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Long Division & MathLine

Long Division . Long Division & MathLine. ____ 4)259. Second Problem:. Long Division . For traditional Long Division, teach the algorithm: 1) Divide or D 2) Multiply or M 3) Subtract or S 4) Check or 5) Bring Down or BD. Long Division . Divide = D Multiply = M

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Long Division & MathLine

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  1. Long Division Long Division & MathLine ____ 4)259 Second Problem:

  2. Long Division • For traditional Long Division, • teach the algorithm: • 1) Divide or D • 2) Multiply or M • 3) Subtract or S • 4) Check or • 5) Bring Down or BD

  3. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Take the problem ____ 4)259

  4. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 4 into 2? ____ 4)259

  5. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Put 2 rings to left ____ 4)259

  6. Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Long Division 4 into 2? No ____ 4)259

  7. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 4 into 25? ____ 4)259

  8. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Put 25 rings on MathLine ____ 4)259

  9. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD For long division on MathLine ALWAYS start dividing from theleft

  10. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD ____ 4)259 4 into 25? Yes, how many times? One Group of 4 2 3 4 1 1

  11. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD ____ 4)259 Two Groups of 4 2 3 4 1 1 2

  12. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD ____ 4)259 Three Groups of 4 2 3 4 1 1 2 3

  13. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD ____ 4)259 Four Groups of 4 2 3 4 1 1 2 3 4

  14. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD ____ 4)259 Five Groups of 4 2 3 4 1 1 2 3 4 5

  15. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD ____ 4)259 Six Groups of 4 2 3 4 1 1 2 3 4 5 6

  16. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Put a 6 above the 5 of 259 6 ____ 4)259

  17. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Now multiply 6 X 4 6 ____ 4)259

  18. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Only multiply 6 X 4, or 6 groups of 4 Make sure the students do not multiply the remainder back in!

  19. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 Multiply 6 x 4 ____ 4)259

  20. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 Multiply 6 x 4 ____ 4)259 6 Groups of 4

  21. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 Multiply 6 x 4 ____ 4)259 6 Groups of 4

  22. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 Multiply 6 x 4 ____ 4)259 6 Groups of 4

  23. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 Multiply 6 x 4 ____ 4)259 6 Groups of 4

  24. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 Multiply 6 x 4 ____ 4)259 6 Groups of 4

  25. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 Multiply 6 x 4 ____ 4)259 6 Groups of 4

  26. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD See 6 x 4 on MathLine 6 _ ___ 4)259

  27. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 _ ___ 4)259 We multiply 6 x 4 and get 24, so we put the 24 below 25 24

  28. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 _ ___ 4)259 -24 Subtract 24 from 25, to get a difference of 1 1

  29. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 _ ___ 4)259 -24 Remainder of 1, ‘s out on MathLine 1

  30. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 6 _ ___ 4)259 -24 Bring down the 9 to get 19 9 1

  31. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Put 19 on MathLine

  32. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD _ 6_ 4)259 -24 19 Does 4 go into 19? How many times? Yes

  33. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD _ 6_ 4)259 -24 19 One group of 4 1 2 3 4

  34. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD _ 6_ 4)259 -24 19 Two groups of 4

  35. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD _ 6_ 4)259 -24 19 Three groups of 4

  36. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD _ 6_ 4)259 -24 19 Four groups of 4 1 2 3 4

  37. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 4 _ 6 _ 4)259 -24 19 Put a 4 above the 9 of 259

  38. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Make sure the students do not multiply the remainder back in!

  39. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 4 _ 6_ 4)259 -24 19 Multiply 4 x 4 4 Groups of 4

  40. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 4 _ 6_ 4)259 -24 19 Multiply 4 x 4 4 Groups of 4

  41. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 4 _ 6_ 4)259 -24 19 Multiply 4 x 4 4 Groups of 4

  42. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD 4 _ 6_ 4)259 -24 19 Multiply 4 x 4 4 Groups of 4

  43. Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Long Division 4 x 4 = 16

  44. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD __64 4) 259 -2419 Put 16 below the 19 16

  45. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD __64 4) 259 -2419 -16 Subtract 16 from 19, leaving 3 3

  46. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD __64 4) 259 -2419 -16 3 Remainder of 3, ‘s out

  47. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD Normally in a curriculum students must show the remainder… 1. As R.3 or “remainder of 3” 2. As a fraction 3. As a decimal

  48. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD __64 4) 259 -2419 -16 3 So 259 divided by 4 is… 64 r.3

  49. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD __64 4) 259 -2419 -16 3 Remainder as a fraction 3 of 4 or 3/4

  50. Long Division • Divide = D • Multiply = M • Subtract = S • Check = • Bring Down = BD _____ 4) 259 -24 19 -16 3 64 ¾ Remainder as a fraction

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