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Unformatted text preview: operations, as the order in which we add or multiply does not change an answer. Example: 4+7=7+4 5•3=3•5 Subtraction and division are not commutative, as changing the order does change the answer. Example: 5–3≠3–5 20 ÷ 5 ≠ 5 ÷ 20 Addition and multiplication are associative, as we may group in any manner and arrive at the same answer. Example: (3 + 4) + 5 = 3 + (4 + 5) (3 • 4) • 5 = 3 • (4 • 5) Subtraction and division are not associative, as regrouping changes an answer. Example: (5 – 4) – 3 ≠ 5 – (4 – 3) (100 ÷ 20) ÷ 5 ≠ 100 ÷ (20 ÷ 5) Multiplication is distributive over addition. If a sum is to be multiplied by a number, we may multiply each addend by the given number and add the results. This will give the same answer as if we had added first and then multiplied. Example: 3(5 + 2 + 4) is either 15 + 6 + 12 or 3(11). The identity for addition is 0 since any number plus 0, or 0 plus any number, is equal to the given number. The identity for multiplication is 1 since any number times 1, or 1 times any number, is equal to the given number. There are no identity elements for subtraction or division. Although 5 – 0 = 5, 0 – 5 ≠ 5. Although 8 ÷ 1 = 8, 1 ÷ 8 ≠ 8. When several operations are involved in a single problem, parentheses are usually included to make the order of operations clear. If there are no parentheses, multiplication and division are always performed prior to addition and subtraction. Example: Find 5 • 4 + 6 ÷ 2 – 16 ÷ 4 Solution: The + and – signs indicate where groupings should begin and end. If we were to insert parentheses to clarify operations, we would have (5 · 4) + (6 ÷ 2) – (16 ÷ 4), giving 20 + 3 – 4 = 19. www.petersons.com 10 Chapter 1 Exercise 8
1. Find 8 + 4 ÷ 2 + 6 · 3  1. (A) 35 (B) 47 (C) 43 (D) 27 (E) 88 2. 16 ÷ 4 + 2 · 3 + 2  8 ÷ 2. (A) 6 (B) 8 (C) 2 (D) 4 (E) 10 3. Match each illustration in the lefthand column with the law it illustrates from the righthand column. a. 475 · 1 = 475 u. Identity for Addition b. 75 + 12 = 12 + 75 v. Associative Law of Addition...
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This note was uploaded on 08/15/2010 for the course MATH a4d4 taught by Professor Colon during the Spring '10 term at EmbryRiddle FL/AZ.
 Spring '10
 Colon
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