An engaging math worksheet teaching multiplication properties with examples and exercises.

Let’s solve each “Try these” problem step by step.

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First section: Commutative Property of Multiplication

This means you can switch the order of numbers when multiplying, and the answer stays the same.

Problem 1:
9 x 3 = ___ x ___
We know 9 x 3 = 27.
Using commutative property, we can write it as 3 x 9.
So:
9 x 3 = 3 x 9
Then:
27 = 27 (since 3 x 9 also equals 27)

Problem 2:
___ x ___ = 10 x 13
We know 10 x 13 = 130.
Using commutative property, we can switch the order: 13 x 10.
So:
13 x 10 = 10 x 13
Then:
130 = 130

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Second section: Associative Property of Multiplication

This means when multiplying three numbers, you can group them in different ways — the answer is still the same.

Problem 1:
6 x (2 x 3) = ________
First, do inside the parentheses: 2 x 3 = 6
Then: 6 x 6 = 36

Next line says:
6 x 6 = ________ → that’s also 36

Then:
36 = ________ → just confirming, so 36

But wait — let’s check if they want us to regroup using associative property.

Original: 6 x (2 x 3)
Associative property lets us rewrite as: (6 x 2) x 3

Let’s try that:

(6 x 2) x 3 = 12 x 3 = 36

Same answer! So either way works.

The blank after “6 x (2 x 3) =” should be filled with the result: 36

Then “6 x 6 =” → 36

Then “36 =” → 36

Actually, looking at the format, maybe they want the regrouped version?

Wait — look at the example above:

Example 1:
5 x (3 x 2) = (5 x 3) x 2
→ They showed both sides equal.

So for this one:

6 x (2 x 3) = (6 x 2) x 3
= 12 x 3
= 36

But the worksheet has:

“6 x (2 x 3) = ________”
then next line: “6 x 6 = ________”
then “36 = ________”

Hmm — perhaps they’re walking through the calculation step by step.

Step 1: 6 x (2 x 3) → first calculate 2 x 3 = 6 → so becomes 6 x 6
Step 2: 6 x 6 = 36
Step 3: 36 = 36

So blanks are:

6 x (2 x 3) = 36
6 x 6 = 36
36 = 36

But that seems redundant. Maybe they meant to show the associative grouping?

Looking again at the example:

In Example 2 under Associative:

10 x (4 x 2) = (10 x 4) x 2
→ Then calculated both sides.

So for Try These #1:

They might expect:

6 x (2 x 3) = (6 x 2) x 3
Then compute right side: (6 x 2) x 3 = 12 x 3 = 36

But the worksheet doesn’t have a blank for the regrouped form — it goes straight to “6 x 6 =”

Ah — I think they’re showing the steps of evaluating left to right.

So:

6 x (2 x 3) → first do 2 x 3 = 6 → now expression is 6 x 6
Then 6 x 6 = 36
Then 36 = 36

So fill in:

6 x (2 x 3) = 36
6 x 6 = 36
36 = 36

That matches the pattern in the examples.

Now Problem 2:

________ = (9 x 5) x 6
Then: ________ = 45 x 6
Then: ________ = 270

We need to find what goes on the left that equals (9 x 5) x 6.

Using associative property, we can regroup: 9 x (5 x 6)

Check:
(9 x 5) x 6 = 45 x 6 = 270
9 x (5 x 6) = 9 x 30 = 270 → same!

So the first blank should be: 9 x (5 x 6)

Then next line: (9 x 5) x 6 = 45 x 6 → so blank is 45 x 6? Wait no — the line says:

“________ = (9 x 5) x 6” → so left side is our regrouped version: 9 x (5 x 6)

Then next line: “________ = 45 x 6” → this is showing the intermediate step: since (9 x 5) = 45, then it becomes 45 x 6 → so blank is (9 x 5) x 6? But that’s already on the right.

Wait — let’s read carefully:

It says:

2. _______________ = (9 x 5) x 6
_______________ = 45 x 6
_______________ = 270

So first blank: something equal to (9 x 5) x 6 → use associative property → 9 x (5 x 6)

Second blank: now evaluate (9 x 5) x 6 → which is 45 x 6 → so the left side here is probably meant to be the same expression evaluated step by step.

Actually, looking at the example above:

Example 2:
10 x (4 x 2) = (10 x 4) x 2
10 x 8 = 40 x 2
80 = 80

So they wrote the original, then the regrouped, then computed both sides.

For this problem:

They start with the regrouped version on the right: (9 x 5) x 6

So left side should be the other grouping: 9 x (5 x 6)

Then next line: they compute inside: 9 x 5 = 45, so (9 x 5) x 6 becomes 45 x 6 → so the left side of second line should be the value of the first expression? Or same structure?

Actually, in the example, they did:

Left: 10 x (4 x 2) → became 10 x 8
Right: (10 x 4) x 2 → became 40 x 2

Here, they have only one side given initially.

Perhaps:

First blank: 9 x (5 x 6) [using associative property]

Then, since 5 x 6 = 30, so 9 x 30 = 270 — but they don’t go that route.

They go: (9 x 5) x 6 = 45 x 6 = 270

So for the blanks:

Line 1: 9 x (5 x 6) = (9 x 5) x 6
Line 2: 9 x 30 = 45 x 6? No, that doesn't match.

Wait — in the example, they kept the structure parallel.

Here, they might mean:

Start with 9 x (5 x 6) = (9 x 5) x 6
Then compute left: 9 x 30 = ?
Compute right: 45 x 6 = ?

But the worksheet writes:

“________ = (9 x 5) x 6”
“________ = 45 x 6”
“________ = 270”

So likely:

First blank: 9 x (5 x 6)
Second blank: 9 x 30 (because 5 x 6 = 30)
Third blank: 270

But then 9 x 30 = 270, and 45 x 6 = 270, so it matches.

Alternatively, they might want:

First blank: 9 x (5 x 6)
Second blank: (9 x 5) x 6 → but that's already on the right.

I think the intended flow is:

Use associative property to write an equivalent expression: 9 x (5 x 6) = (9 x 5) x 6

Then, evaluate the right side step by step:

(9 x 5) x 6 = 45 x 6
45 x 6 = 270

So the blanks on the left are meant to mirror the evaluation.

Thus:

First line: 9 x (5 x 6) = (9 x 5) x 6
Second line: 9 x 30 = 45 x 6 ? But 9 x 30 is not written; instead, they have "________ = 45 x 6"

Perhaps the second blank is the numerical value before final multiplication? This is confusing.

Look back at the commutative section — they had:

For 9 x 3 = __ x __
Then 27 = ____

So they computed the product.

Similarly here, for associative:

After writing the equality, they compute the values.

In Example 2:

10 x (4 x 2) = (10 x 4) x 2
10 x 8 = 40 x 2
80 = 80

So they replaced the grouped parts with their products.

Applying that here:

Given: ________ = (9 x 5) x 6

We write the associative counterpart: 9 x (5 x 6)

Then, compute inside the groups:

Left: 5 x 6 = 30, so 9 x 30
Right: 9 x 5 = 45, so 45 x 6

So:

9 x (5 x 6) = (9 x 5) x 6
becomes
9 x 30 = 45 x 6
then
270 = 270

Perfect! That matches the example format.

So blanks:

First: 9 x (5 x 6)
Second: 9 x 30
Third: 270

Yes.

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Now, compiling all answers:

Commutative Section:

1. 9 x 3 = 3 x 9
27 = 27

2. 13 x 10 = 10 x 13
130 = 130

Associative Section:

1. 6 x (2 x 3) = 36
6 x 6 = 36
36 = 36

Wait — but according to the example, they showed the regrouping. In the "Try these" for associative, problem 1 doesn't have a regrouping blank — it starts with the expression and then computes.

In the example, they had two expressions set equal, then computed both.

Here, for problem 1, it's written as:

6 x (2 x 3) = ________
6 x 6 = ________
36 = ________

So they are computing step by step without showing the regrouped form explicitly in the blanks.

Whereas in problem 2, they have the regrouped form on the right, so we supply the left.

To be consistent with the worksheet's presentation:

For problem 1, since it's "6 x (2 x 3) = ____", and then they break it down, we fill the results:

- First blank: the result of 6 x (2 x 3) = 6 x 6 = 36 → so 36
- Second blank: 6 x 6 = 36
- Third blank: 36 = 36

For problem 2:

- First blank: the associative counterpart: 9 x (5 x 6)
- Second blank: after computing 5 x 6 = 30, so 9 x 30
- Third blank: the final product: 270

And indeed, 9 x 30 = 270, and 45 x 6 = 270, so it checks out.

Final verification:

Commutative 1: 9x3=27, 3x9=27 ✓
Commutative 2: 13x10=130, 10x13=130 ✓
Associative 1: 6x(2x3)=6x6=36 ✓
Associative 2: 9x(5x6)=9x30=270, (9x5)x6=45x6=270 ✓

All correct.

Final Answer:

Commutative Property Try These:

1. 9 x 3 = 3 x 9
27 = 27

2. 13 x 10 = 10 x 13
130 = 130

Associative Property Try These:

1. 6 x (2 x 3) = 36
6 x 6 = 36
36 = 36

2. 9 x (5 x 6) = (9 x 5) x 6
9 x 30 = 45 x 6
270 = 270