Fundamentals of Mathematics, 2008a

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488 CHAPTER 8. TECHNIQUES OF ESTIMATION 8.4.2 The Distributive Property Distributive Property The distributive property is a characteristic of numbers that involves both addition and multiplication. It is used often in algebra, and we can use it now to obtain exact results for a multiplication. Suppose we wish to compute 3 (2 + 5). We can proceed in either of two ways, one way which is known to us already (the order of operations), and a new way (the distributive property). 1. Compute 3 (2 + 5) using the order of operations. 3 (2 + 5) Operate inside the parentheses rst: 2 + 5 = 7. 3 (2 + 5) = 3 · 7 Now multiply 3 and 7. 3 (2 + 5) = 3 · 7 = 21 Thus, 3 (2 + 5) = 21. 2. Compute 3 (2 + 5) using the distributive property. We know that multiplication describes repeated addition. Thus, 3 (2 + 5) = 2 + 5 + 2 + 5 + 2 + 5 } {{ } 2 + 5 appears 3 times = 2 + 2 + 2 + 5 + 5 + 5 (by the commutative property of addition) = 3 · 2 + 3 · 5 (since multiplication describes repeated addition) = 6 + 15 = 21 Thus, 3 (2 + 5) = 21. Let's look again at this use of the distributive property. 3 (2 + 5) = 2 + 5 + 2 + 5 + 2 + 5 } {{ } 2 + 5 appears 3 times 3 (2 + 5) = 2 + 2 + 2 } {{ } 2 appears 3 times + 5 + 5 + 5 } {{ } 5 appears 3 times The 3 has been distributed to the 2 and 5. This is the distributive property. We distribute the factor to each addend in the parentheses. The distributive property works for both sums and dierences. Available for free at Connexions
489 8.4.2.1 Sample Set A Example 8.15 Using the order of operations, we get 4 (6 + 2) = 4 · 8 = 32 Example 8.16 Using the order of operations, we get 8 (9 + 6) = 8 · 15 = 120 Example 8.17 Example 8.18 8.4.2.2 Practice Set A Use the distributive property to compute each value. Exercise 8.4.1 (Solution on p. 507.) 6 (8 + 4) Exercise 8.4.2 (Solution on p. 507.) 4 (4 + 7) Exercise 8.4.3 (Solution on p. 507.) 8 (2 + 9) Exercise 8.4.4 (Solution on p. 507.) 12 (10 + 3) Exercise 8.4.5 (Solution on p. 507.) 6 (11 − 3) Exercise 8.4.6 (Solution on p. 507.) 8 (9 − 7) Exercise 8.4.7 (Solution on p. 507.) 15 (30 − 8) Available for free at Connexions
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iv 4.10 Prociency Exam . . . . . .
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vi Available for free at Connexions
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2 • Section Exercises • Exercis
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4 Addition and Subtraction of Fract
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10 CHAPTER 1. ADDITION AND SUBTRACT
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100 CHAPTER 2. MULTIPLICATION AND D
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154 CHAPTER 3. 3.2 Exponents and Ro
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156 3.2.4 Roots CHAPTER 3. EXPONENT
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158 CHAPTER 3. EXPONENTS, ROOTS, AN
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164 3.3.3.1 Sample Set B CHAPTER 3.
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176 3.4.6.1 Sample Set C CHAPTER 3.
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186 3.6.3.2 Practice Set B CHAPTER
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188 3.6.5.2 Practice Set C CHAPTER
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200 CHAPTER 3. Solutions to Exercis
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214 CHAPTER 4. INTRODUCTION TO FRAC
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220 4.2.6 Exercises CHAPTER 4. INTR
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226 Thus, CHAPTER 4. INTRODUCTION T
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236 4.4.3.1.1 Sample Set B CHAPTER
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238 CHAPTER 4. 4.4.4 Raising Fracti
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250 √ 9 100 = 3 10 Example 4.45 4
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262 CHAPTER 4. 4.7.2 Multiplication
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268 CHAPTER 4. 4.8 Summary of Key C
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278 CHAPTER 4. Solutions to Exercis
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296 CHAPTER 5. ADDITION AND SUBTRAC
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304 5.3.4 Exercises CHAPTER 5. ADDI
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340 CHAPTER 6. DECIMALS • underst
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344 CHAPTER 6. DECIMALS 0.17 6.2.5.
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346 CHAPTER 6. DECIMALS 6.2.6.1 Exe
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348 CHAPTER 6. DECIMALS 4 + .006 1
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352 CHAPTER 6. DECIMALS 6.4.3 Exerc
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354 CHAPTER 6. DECIMALS Exercise 6.
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356 CHAPTER 6. DECIMALS 841.0056 47
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358 CHAPTER 6. DECIMALS The sum is
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362 CHAPTER 6. DECIMALS Thus, 6.5
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364 CHAPTER 6. DECIMALS Table 6.15
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366 CHAPTER 6. DECIMALS 6.6.6.1 Sam
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372 CHAPTER 6. DECIMALS 6.7.3 A Met
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374 CHAPTER 6. DECIMALS Method of D
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378 CHAPTER 6. DECIMALS 816.241 10)
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382 CHAPTER 6. DECIMALS Table 6.29
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384 CHAPTER 6. DECIMALS Repeating D
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386 CHAPTER 6. DECIMALS .1818 11)2.
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390 CHAPTER 6. DECIMALS .125 8)1.00
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396 CHAPTER 6. DECIMALS 6.10.3 Exer
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398 CHAPTER 6. DECIMALS 6.11 Summar
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400 CHAPTER 6. DECIMALS 6.12.1.2 Co
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404 CHAPTER 6. DECIMALS Solutions t
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406 CHAPTER 6. DECIMALS Solution to
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420 CHAPTER 7. RATIOS AND RATES 7.2
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422 CHAPTER 7. RATIOS AND RATES are
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434 CHAPTER 7. RATIOS AND RATES Exa
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538 CHAPTER 9. MEASUREMENT AND GEOM
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578 CHAPTER 10. SIGNED NUMBERS 10.2
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580 CHAPTER 10. SIGNED NUMBERS Some
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594 CHAPTER 10. SIGNED NUMBERS Thus
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600 CHAPTER 10. SIGNED NUMBERS Exam
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632 CHAPTER 11. ALGEBRAIC EXPRESSIO
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694 INDEX Index of Keywords and Ter
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696 INDEX Ÿ 3.4(172), Ÿ 3.5(180),
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698 INDEX reading, Ÿ 1.3(15) readi
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700 ATTRIBUTIONS Module: "Addition
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702 ATTRIBUTIONS Module: "Multiplic
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704 ATTRIBUTIONS Module: "Introduct
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706 ATTRIBUTIONS Module: "Addition
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708 ATTRIBUTIONS Module: "Decimals:
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710 ATTRIBUTIONS Module: "Ratios an
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716 ATTRIBUTIONS Module: "Algebraic
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Fundamentals of Mathematics Fundame
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Fundamentals of Mathematics, 2008a

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