The document provides step-by-step instructions for multiplying decimals by whole numbers. It demonstrates multiplying 0.12 x 5, 9.74 x 8, and 219 x 7.2. For each problem, it lists the steps of multiplying the numbers, placing placeholders, adding products, and including the correct number of decimal places in the final answer.

1. 6-2 Multiplying Decimals
by Whole Numbers
Math Notes
Number Sense 2.1

2. Find 0.12 x 5
0.12
x 5

3. Find 0.12 x 5
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat.

4. Find 0.12 x 5
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat.

5. Find 0.12 x 5
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat.
STEP ONE:
Multiply by
the ones. Regroup
if necessary.

6. Find 0.12 x 5
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat.
STEP ONE:
Multiply by
the ones. Regroup
if necessary.

7. Find 0.12 x 5
1
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat.
STEP ONE:
0
Multiply by
the ones. Regroup
if necessary.

8. Find 0.12 x 5
1
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat.
STEP ONE:
0
Multiply by
the ones. Regroup
if necessary.

9. Find 0.12 x 5
1
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat.
STEP ONE:
60
Multiply by
the ones. Regroup
if necessary.

10. Find 0.12 x 5
1
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat.
STEP ONE:
60
Multiply by
the ones. Regroup
if necessary.
STEP TWO:
Count the number of
decimal places.

11. Find 0.12 x 5
1
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat. 2 decimal places
STEP ONE:
60
Multiply by
the ones. Regroup
if necessary.
STEP TWO:
Count the number of
decimal places.

12. Find 0.12 x 5
1
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat. 2 decimal places
STEP ONE:
60
Multiply by
the ones. Regroup
if necessary.
STEP THREE:
Make sure the
number of decimals
STEP TWO:
places is included in
Count the number of
your answer.
decimal places.

13. Find 0.12 x 5
1
0.12
STEP ZERO:
Use guidelines
to keep work
x 5
neat. 2 decimal places
STEP ONE:
0.60
Multiply by
the ones. Regroup
if necessary.
STEP THREE:
Make sure the
number of decimals
STEP TWO:
places is included in
Count the number of
your answer.
decimal places.

14. Find 9.74 x 8
9.74
x 8

15. Find 9.74 x 8
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.

16. Find 9.74 x 8
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.

17. Find 9.74 x 8
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.
STEP ONE:
Multiply by
the ones. Regroup
if necessary.

18. Find 9.74 x 8
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.
STEP ONE:
Multiply by
the ones. Regroup
if necessary.

19. Find 9.74 x 8
3
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.
STEP ONE:
Multiply by
2
the ones. Regroup
if necessary.

20. Find 9.74 x 8
3
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.
STEP ONE:
Multiply by
2
the ones. Regroup
if necessary.

21. Find 9.74 x 8
5 3
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.
STEP ONE:
Multiply by
92
the ones. Regroup
if necessary.

22. Find 9.74 x 8
5 3
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.
STEP ONE:
Multiply by
92
the ones. Regroup
if necessary.

23. Find 9.74 x 8
5 3
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.
STEP ONE:
Multiply by
7792
the ones. Regroup
if necessary.

24. Find 9.74 x 8
5 3
9.74
STEP ZERO:
Use guidelines
to keep work
x 8
neat.
STEP ONE:
Multiply by
7792
the ones. Regroup
if necessary.
STEP TWO:
Count the number of
decimal places.

25. Find 9.74 x 8
5 3
9.74
STEP ZERO:
Use guidelines
to keep work 2 decimal places
x 8
neat.
STEP ONE:
Multiply by
7792
the ones. Regroup
if necessary.
STEP TWO:
Count the number of
decimal places.

26. Find 9.74 x 8
5 3
9.74
STEP ZERO:
Use guidelines
to keep work 2 decimal places
x 8
neat.
STEP ONE:
Multiply by
7792
the ones. Regroup
if necessary.
STEP THREE:
Make sure the STEP TWO:
number of decimals Count the number of
places is included in decimal places.
your answer.

27. Find 9.74 x 8
5 3
9.74
STEP ZERO:
Use guidelines
to keep work 2 decimal places
x 8
neat.
STEP ONE:
Multiply by
77.92
the ones. Regroup
if necessary.
STEP THREE:
Make sure the STEP TWO:
number of decimals Count the number of
places is included in decimal places.
your answer.

28. Find 219 x 7.2
219
x 7.2

29. Find 219 x 7.2
219
STEP ZERO:
Use guidelines
to keep work
x 7.2
neat.

30. Find 219 x 7.2
219
STEP ZERO:
Use guidelines
to keep work
x 7.2
neat.

31. Find 219 x 7.2
STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.

32. Find 219 x 7.2
STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.

33. Find 219 x 7.2
1 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
8

34. Find 219 x 7.2
1 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
8

35. Find 219 x 7.2
1 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
38

36. Find 219 x 7.2
1 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
38

37. Find 219 x 7.2
1 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38

38. Find 219 x 7.2
1 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP TWO:
Place a zero in the
ones place.
(PLACEHOLDER)
Scratch out
previous work.

39. Find 219 x 7.2
STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP TWO:
Place a zero in the
ones place.
0
(PLACEHOLDER)
Scratch out
previous work.

40. Find 219 x 7.2
STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
0
if necessary. (PLACEHOLDER)
Scratch out
previous work.

41. Find 219 x 7.2
STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
0
if necessary. (PLACEHOLDER)
Scratch out
previous work.

42. Find 219 x 7.2
6 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
30
if necessary. (PLACEHOLDER)
Scratch out
previous work.

43. Find 219 x 7.2
6 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
30
if necessary. (PLACEHOLDER)
Scratch out
previous work.

44. Find 219 x 7.2
1 6 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
33 0
if necessary. (PLACEHOLDER)
Scratch out
previous work.

45. Find 219 x 7.2
1 6 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
33 0
if necessary. (PLACEHOLDER)
Scratch out
previous work.

46. Find 219 x 7.2
1 6 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
15 3 3 0
if necessary. (PLACEHOLDER)
Scratch out
previous work.

47. Find 219 x 7.2
1 6 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
+ 15 3 3 0
if necessary. (PLACEHOLDER)
Scratch out
previous work.

48. Find 219 x 7.2
1 6 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
+ 15 3 3 0
if necessary. (PLACEHOLDER)
Scratch out
previous work.
STEP FOUR:
Add the products.
Regroup if necessary.

49. Find 219 x 7.2
1 6 STEP ONE:
219
STEP ZERO:
Multiply by
Use guidelines
the ones. Regroup
to keep work
if necessary.
x 7.2
neat.
1
4 38
STEP THREE: STEP TWO:
Multiply by the Place a zero in the
tens. Regroup ones place.
+ 15 3 3 0
if necessary. (PLACEHOLDER)
Scratch out
previous work.
STEP FOUR:
Add the products.
Regroup if necessary.
15 7 6 8

50. Find 219 x 7.2
1 6
219
x 7.2
1
4 38
+ 15 3 3 0
15 7 6 8

51. Find 219 x 7.2
1 6
219
STEP FIVE:
Count the number of
decimal places.
x 7.2
1
4 38
+ 15 3 3 0
15 7 6 8

52. Find 219 x 7.2
1 6
219
STEP FIVE:
Count the number of
decimal places.
x 7.2
1 1 decimal place
4 38
+ 15 3 3 0
15 7 6 8

53. Find 219 x 7.2
1 6
219
STEP FIVE:
Count the number of
decimal places.
STEP SIX:
Make sure the x 7.2
1 1 decimal place
4 38
number of decimals
places is included in
+ 15 3 3 0
your answer.
15 7 6 8

54. Find 219 x 7.2
1 6
219
STEP FIVE:
Count the number of
decimal places.
STEP SIX:
Make sure the x 7.2
1 1 decimal place
4 38
number of decimals
places is included in
+ 15 3 3 0
your answer.
15 7 6.8