Partial Products - Multiplication Strategies - Free Printable

This worksheet is teaching multiplication strategies, specifically the distributive property of multiplication over addition. This means breaking one of the numbers into parts (usually tens and ones), multiplying each part separately, and then adding the results.

The example given:
> 58 × 4 becomes 50 × 4 + 8 × 4

This works because:
- 58 = 50 + 8
- So, 58 × 4 = (50 + 8) × 4 = 50 × 4 + 8 × 4

We’ll apply this same strategy to each problem by breaking the first number (the multiplicand) into its tens and ones (or hundreds and tens if needed), then multiply each part by the second number (the multiplier).

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Let’s solve each one:

#### 1. 36 × 7 becomes ______

Break 36 into 30 + 6
→ 30 × 7 + 6 × 7

✔ Answer: 30 × 7 + 6 × 7

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#### 2. 82 × 4 becomes ______

Break 82 into 80 + 2
→ 80 × 4 + 2 × 4

✔ Answer: 80 × 4 + 2 × 4

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#### 3. 6 × 91 becomes ______

Here, the first number is small (6), but the second is large (91). The worksheet shows breaking the first number, so we follow that pattern — even though it’s less common, it still works mathematically.

Break 6 into... well, 6 is just 6. But we can think of it as 5 + 1 or 4 + 2, etc. However, since 91 is big, it’s more natural to break 91 — but the worksheet example breaks the *first* number.

Wait — let’s look again at the example: they broke 58 (the first number) in 58 × 4.

So for consistency, we should break 6.

But 6 is a single digit — how do we break it? We could break it as 5 + 1, or 4 + 2, etc. But that’s not helpful.

Actually, looking at the structure — the worksheet may intend for us to break the larger number, even if it’s the second one. But the instruction says “show another way to write each problem” — and the example breaks the first number.

Alternatively — maybe the worksheet allows flexibility? Let’s check the other problems.

Look at 10 × 8 — 10 is easy to break as 10 + 0, but that’s silly.

Actually, in standard distributive property teaching, we usually break the larger number — especially if it's two-digit.

But to stay consistent with the example — where they broke the first number — we should try to break the first number in each case.

So for 6 × 91, we break 6 → say, 5 + 1
→ 5 × 91 + 1 × 91

That works! It’s valid math.

✔ Answer: 5 × 91 + 1 × 91

*(Note: Some teachers might prefer breaking 91 into 90 + 1, making it 6 × 90 + 6 × 1 — which is also correct and often easier. But since the example breaks the first number, we’ll stick with breaking 6.)*

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#### 4. 10 × 8 becomes ______

Break 10 into 10 + 0? That’s trivial.

Or break it as 5 + 5? Or 9 + 1?

But 10 is already a round number. The most natural breakdown is 10 = 10 + 0, but that’s not useful.

Alternatively, break 10 as 5 + 5 → 5 × 8 + 5 × 8

Or 9 + 1 → 9 × 8 + 1 × 8

Either is fine. Since 10 is easy, any split works.

Let’s use 5 × 8 + 5 × 8 — symmetric and clear.

✔ Answer: 5 × 8 + 5 × 8

*(Alternatively, 9 × 8 + 1 × 8 is also fine — both are correct.)*

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#### 5. 33 × 2 becomes ______

Break 33 into 30 + 3
→ 30 × 2 + 3 × 2

✔ Answer: 30 × 2 + 3 × 2

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## ✔ Final Answers:

- 36 × 7 becomes → 30 × 7 + 6 × 7
- 82 × 4 becomes → 80 × 4 + 2 × 4
- 6 × 91 becomes → 5 × 91 + 1 × 91 *(or 6 × 90 + 6 × 1 if allowed to break second number — but following example, we break first)*
- 10 × 8 becomes → 5 × 8 + 5 × 8 *(or 9 × 8 + 1 × 8)*
- 33 × 2 becomes → 30 × 2 + 3 × 2

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## 💡 Teaching Tip:

This strategy helps students understand that multiplication can be broken down into simpler parts. It builds mental math skills and prepares them for algebra (where distributive property is essential).

You can always check your answer by computing both ways:

Example: 36 × 7 = 252
30×7 = 210, 6×7=42 → 210+42=252 ✓

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✔ All done! Let me know if you’d like to see the answers written in a boxed format or formatted for printing.