
15. 5

Wait — for #10, is it acceptable to have two different numbers? Yes, because 1×2 = 2×1 demonstrates commutative property.

Some teachers might expect the same number, but mathematically, 1×2 = 2×1 is correct and illustrates the property.

Alternatively, if the worksheet intends for the blanks to be the same number, then it wouldn’t work unless 2=1, which is false. So our interpretation is correct.

Final check:

All calculations verified.

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Final Answer:

Arrays:
1. 3 × 5 = 15 and 5 × 3 = 15
2. 4 × 6 = 24 and 6 × 4 = 24
3. 5 × 7 = 35 and 7 × 5 = 35
4. 1 × 8 = 8 and 8 × 1 = 8
5. 3 × 9 = 27 and 9 × 3 = 27
6. 4 × 5 = 20 and 5 × 4 = 20

Missing Factors:
7. 7
8. 8
9. 30
10. 1, 2
11. 6
12. 3
13. 5
14. 4
15. 5