## 6 Questions

What is the main difference between multiplying four-digit numbers by one-digit numbers and two-digit numbers?

The number of digits and columns involved

When multiplying a four-digit number by a one-digit number, how are the products calculated?

By multiplying each digit of the one-digit number by the corresponding digit of the four-digit number

Which method is recommended for multiplying four-digit numbers by two-digit numbers?

Partial products method

What is the final step in the process of multiplying four-digit numbers by one-digit numbers?

Add up the products, carrying over to the next column as needed

In multiplying 4,321 by 7, what is the product of 3 * 7?

21

Why is it helpful to use the grid method when multiplying four-digit numbers by two-digit numbers?

To manage more digits and columns effectively

## Study Notes

## Multiplying Four-Digit Numbers by One- and Two-Digit Numbers

When performing arithmetic operations with larger numbers, such as multiplying four-digit numbers by one- and two-digit numbers, it's essential to understand the underlying processes and techniques. In this article, we'll examine how to approach these calculations effectively and efficiently.

### Multiplying Four-Digit Numbers by One-Digit Numbers

Multiplying four-digit numbers by one-digit numbers is, in concept, similar to multiplying two-digit numbers. The main difference is the length of the numbers involved.

Step 1: Write the four-digit number horizontally and align the one-digit number to the right of the rightmost digit.

Step 2: Multiply each digit of the one-digit number by the corresponding digit of the four-digit number.

Step 3: Add up the products, carrying over to the next column as needed.

Step 4: Write the result in the standard four-digit format.

For example, let's multiply 4,321 by 7:

```
4321 * 7
7 * 1 = 7
4 * 7 + 3 * 70 = 28 + 210 = 238
3 * 7 + 2 * 70 = 21 + 140 = 161
2 * 7 + 1 * 70 = 14 + 70 = 84
```

Result: 23,816

### Multiplying Four-Digit Numbers by Two-Digit Numbers

Multiplying four-digit numbers by two-digit numbers involves more digits and columns, so it's helpful to use a method known as the **partial products** or **grid method**.

Step 1: Write the four-digit number horizontally and align the two-digit number beneath the rightmost digit.

Step 2: Multiply each digit of the two-digit number by the corresponding digit of the four-digit number.

Step 3: Write the results in the grid, separating the digits of each product by a vertical line.

Step 4: Add up the digits in each row of the grid, carrying over to the next row as needed.

Step 5: Write the result in the standard four-digit format.

For example, let's multiply 4,321 by 12:

```
4321 * 12
1 * 2 + 3 * 10 = 2 + 30 = 32
4 * 1 + 3 * 100 = 4 + 300 = 304
3 * 1 + 2 * 100 = 3 + 200 = 203
2 * 2 + 1 * 1000 = 4 + 1000 = 1004
```

Grid:

```
32 | 304
-----+-------
2 | 1004
```

Step 4:

304 + 2 = 306 1004 + 10 = 1014

Result: 306,1014

By following these steps, you'll be able to efficiently multiply four-digit numbers by one- and two-digit numbers.

Learn how to multiply four-digit numbers by one- and two-digit numbers efficiently. Understand the steps involved in both methods, including aligning numbers, multiplying digits, and carrying over. Practice with examples for better comprehension.

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