1. Math 50 1.4 – Dividing Whole Numbers; Solving Equations 1

2. Natural numbers: ______________________ Whole numbers: ______________________ 2

3. Natural numbers: ______________________ Whole numbers: ______________________ 3 1, 2, 3, 4, 5, 6, …

4. Natural numbers: ______________________ Whole numbers: ______________________ 4 1, 2, 3, 4, 5, 6, … 0, 1, 2, 3, 4, 5, 6, …

5. 5 How to divide

6. 6

7. 7

8. 8

9. 9

10. 10 How to divide

11. 11 How to divide

12. 12 How to divide

13. What does division mean? In math, it means separating into equal parts. Division problems come in two main flavors. 13 When to divide

14. 1. If a deck of 52 cards are divided between 13 players, how many cards does each player get? (Imagine dealing out the cards, and each player would end up with 4 cards.) 14 When to divide

15. 2. How many bags of 5 oranges could be made from a box of 40 oranges? (Imagine making each bag of 5 oranges until you run out of oranges) 15 When to divide

16. Ex 3. How many 15-cent stamps can you buy with $10? (Imagine buying each 15-cent stamp until you run out of money.) 16 When to divide

17. Ex 4. Suppose Roger’s annual salary is $42552, and he gets paid monthly. What is his monthly salary? (Imagine “dealing out” the $42552 into each of the 12 months.) 17 When to divide

18. Note: We can check our answers using ____________________ (which is the “inverse” of division). That is, take your answer and multiply it by the ____________. Then add the ______________. 18

19. Note: We can check our answers using ____________________ (which is the “inverse” of division). That is, take your answer and multiply it by the ____________. Then add the ______________. 19 multiplication

20. Note: We can check our answers using ____________________ (which is the “inverse” of division). That is, take your answer and multiply it by the ____________. Then add the ______________. 20 multiplication divisor

21. Note: We can check our answers using ____________________ (which is the “inverse” of division). That is, take your answer and multiply it by the ____________. Then add the ______________. 21 multiplication divisorremainder

22. 22 Some things to know about division

23. 23 Some things to know about division commutative

24. 24 Some things to know about division associative commutative

25. 25 Some things to know about division associative commutative

26. 26 Some things to know about division associative commutative

27. 27 Some things to know about division

28. 28 Some things to know about division undefined

29. 29 Some things to know about division indeterminate undefined

30. 30 Some things to know about division indeterminate undefined

31. When is a number divisible by 2? _________________________________________ When is a number divisible by 3? _________________________________________ When is a number divisible by 5? _________________________________________ 31 Divisibility rules

32. When is a number divisible by 2? _________________________________________ When is a number divisible by 3? _________________________________________ When is a number divisible by 5? _________________________________________ 32 Divisibility rules When it ends in 0, 2, 4, 6, or 8 (i.e. is even)

33. When is a number divisible by 2? _________________________________________ When is a number divisible by 3? _________________________________________ When is a number divisible by 5? _________________________________________ 33 Divisibility rules When the sum of the digits is divisible by 3 When it ends in 0, 2, 4, 6, or 8 (i.e. is even)

34. When is a number divisible by 2? _________________________________________ When is a number divisible by 3? _________________________________________ When is a number divisible by 5? _________________________________________ 34 Divisibility rules When it ends in 0 or 5 When the sum of the digits is divisible by 3 When it ends in 0, 2, 4, 6, or 8 (i.e. is even)

35. Ex 5. Circle the numbers that are divisible by 2: 30 3894 84371 6809 58390 457489205 Ex 6. Now circle the numbers that are divisible by 3: 30 3894 84371 6809 58390 457489205 Ex 7. Now circle the numbers that are divisible by 5: 30 3894 84371 6809 58390 457489205 35

36. Ex 5. Circle the numbers that are divisible by 2: 30 3894 84371 6809 58390 457489205 Ex 6. Now circle the numbers that are divisible by 3: 30 3894 84371 6809 58390 457489205 Ex 7. Now circle the numbers that are divisible by 5: 30 3894 84371 6809 58390 457489205 36

37. Ex 5. Circle the numbers that are divisible by 2: 30 3894 84371 6809 58390 457489205 Ex 6. Now circle the numbers that are divisible by 3: 30 3894 84371 6809 58390 457489205 Ex 7. Now circle the numbers that are divisible by 5: 30 3894 84371 6809 58390 457489205 37

38. Ex 5. Circle the numbers that are divisible by 2: 30 3894 84371 6809 58390 457489205 Ex 6. Now circle the numbers that are divisible by 3: 30 3894 84371 6809 58390 457489205 3+0=36+8+0+9=23 3+8+9+4=245+8+3+9+0=25 8+4+3+7+1=234+5+7+4+8+9+2+0+5=44 Ex 7. Now circle the numbers that are divisible by 5: 30 3894 84371 6809 58390 457489205 38

39. Ex 5. Circle the numbers that are divisible by 2: 30 3894 84371 6809 58390 457489205 Ex 6. Now circle the numbers that are divisible by 3: 30 3894 84371 6809 58390 457489205 3+0=36+8+0+9=23 3+8+9+4=245+8+3+9+0=25 8+4+3+7+1=234+5+7+4+8+9+2+0+5=44 Ex 7. Now circle the numbers that are divisible by 5: 30 3894 84371 6809 58390 457489205 39 div. by 3

40. Ex 5. Circle the numbers that are divisible by 2: 30 3894 84371 6809 58390 457489205 Ex 6. Now circle the numbers that are divisible by 3: 30 3894 84371 6809 58390 457489205 3+0=36+8+0+9=23 3+8+9+4=245+8+3+9+0=25 8+4+3+7+1=234+5+7+4+8+9+2+0+5=44 Ex 7. Now circle the numbers that are divisible by 5: 30 3894 84371 6809 58390 457489205 40 div. by 3

41. Ex 5. Circle the numbers that are divisible by 2: 30 3894 84371 6809 58390 457489205 Ex 6. Now circle the numbers that are divisible by 3: 30 3894 84371 6809 58390 457489205 3+0=36+8+0+9=23 3+8+9+4=245+8+3+9+0=25 8+4+3+7+1=234+5+7+4+8+9+2+0+5=44 Ex 7. Now circle the numbers that are divisible by 5: 30 3894 84371 6809 58390 457489205 41 div. by 3

42. Ex 5. Circle the numbers that are divisible by 2: 30 3894 84371 6809 58390 457489205 Ex 6. Now circle the numbers that are divisible by 3: 30 3894 84371 6809 58390 457489205 3+0=36+8+0+9=23 3+8+9+4=245+8+3+9+0=25 8+4+3+7+1=234+5+7+4+8+9+2+0+5=44 Ex 7. Now circle the numbers that are divisible by 5: 30 3894 84371 6809 58390 457489205 42 div. by 3

43. 43 Solving equations