1. Multiplying Whole Numbers and Decimals Lesson 2-2

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. Strategy #1 405 59 = x 405 x 59 or 405 x 50 405 x 9 + 45 5 x 9 = 45 Put the 5 in the answer and carry the 4 (it’s really 40) to the next place value (tens) 4 (9 x 0) + 4 = 4 Write down the 4. 36 (9 x 4) = 36 Since there are no other numbers to multiply, write down the 36. Zero is a place holder. Put a zero in your answer to hold its place. 025 5 x 5 = 25 Put the 5 in the answer and carry the 2 (it’s really 20) to the next place value (tens) (5 x 0) + 2 = 2 Write down the 2. 02 (5 x 4) = 20 Since there are no other numbers to multiply, write down the 20. 2

4. Strategy #1 405 59 = x 405 x 59 or 405 x 50 405 x 9 + 45436025022 23,895 The final answer is:

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

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

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

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

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

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

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

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

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

15. Strategy #2 The Lattice 405 x 59 405 5 9 x 2 0 0 0 2 5 3 6 0 0 4 5 5983 22 3895

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… 4.05 x 5.9 23,895 4.05 x 5.9 405 x 59 23.895.405 x.059.405 x.059.023895 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 #2 The 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 #2 The Lattice 3 digits 2 digits 395 x 84

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

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

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

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

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

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

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

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

29. Strategy #2 The Lattice 395 8 4 x 2 4 7 2 4 0 1 2 3 6 2 0 0813 3 3 380 395 x 84 111

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 33180 39.5 x 8.4 331.80.395 x.084.395 x.084.033180 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. 395 x 84

32. Let’s Practice…

33. 78.6 x 983 7 9 8 86 3 6 3 7 2 5 4 5 6 6 4 4 8 2 1 2 4 1 8 83 1 6 1 2 2 7 1 7 77263.8 There is one digit after a decimal point. 772638

34. .392 x.008 3 0 0 92 8 0 0 0 0 0 0 0 0 0 0 0 0 2 4 7 2 1 6 631 1 3 0 0.003136 There are 6 digits after a decimal point. 003136

35. 9358 x.3 2807.4

36. 115.6 x.004.4624

37. .0018 x 7.0216