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Multiplying Whole Numbers and Decimals

Multiplying Whole Numbers and Decimals. Ms. Joseph 6 th Grade Mathematics. Things you need to know…. Do not line up the decimal points! Pretend all decimals are whole numbers until the very end Only look at the decimals when trying to figure out where to put the decimal point in your answer.

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Multiplying Whole Numbers and Decimals

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  1. Multiplying Whole Numbers and Decimals Ms. Joseph 6th Grade Mathematics

  2. Things you need to know… • Do not line up the decimal points! • Pretend all decimals are whole numbers until the very end • Only look at the decimals when trying to figure out where to put the decimal point in your answer

  3. or Strategy #1: Using Distributive Property 405 • 59 = x 405 x 59 405 x 9 405 x 50 + 3 6 4 4 5 2 0 2 2 5 0 (5 x 4) = 20 Since there are no other numbers to multiply, write down the 20. (5 x 0) + 2 = 2 Write down the 2. Zero is a place holder. Put a zero in your answer to hold its place. (9 x 0) + 4 = 4 Write down the 4. 5 x 9 = 45 Put the 5 in the answer and carry the 4 (it’s really 40) to the next place value (tens) 5 x 5 = 25 Put the 5 in the answer and carry the 2 (it’s really 20) to the next place value (tens) (9 x 4) = 36 Since there are no other numbers to multiply, write down the 36.

  4. or Strategy #1 405 • 59 = x 405 x 59 405 x 9 405 x 50 + 3 6 4 4 5 2 0 2 2 5 0 23,895 The final answer is:

  5. Strategy #2The Lattice 405 x 59 There are 3 digits in this number There are 2 digits in this number We will start by making a 3 x 2 window…

  6. Strategy #2The Lattice 3 digits 405 x 59 2 digits

  7. Strategy #2The Lattice x 4 0 5 405 x 59 5 9 Put diagonal lines in each of the windows.

  8. Strategy #2The Lattice x 4 0 5 405 x 59 2 5 0 9 4 x 5 = 20 Multiply one number from the top with one from the side. Put your answer in the box where they meet.

  9. Strategy #2The Lattice x 4 0 5 0 405 x 59 2 5 0 0 9 5 x 0 = 0

  10. Strategy #2The Lattice x 4 0 5 0 405 x 59 2 2 5 0 0 5 9 5 x 5 = 25

  11. Strategy #2The Lattice x 4 0 5 0 405 x 59 2 2 5 0 0 5 3 9 6 4 x 9 = 36

  12. Strategy #2The Lattice x 4 0 5 0 405 x 59 2 2 5 0 0 5 3 0 9 6 0 0 x 9 = 0

  13. Strategy #2The Lattice x 4 0 5 0 405 x 59 2 2 5 0 0 5 3 0 4 9 6 0 5 5 x 9 = 45

  14. Strategy #2The Lattice x 4 0 5 0 405 x 59 2 2 5 0 0 5 3 0 4 9 6 0 5 Now we will add numbers diagonally from right to left…

  15. Strategy #2The Lattice x 4 0 5 0 405 x 59 2 2 5 0 0 5 3 0 4 9 6 0 5 2 2 3 3 8 8 9 9 5 5

  16. What if I have a decimal point in my problem? • Multiply your numbers using one of the steps just shown. • When done, count all the numbers after a decimal point in your problem. • Make sure your answer has exactly that number of digits in the decimal spaces.

  17. If my problem has decimals… 405 x 59 4.05 x 5.9 4.05 x 5.9 .405 x .059 .405 x .059 23,895 23.895 .023895 I had to add a zero because there are six total decimals spots in my problem, but I only had 5 digits in my answer. Notice that the zero came between the decimal point and my old answer.

  18. Let’s try one more…

  19. Strategy #2The Lattice 395 x 84 There are 3 digits in this number There are 2 digits in this number We will start by making a 3 x 2 window…

  20. Strategy #2The Lattice 3 digits 395 x 84 2 digits

  21. Strategy #2The Lattice x 3 9 5 395 x 84 8 4 Put diagonal lines in each of the windows.

  22. Strategy #2The Lattice x 3 9 5 395 x 84 2 8 4 4 8 x 3 = 24 Multiply one number from the top with one from the side. Put your answer in the box where they meet.

  23. Strategy #2The Lattice x 3 9 5 7 395 x 84 2 8 2 4 4 8 x 9 = 72

  24. Strategy #2The Lattice x 3 9 5 7 395 x 84 2 4 8 2 4 0 4 8 x 5 = 40

  25. Strategy #2The Lattice x 3 9 5 7 395 x 84 2 4 8 2 4 0 1 4 2 4 x 3 = 12

  26. Strategy #2The Lattice x 3 9 5 7 395 x 84 2 4 8 2 4 0 1 3 4 2 6 4 x 9 = 36

  27. Strategy #2The Lattice x 3 9 5 7 395 x 84 2 4 8 2 4 0 1 3 2 4 2 6 0 4 x 5 = 20

  28. Strategy #2The Lattice x 3 9 5 7 395 x 84 2 4 8 2 4 0 1 3 2 4 2 6 0 Now we will add numbers diagonally from right to left…

  29. Strategy #2The Lattice x 3 9 5 7 395 x 84 2 4 8 2 4 0 1 3 2 4 2 6 0 3 3 1 3 3 1 1 1 8 8 0 0

  30. What if I have a decimal point in my problem? • Multiply your numbers using one of the steps just shown. • When done, count all the numbers after a decimal point in your problem. • Make sure your answer has exactly that number of digits in the decimal spaces.

  31. If my problem has decimals… 39.5 x 8.4 39.5 x 8.4 .395 x .084 .395 x .084 395 x 84 .033180 331.80 33180 I had to add a zero because there are six total decimals spots in my problem, but I only had 5 digits in my answer. Notice that the zero came between the decimal point and my old answer.

  32. The Traditional way

  33. 7 8 6 6 7 5 9 3 2 4 4 5 6 8 8 6 4 2 2 1 3 1 4 8 78.6 x 983 1 2 There is one digit after a decimal point. 1 1 7 7 2 6 3 8 77263.8 772638

  34. 3 9 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 1 8 4 2 6 .392 x .008 1 There are 6 digits after a decimal point. 0 0 3 1 3 6 .003136 003136

  35. 9358 x .3 2807.4

  36. 115.6 x .004 .4624

  37. .0018 x 7 .0216

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