Lesson 6Multiplying Whole Numbers

Multiplication is streamlined version of   addition. Suppose you have four cartons of eggs and each carton contains a dozen (12) eggs. How many eggs do you have here?

• You could open all the cartons and count each egg individually:  one egg, two eggs, three eggs, ... and so on.
• Or you can add four 12s: 12 eggs + 12 eggs + 12 eggs + 12 eggs  = 48 eggs
• Or you can multiply: 12 eggs/carton times 4 cartons = 48 eggs

It is clearly simpler and faster to use the multiplication approach.

Topic 1
Introduction to Multiplying Whole Numbers

Definitions

 The number being multiplied is called the multiplicand. The number to be multiplied by is called the multiplier. The result of the multiplication is called the product. Taken together, the multiplicand and multiplier are known as factors of the multiplication operation. The multiplication sign (x) indicates the multiplication operation.

Multiplication problems are sometimes written in a horizontal form such as:

3 x 5 = 15

This form is called a number sentence. It is read as, "Three times five equals fifteen."

• The multiplication sign (x) indicates the multiplication operation.
• The equal sign (=) expresses the equality of the two parts of the sentence.

There are three different symbols for indicating the multiplication operation in the horizontal form::

1. Factors separated by the x multiplication symbol.                          Example:  4 x 2 = 8
2. Factors separated by a dot.                                                        Example:   4 · 2 = 8
3. Each factor enclosed in parentheses with no symbol between.        Example:   ( 4 )( 2 ) = 8

Notes

 Any value multiplied by one is equal to the original value. Example: 5  x 1 = 5 Zero multiplied by any value is equal to zero. Example:  0 x 2 = 0 Factors may be multiplied in any order. (This is known as the commutative law of multiplication) Example:  3 x 2 = 6 and 2 x 3 = 6In other words, 3 x 2 = 2 x 3

Topic 2
Multiplying With a One-Digit Multiplier

Here is an example of a multiplication problem that has a one-digit multiplier:

52
x   4

First, multiply the 4 times the 2.
Technically speaking this means you should first multiply the multiplier by the 1s digit in the multiplicand

52
x   4
8

Then multiply the 4 times the 5.
Technically speaking, this means you should then multiply the multiplier by the10s digit in the multiplicand.

52
x   4
208

The job is done when you have multiplied the multiplier by each of the digits in the multiplicand--one at a time, and from right to left.

 Important Note from the Author It is likely that you have already mastered the procedures for multiplying whole numbers, and have applied them successfully for a long time. However, this review of multiplication might not be a total waste of your time, because it points out some definitions and underlying principles that need to be more clearly recognized in today's workplaces and learning environments.

Topic 3
Multiplying With a Multiplier That Has More Than One Digit

 When when the multiplier has more than one digit, you need to work with partial products.

Example

Use these interactive examples and exercises to strengthen your understanding and build your skills:

 If would like to see more examples or work on a wider range of exercises, you can go to a more detailed tutorial .