Partial Product Multiplication Worksheet for practicing multiplication using the partial products method.

Let's solve each of these multiplication problems using the partial product method. This method breaks down multiplication into smaller, more manageable parts by using place value.

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🔷 What is Partial Product Multiplication?

We break each number into its place values (hundreds, tens, ones), multiply each part separately, and then add the results.

For example:
To compute $ 617 \times 5 $:
- Break 617 into: 600 + 10 + 7
- Multiply each by 5:
- $ 600 \times 5 = 3000 $
- $ 10 \times 5 = 50 $
- $ 7 \times 5 = 35 $
- Add: $ 3000 + 50 + 35 = 3085 $

Now let’s solve each problem step-by-step.

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1) 617 × 5

Break 617 → 600 + 10 + 7

- $ 600 \times 5 = 3000 $
- $ 10 \times 5 = 50 $
- $ 7 \times 5 = 35 $

Add:
$$
\begin{align*}
&\phantom{+}3000 \\
&\phantom{+}+\phantom{0}50 \\
&\phantom{+}+\phantom{0}35 \\
&\overline{3085}
\end{align*}
$$

✔ Answer: 3085

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2) 529 × 8

Break 529 → 500 + 20 + 9

- $ 500 \times 8 = 4000 $
- $ 20 \times 8 = 160 $
- $ 9 \times 8 = 72 $

Add:
$$
\begin{align*}
&\phantom{+}4000 \\
&\phantom{+}+\phantom{0}160 \\
&\phantom{+}+\phantom{0}72 \\
&\overline{4232}
\end{align*}
$$

✔ Answer: 4232

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3) 825 × 6

Break 825 → 800 + 20 + 5

- $ 800 \times 6 = 4800 $
- $ 20 \times 6 = 120 $
- $ 5 \times 6 = 30 $

Add:
$$
\begin{align*}
&\phantom{+}4800 \\
&\phantom{+}+\phantom{0}120 \\
&\phantom{+}+\phantom{0}30 \\
&\overline{4950}
\end{align*}
$$

✔ Answer: 4950

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4) 137 × 3

Break 137 → 100 + 30 + 7

- $ 100 \times 3 = 300 $
- $ 30 \times 3 = 90 $
- $ 7 \times 3 = 21 $

Add:
$$
\begin{align*}
&\phantom{+}300 \\
&\phantom{+}+\phantom{0}90 \\
&\phantom{+}+\phantom{0}21 \\
&\overline{411}
\end{align*}
$$

✔ Answer: 411

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5) 764 × 4

Break 764 → 700 + 60 + 4

- $ 700 \times 4 = 2800 $
- $ 60 \times 4 = 240 $
- $ 4 \times 4 = 16 $

Add:
$$
\begin{align*}
&\phantom{+}2800 \\
&\phantom{+}+\phantom{0}240 \\
&\phantom{+}+\phantom{0}16 \\
&\overline{3056}
\end{align*}
$$

✔ Answer: 3056

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6) 238 × 9

Break 238 → 200 + 30 + 8

- $ 200 \times 9 = 1800 $
- $ 30 \times 9 = 270 $
- $ 8 \times 9 = 72 $

Add:
$$
\begin{align*}
&\phantom{+}1800 \\
&\phantom{+}+\phantom{0}270 \\
&\phantom{+}+\phantom{0}72 \\
&\overline{2142}
\end{align*}
$$

✔ Answer: 2142

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7) 231 × 7

Break 231 → 200 + 30 + 1

- $ 200 \times 7 = 1400 $
- $ 30 \times 7 = 210 $
- $ 1 \times 7 = 7 $

Add:
$$
\begin{align*}
&\phantom{+}1400 \\
&\phantom{+}+\phantom{0}210 \\
&\phantom{+}+\phantom{0}7 \\
&\overline{1617}
\end{align*}
$$

✔ Answer: 1617

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8) 953 × 8

Break 953 → 900 + 50 + 3

- $ 900 \times 8 = 7200 $
- $ 50 \times 8 = 400 $
- $ 3 \times 8 = 24 $

Add:
$$
\begin{align*}
&\phantom{+}7200 \\
&\phantom{+}+\phantom{0}400 \\
&\phantom{+}+\phantom{0}24 \\
&\overline{7624}
\end{align*}
$$

✔ Answer: 7624

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9) 337 × 2

Break 337 → 300 + 30 + 7

- $ 300 \times 2 = 600 $
- $ 30 \times 2 = 60 $
- $ 7 \times 2 = 14 $

Add:
$$
\begin{align*}
&\phantom{+}600 \\
&\phantom{+}+\phantom{0}60 \\
&\phantom{+}+\phantom{0}14 \\
&\overline{674}
\end{align*}
$$

✔ Answer: 674

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) 617 × 5 | 3085 |
| 2) 529 × 8 | 4232 |
| 3) 825 × 6 | 4950 |
| 4) 137 × 3 | 411 |
| 5) 764 × 4 | 3056 |
| 6) 238 × 9 | 2142 |
| 7) 231 × 7 | 1617 |
| 8) 953 × 8 | 7624 |
| 9) 337 × 2 | 674 |

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📌 Summary:

The partial product method helps students understand how multiplication works by breaking numbers apart based on place value. It reinforces understanding of place value and builds a foundation for multi-digit multiplication.

Let me know if you'd like this formatted as a printable worksheet or need visual diagrams!