Section 1.5 Multiplication of Whole Numbers and Area 39 Multiplication of Whole Numbers and Area Section 1.5 1. Introduction to Multiplication Suppose that Carmen buys three cartons of eggs to prepare a large family brunch. If there are 12 eggs per carton, then the total number of eggs can be found by adding three 12s. When each addend in a sum is the same, we have what is called repeated addition. Repeated addition is also called multiplication. We use the multiplication sign to express repeated addition more concisely. 12 12 12 is equal to 3 12 The expression 3 12 is read “3 times 12” to signify that the number 12 is added 3 times. The numbers 3 and 12 are called factors, and the result, 36, is called the product. The symbol may also be used to denote multiplication such as in the expression 3 12 36. Two factors written adjacent to each other with no other operator between them also implies multiplication. The quantity 2y, for example, is understood to be 2 times y. If we use this notation to multiply two numbers, parentheses are used to group one or both factors. For example: 31122 36 13212 36 and 132 1122 36 all represent the product of 3 and 12. 12 eggs 12 eggs 12 eggs 36 eggs Concepts 1. Introduction to Multiplication 2. Properties of Multiplication 3. Multiplying Many-Digit Whole Numbers 4. Estimating Products by Rounding 5. Translations and Applications Involving Multiplication 6. Area of a Rectangle Concept Connections 1. How can multiplication be used to compute the sum 4444444? Answers 1. 7 4 2. Factors: 3 and 11; product: 33 3. Factors: 2, 5, and 8; product: 80 TIP: In the expression 3(12), the parentheses are necessary because two adjacent factors written together with no grouping symbol would look like the number 312. The products of one-digit numbers such as 4 5 20 and 2 7 14 are basic facts. All products of one-digit numbers should be memorized (see Exercise 6). Identifying Factors and Products Example 1 Identify the factors and the product. a. 6 3 18 b. 5 2 7 70 Solution: a. Factors: 6, 3; product: 18 b. Factors: 5, 2, 7; product: 70 2. Properties of Multiplication Recall from Section 1.2 that the order in which two numbers are added does not affect the result. The same is true for multiplication. This is stated formally as the commutative property of multiplication. Skill Practice Identify the factors and the product. 2. 3 11 33 3. 2 5 8 80
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