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

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.