Partial products provide a structured way to multiply a two-digit number by a one-digit number by breaking the larger number into its tens and ones, multiplying each part separately, and then adding these partial products together. This approach mirrors the area model method, but does not include drawing the square or rectangle.
Here's a step-by-step explanation:
- Break down the two-digit number: Separate the two-digit number into its tens and ones components. For instance, 56 becomes 50 (tens place) and 6 (ones place).
- Multiply each part: Multiply the one-digit number by both the tens and ones components separately, creating partial products. Using the reference, let's say you are multiplying 56 by 3. You would calculate:
- 3 x 50 = 150
- 3 x 6 = 18
- Add the partial products: Add the products you just obtained. In this example, 150 + 18 = 168.
Here’s an example in a table format to illustrate how you would apply partial products to solve 56 x 3:
| Step | Calculation | Partial Product |
|---|---|---|
| Multiply tens | 3 x 50 | 150 |
| Multiply ones | 3 x 6 | 18 |
| Add Partial Products | 150 + 18 | 168 |
Therefore, using partial products to multiply 56 by 3, the answer is 168. As the reference points out, the method mirrors the area model but without the visual aid of the shape. You are essentially calculating smaller parts and adding these to find the larger solution.
