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Tuesday, September 6, 2022

Multiply | How do you Multeply? - Type and Examples


How do you Multiply? - Types and Examples
Lesson
Transcript Emily Oxford, Cori Hodges
Explore different multiplication methods. Learn how to multiply by using four types of multiplication and see examples of the differant ways to multiply. Updated: 02/07/2022





Table of Contents
  • Multiplication Methods
  • Types of Multiplication
  • Lesson Summary


Multiplication Methods

How do you multiply? Multiplication is a shortcut for adding a number to itself multiple times. Multiplication can be thought of as 'groups of'. For example, 5 x 3 simply means 5 groups of 3. The numbers being multiplied are called factors and the answer is called the product. There are many strategies for multiplying. Read to find out four different ways to multiply.


Types of Multiplication

There are many strategies for multiplying. In school, teachers may require certain methods to be practiced and used but it is important for each person to find the multiplication method that works well for them. All methods of multiplication can be used to accurately solve any multiplication problem, though some methods are better suited to certain types of problems. Keep reading to learn about four types of multiplication: addition method, long multiplication, grid method, and drawing lines. Some other strategies for multiplication include partial products, area model, and lattice.


Addition Method

The addition method for multiplying is simply repeatedly adding the same number to itself. For example, to solve 20 x 5, 20 would be added to itself 5 times.

20 + 20 + 20 + 20 + 20 = 100

This is a good strategy for small numbers or just a few groups of a large number. It also works well for multiples of ten because it is relatively easy to add those mentally. Using this strategy for multiplying large numbers becomes cumbersome and is prone to errors. Imagine trying to solve 473 x 75 by adding 473 to itself 75 times. This would be very inefficient and there is a high chance of making a mistake.

The addition method works because multiplication is simply a shortcut for adding equal groups.


Long Multiplication Method

Long multiplication is also known as the traditional algorithm. This is the method most commonly taught in the United States and is usually accepted as the best method. 


  1. Write the factors vertically, one above the other. Make sure the place values are lined up. The product with the most digits should go on top.
  2. Draw a horizontal line under the equation.
  3. Multiply the digit in the ones place of the bottom factor by the digit in the ones place of the top factor. In this case it is 2 x 4. The product goes in the ones place below the line.
  4. Multiply the digit in the ones place of the bottom factor by the digit in the tens place of the top factor. In this case it is 2 x 6 to get a product of 12. Since 12 is a two-digit number, the 1 must be 'carried' to the hundreds place.
  5. Multiply the digit in the ones place of the bottom factor by the digit in the hundreds place of the top factor. In this case it is 2 x 3 to get 6. Since the 1 was 'carried' to the hundred place, this must be added to get 7.
  6. Multiply the digit in the ones place of the bottom factor by the remaining digits in the top factor in order (thousands, ten thousands, etc.). If a product has two digits, the first digit should be 'carried' to the top of the next place. Now the first factor has been multiplied completely by the digit in the ones place of the second factor. In this case, 364 x 2 = 728.
  7. The same steps are repeated using the digit in the tens place of the second factor. The only difference is that since we are working in the tens place now, the product will begin in the tens place. Usually, a 0 is written as a placeholder in the ones place of the second product.
  8. Write the product of 364 x 30 under the first product.
  9. Add the two products together: 728 + 10,920 = 11,648.


As with the addition method, this strategy will work for any multiplication problem. There are fewer errors to be made using the long multiplication method than with repeated addition. However, this method is not fool-proof. The most common error is to start recording the second product in the ones place. Another common error is to forget to add any carried digits to the product.

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The long multiplication method, or traditional algorithm, works because of the distributive property. Each place value of the second factor is multiplied by the first factor. Then the products are added together to get a total product.

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