What is Multiplication? – Definition, Symbol and Examples

How To Do Multiplication?

There are various methods for performing multiplication. Each method offers a unique approach to solving multiplication problems and can be applied based on the given numbers and the preferred approach. One of the primary methods involves multiplying digits individually and then adding the results, a process often referred to as multiplication without regrouping. However, when dealing with multi-digit numbers, regrouping may be necessary to ensure accuracy. Additionally, leveraging the multiplication table, a grid displaying the products of multiplying numbers from 1 to 10 (or higher), can greatly aid in memorizing multiplication facts and facilitating quicker calculations. Understanding these fundamental principles and tools lays the groundwork for mastering various methods of multiplication, ensuring efficiency and accuracy in mathematical computations.

Multiplication without Regrouping

Multiplication with Regrouping

When multiplying more than two numbers with regrouping, particularly when dealing with numbers resulting in a two-digit product, we encounter the need to carry over to the next higher place value. Let’s explore this concept further using an illustrative example.

Let’s explore the process of multiplying 3826 by 7, a scenario where we need to regroup and carry over to the next higher place value:

Step 1: We start with the ones place, multiplying 7 by 6, resulting in 42 ones. This translates to 4 tens and 2 ones. We carry over the 4 tens to the tens column.

Step 2: Moving to the tens place, we multiply 7 by 2, resulting in 14 tens. Adding the carry-over of 4 from the previous step, we get 18 tens. We carry over the 1 to the hundreds column.

Step 3: Continuing to the hundreds place, we multiply 7 by 8, yielding 56 hundreds. Adding the carry-over from the previous step (1), we get 57 hundreds. We carry over the 5 to the thousands column.

Step 4: Proceeding to the thousands place, we multiply 7 by 3, resulting in 21 thousands. Adding the carry-over from the previous step (5), we get 26 thousands.

Step 5: Therefore, the product of 3826 × 7 equals 26782.

In this example, each step involves multiplying 7 by the corresponding digit of 3826 and appropriately carrying over any excess to the next higher place value. This systematic approach ensures an accurate calculation of the final product, providing a clear demonstration of multiplication with regrouping.

Multiplication with Number Line

Multiplying on a number line is a way to use a visual tool—a line marked with numbers—to understand multiplication better. Imagine the line starts at zero and stretches to the right. Each number on the line represents a point. To multiply a number, like 3, by another number, like 4, on the number line, we make jumps of the same size (in this case, 3) a certain number of times (in this case, 4). Each jump represents one multiplication. So, if we jump 3 units four times, as represented in the number line below, we’ll land at the point that shows the answer, which is 12. This method helps us see how multiplication works step by step.