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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 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.

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   facts
 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 = 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:

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