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5th Grade Division

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  1. 5th Grade Division Mrs. Berish

  2. Setting the PowerPoint View • Use Normal View for the Interactive Elements • To use the interactive elements in this presentation, do not select the Slide Show view. Instead, select Normal view and follow these steps to set the view as large as possible: • On the View menu, select Normal. • Close the Slides tab on the left. • In the upper right corner next to the Help button, click the ^ to minimize the ribbon at the top of the screen.  • On the View menu, confirm that Ruler is deselected. • On the View tab, click Fit to Window. • Use Slide Show View to Administer Assessment Items • To administer the numbered assessment items in this presentation, use the Slide Show view. (See Slide 12 for an example.)

  3. Click on the topic to go to that section Division Unit Topics • Divisibility Rules • Patterns in Multiplication and Division • Division of Whole Numbers • Division of Decimals

  4. Divisibility Rules Click to return to the table of contents

  5. Divisible When one number can be divided by another and the result is an exact whole number. five three Example: 15 is divisible by 3 because 15 ÷ 3 = 5 exactly BUT 9 is not divisible by 2 because 9 ÷ 2 is 4 with one left over.

  6. Divisibility A number is divisible by another number when the remainder is 0. There are rules to tell if a number is divisible by certain other numbers.

  7. Divisibility Rules Look at the last digit in the Ones Place! 2 Last digit is even-0,2,4,6,8 5 Last digit is 5 OR 0 10 Last digit is 0 Check the Sum! 3 Sum of digits is divisible by 3 6 Number is divisible by 3 AND 2 9 Sum of digits is divisible by 9 Look at Last Digits 4 Last 2 digits form a number divisible by 4

  8. x Let's Practice! Is 34 divisible by 2? Yes, because the digit in the ones place is an even number. Therefore, 34 / 2 = 17 Is 1,075 divisible by 5? Yes because the digit in the ones place is a 5. Therefore, 1,075 / 5 = 215 Is 740 divisible by 10? Yes, because the digit in the ones place is a 0. Therefore, 740 / 10 = 74

  9. Is 258 divisible by 3? Yes, because the sum of its digits is divisible by 3. 2 + 5 + 8 = 15 Look 15 / 3 = 5 Therefore, 258 / 3 = 86 Is 193 divisible by 6? Yes, because the sum of its digits is divisible by 3 AND 2. 1 + 9 + 2 = 12 Look 12 /3 = 4 Therefore, 192 / 6 = 32 x

  10. Is 6,237 divisible by 9? Yes, because the sum of its digits is divisible by 9. 6 + 2 + 3 + 7 = 18 Look 18 / 9 = 2 Therefore, 6,237 /9=693 Is 520 divisible by 4? Yes, because the number made by the last two digits is divisible by 4. 20 / 4 = 5 Therefore, 520 / 4 = 130 x

  11. Is 198 divisible by 2? 1 Yes No

  12. 2 Is 315 divisible by 5? Yes No

  13. 3 Is 483 divisible by 3? Yes No

  14. 4 294 divisible by 6? True False

  15. 5 3,926 is divisible by 9 True False

  16. Some numbers are divisible by more than one digit. Using the Divisibility Rules, let's practice. 18 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2, 3, 6 and 9? 165 is divisible by how many digits? Let's see if your choices are correct. Did you guess 3 and 5? Click Click

  17. 28 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2 and 4? 530 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2, 5, and 10? Now it's your turn...... Click Click

  18. Complete the table using the Divisibility Rules (Click on the cell to reveal the answer) • 1,218

  19. 6 What are all the digits 15 is divisible by?

  20. 7 What are all the digits 36 is divisible by?

  21. 8 What are all the digits 1,422 are divisible by?

  22. 9 What are all the digits 240 are divisible by?

  23. 10 What are all the digits 64 is divisible by?

  24. Patterns in Multiplication and Division Click to return to the table of contents

  25. Powers of 10 Numbers like 10, 100 and 1,000 are called powers of 10. They are numbers that can be written as products of tens. 100 can be written as 10 x 10 or 102. 1,000 can be written as 10 x 10 x 10 or 103.

  26. 103 The raised digit is called the exponent. The exponent tells how many tens are multiplied.

  27. A number written with an exponent, like 103, is in exponential notation. A number written in a more familiar way, like 1,000 is in standard notation.

  28. Powers of 10 from ten to one million. (greater than 1) Powers of 10 Standard Product Exponential Notation of 10s Notation 10 10 101 100 10 x 10 102 1,000 10 x 10 x 10 103 10,000 10 x 10 x 10 x 10 10 100,000 10 x 10 x 10 x 10 x 10 105 1,000,000 10 x 10 x 10 x 10 x 10 x 10 106 4

  29. It is easy to MULTIPLY a whole number by a power of 10. Add on as many 0s as appear in the power of 10. Examples: 28 x 10 = 280 Add on one 0 28 x 100 = 2,800 Add on two 0s 28 x 1,000 = 28,000 Add on three 0s

  30. If you have memorized the basic multiplication facts, you can solve problems mentally. Use a pattern when multiplying by powers of 10. steps 1. Multiply the digits to the left of the zeros in each factor. 50 x 100 5 x 1 = 5 2. Count the number of zeros in each factor. 50 x 100 3. Write the same number of zeros in the product. 5,000 50 x 100 = 5,000 50 x 100 5,000

  31. 60 x 400 = _______ steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = 24 2. Count the number of zeros in each factor. 3. Write the same number of zeros in the product.

  32. 60 x 400 = _______ steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = 24 2. Count the number of zeros in each factor. 60 x 400 3. Write the same number of zeros in the product.

  33. 60 x 400 = _______ steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = 24 2. Count the number of zeros in each factor. 60 x 400 3. Write the same number of zeros in the product. 60 x 400 = 24,000

  34. 500 x 70,000 = _______ steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = 35 2. Count the number of zeros in each factor. 3. Write the same number of zeros in the product.

  35. 500 x 70,000 = _______ steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = 35 2. Count the number of zeros in each factor. 500 x 70,000 3. Write the same number of zeros in the product.

  36. 500 x 70,000 = _______ Steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = 35 2. Count the number of zeros in each factor. 500 x 70,000 3. Write the same number of zeros in the product. 500 x 70,000 = 35,000,000

  37. Your Turn.... Write a rule. Input Output rule 15,000 50 2,100 7 90,000 300 6,000 20

  38. Write a rule. Input Output 18,000 rule 20 6,300 7 8,100,000 9,000 72,000 80

  39. 30 x 10 = 11

  40. 12 800 x 1,000 =

  41. 13 900 x 10,000 =

  42. 14 700 x 5,100 =

  43. 15 70 x 8,000 =

  44. 16 40 x 500 =

  45. 17 1,200 x 3,000 =

  46. 18 35 x 1,000 =

  47. It is easy to DIVIDE a whole number by a power of 10. Take off as many 0s as appear in the power of 10. Example: 42,000 / 10 = 4,200 Take off one 0 42,000 / 100 = 420 Take off two 0s 42,000 / 1,000 = 42 Take off three 0s

  48. If you have memorized the basic division facts, you can solve problems mentally. Use a pattern when dividing by powers of 10. 60 / 10 = 60 / 10 = 6 steps Cross out the same number of 0s in the dividend as in the divisor. 2. Complete the division fact.

  49. More Examples: 8,000 / 10 8,000 / 10 = 800 700 / 10 700 / 10 = 70 9,000 / 100 9,000 / 100 = 90

  50. This pattern can be used in other problems . 120 / 30 44,600 / 200 44,600 / 200 = 223 1,400 / 700 1,400 / 700 = 2 120 / 30 = 4