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**Chapter 1—Whole Numbers

1-6 Multiplying Whole Numbers

When you complete the work for this section, you should be able to: - Multiply small whole numbers without making any errors.
- Explain how to use a multiplication table.
- Explain when and how to use the
*carrying *principle in multiplication. |

**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.

Introduction to Multiplying Whole Numbers

**Definitions** The multiplication sign (x) indicates the multiplication operation. |

Here is the standard multiplication table. It shows the results of adding all possible combinations of two digits, from 0 x 0 = 0 through 9 x 9 = 81. Study the table carefully, and see if you can figure out how it works.

**Multiplication table**

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

- Factors separated by the x multiplication symbol. Example: 4 x 2 = 8
- Factors separated by a dot. Example: 4
**·** 2 = 8 - 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 = 6 In other words, 3 x 2 = 2 x 3 | |

Examples and Exercises

**Multiplication Facts** Use these interactive examples and exercises to strengthen your understanding and build your skills: | |

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.

Example 1

Example 2

When the product in the 1's column in greater than 9, **carry** the 10's digit of the product to the top of the 10's column of factors.

Example 3

Examples and Exercises

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

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 4

Examples and Exercises

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