1. Chapter 7 Lesson 35 Testing for Divisibility 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.

6. Is 36 divisible by 2? Let’s try to express 36 as repeated addition of 2.

11. Check for Understanding 1. Determine whether the number is divisible by 2. a. 23 b. 78 c. 504 d. 8,241 e. 6,794 Not divisible by 2. Divisible by 2. Not divisible by 2. Divisible by 2. Divisible by 2.

14. Check for Understanding 2. Determine if the number is divisible by 5. a. 70 b. 553 d. 72865 c. 10003 e. 8003000 Divisible by 5. Divisible by 5. Divisible by 5. Not divisible by 5. Not divisible by 5.

18. 7 + 5 + 6 = 18 Since 18 is divisible by 9, we conclude that 756 is also divisible by 9. What about larger numbers? Is 756 divisible by 9?

20. Check for Understanding 3. Determine whether the number is divisible by 9. a. 73 b. 108 c. 7812 d. 6873 e. 98016 Not divisible by 9. Not divisible by 9. Not divisible by 9. Divisible by 9. Divisible by 9.

24. Check for Understanding 4. Test whether the number is divisible by 3. Verify the result using long division. 5. Using what you learned in this lesson, how can you quickly determine if 1,335 is divisible by 15? Is it? 6. What is the smallest number you can add to 7,120 to make it divisible by 3? 7. When you divide 2,349,684 by 5, will there be a remainder? What will the remainder be? a. 84 b. 275 c. 1086 d. 23938 e. 62505 Yes Yes Yes No No You check to see if it is divisible by 3 and divisible by 5. Thus 1,335 is divisible by 15. Add 2. 7,122 is divisible by 3. Yes; 4

25. Multiple Choice Practice 1. Which of the following numbers is NOT a factor of 29,910? 2 3 5 9

26. A student made the following claims about divisibility. What is the student misunderstanding? What would you tell this student to correct their understanding? Find the Errors 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.