Transcript Lesson 35
Chapter 7 Lesson 35 Testing for Divisibility Lesson 35 WO.17 Use long division to determine if one number is divisible by another. WO.23 Use divisibility rules to determine if a number is divisible by 2, 3, 5, or 9 and understand the justification for these rules. Slide 1 Objectives • Understand and use the divisibility rules for 2, 3, 5 and 9. Lesson 35 Slide 2 Remember from Before • What is a factor? • What is a multiple? • How are multiples and factors related? Lesson 35 Slide 3 Get Your Brain in Gear 1. Use mental math to divide 369 by 9. 41 2. Use mental math to divide 85 by 5. 17 Lesson 35 Slide 4 Multiples of 2. All multiples of 2 can be expressed as the repeated addition of 2. 10 = 2 + 2 + 2 + 2 + 2 Lesson 35 Slide 5 Is 36 divisible by 2? Let’s try to express 36 as repeated addition of 2. Lesson 35 Slide 6 Let’s try 21. We have a unit square left over. This means that 21 is not divisible by 2. Lesson 35 Slide 7 What about larger powers of 10? 100 = 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 100 = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+ 2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+ 2+2+2+2+2+2 Since all the powers of ten are multiples of 10, they also are all multiples of 2. Lesson 35 Slide 8 Divisible by 2 rule: If a whole number ends in 0, 2, 4, 6 or 8, then the number is divisible by 2. Otherwise it is not divisible by 2. Lesson 35 Slide 9 Applying the rule, is the following number divisible by 2? 47,297,593 0 The digit in the 10 place is 3, and 3 is not divisible by 2. Lesson 35 Slide 10 Check for Understanding 1. Determine whether the number is divisible by 2. a. 23 Not divisible by 2. b. 78 Divisible by 2. c. 504 Divisible by 2. d. 8,241 Not divisible by 2. e. 6,794 Divisible by 2. Lesson 35 Slide 11 Divisibility by 5 Is 10 divisible by 5? 10 = 5 + 5 Since 10 is divisible by 5, so are all the larger powers of 10. Lesson 35 Slide 12 Divisibility by 5 rule: If a whole number ends in 0 or 5, then the number is divisible by 5. Otherwise it is not divisible by 5. According to this rule, would 365 be divisible by 5? Lesson 35 Slide 13 Check for Understanding 2. Determine if the number is divisible by 5. a. 70 Divisible by 5. b. 553 Not divisible by 5. c. 10003 Not divisible by 5. d. 72865 Divisible by 5. e. 8003000 Divisible by 5. Lesson 35 Slide 14 Divisibility by 9 Since 10 is not divisible by 9, we can’t simply check the last digit. Let’s see if 27 is divisible by 9: 27 = 9 + 9 + 9 Lesson 35 Slide 15 Is 52 divisible by 9? When testing for divisibility by 9, we see that each 10 leaves 1 left over, so we can treat each 10 as a 1. Since 5 + 2 equals 7, we conclude 52 is not divisible by 9. Lesson 35 Slide 16 Is 63 divisible by 9? Remember, each 10 is treated as a 1. Since 6 + 3 equals 9, this means 63 is divisible by 9. Is 85 divisible by 9? How do you know? Lesson 35 Slide 17 What about larger numbers? Is 756 divisible by 9? 7 + 5 + 6 = 18 Since 18 is divisible by 9, we conclude that 756 is also divisible by 9. Lesson 35 Slide 18 If the digits of a whole number add up to a multiple of 9, then the number is divisible by 9. Otherwise it is not divisible by 9. Lesson 35 Slide 19 Check for Understanding 3. Determine whether the number is divisible by 9. a. 73 Not divisible by 9. b. 108 Divisible by 9. c. 7812 Divisible by 9. d. 6873 Not divisible by 9. e. 98016 Not divisible by 9. Lesson 35 Slide 20 Let’s develop a test for divisibility by 3. Let’s check if 42 is divisible by 3. Lesson 35 Slide 21 If the digits of a whole number add up to a multiple of 3, then the number is divisible by 3. Otherwise it is not divisible by 3. Is 592 divisible by 3? 5 + 9 + 2 = 16 1+6= 7 Lesson 35 Slide 22 We can verify that 592 is not divisible by 3 using long division: Lesson 35 Slide 23 Check for Understanding 4. Test whether the number is divisible by 3. Verify the result using long division. a. 84 b. 275 No Yes d. 23938 No c. 1086 Yes e. 62505 Yes 5. Using what you learned in this lesson, how can you quickly determine if 1,335 is divisible by 15? Is it? You check to see if it is divisible by 3 and divisible by 5. Thus 1,335 is divisible by 15. 6. What is the smallest number you can add to 7,120 to make it divisible by 3? Add 2. 7,122 is divisible by 3. 7. When you divide 2,349,684 by 5, will there be a remainder? What will the remainder be? Yes; 4 Lesson 35 Slide 24 Multiple Choice Practice 1. Which of the following numbers is NOT a factor of 29,910? 2 3 5 9 Lesson 35 Slide 25 Find the Errors A student made the following claims about divisibility. What is the student misunderstanding? What would you tell this student to correct their understanding? The student was able to correctly determine if a number is divisible by 2 or 5, but misunderstood how to test for divisibility of 3. You cannot in general look at the last digit to determine if it is divisible by 3, you must add all the digits together and check if the number is a multiple of 3. 5 + 2 + 3 = 10, which is not a multiple of 3. Therefore, 523 is not divisible by 3. Lesson 35 Slide 26