Multiplying Whole Numbers and Decimals

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
405 x 50
405 x 9

4
5
4
3
6
0
2
5
0
2
2
Zero is a place holder. Put a zero in your
answer to hold its place.
(5 x 0) 2 2 Write down the 2.
(5 x 4) 20 Since there are no other numbers to
multiply, write down the 20.
(9 x 0) 4 4 Write down the 4.
5 x 9 45 Put the 5 in the answer and carry the
4 (its really 40) to the next place value (tens)
5 x 5 25 Put the 5 in the answer and carry the
2 (its 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
Strategy 1
405 59 x
405 x 59
405 x 50
405 x 9

4
5
4
3
6
0
2
5
0
2
2
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
4
0
5
x
405 x 59
5
9
Put diagonal lines in each of the windows.
8
Strategy 2The Lattice
4
0
5
x
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
4
0
5
x
0
405 x 59
2
5
0
0
9
5 x 0 0
10
Strategy 2The Lattice
4
0
5
x
0
405 x 59
2
2
5
0
0
5
9
5 x 5 25
11
Strategy 2The Lattice
4
0
5
x
0
405 x 59
2
2
5
0
0
5
3
9
6
4 x 9 36
12
Strategy 2The Lattice
4
0
5
x
0
405 x 59
2
2
5
0
0
5
3
0
9
6
0
0 x 9 0
13
Strategy 2The Lattice
4
0
5
x
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
4
0
5
x
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
4
0
5
x
0
405 x 59
2
2
5
0
0
5
3
0
4
9
6
0
5
2
2
5
9
8
3
3
8
9
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
4.05 x 5.9
4.05 x 5.9
405 x 59
.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
Lets 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
3
9
5
x
395 x 84
8
4
Put diagonal lines in each of the windows.
22
Strategy 2The Lattice
3
9
5
x
2
395 x 84
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
3
9
5
x
7
2
395 x 84
8
2
4
4
8 x 9 72
24
Strategy 2The Lattice
3
9
5
x
7
2
4
395 x 84
8
2
4
0
4
8 x 5 40
25
Strategy 2The Lattice
3
9
5
x
7
2
4
395 x 84
8
2
4
0
1
4
2
4 x 3 12
26
Strategy 2The Lattice
3
9
5
x
7
2
4
395 x 84
8
2
4
0
1
3
4
2
6
4 x 9 36
27
Strategy 2The Lattice
3
9
5
x
7
2
4
395 x 84
8
2
4
0
1
3
2
4
2
6
0
4 x 5 20
28
Strategy 2The Lattice
3
9
5
x
7
2
4
395 x 84
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
3
9
5
x
7
2
4
395 x 84
8
2
4
0
1
3
2
4
2
6
0
3
3
0
8
1
3
3
8
0
1
1
1
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
Lets Practice
33
78.6 x 983
1
2
1
There is one digit after a decimal point.
1
7
7
2
8
3
6
77263.8
772638
34
.392 x .008
1
There are 6 digits after a decimal point.
0
0
3
6
3
1
.003136
003136
35
9358 x .3
2807.4
36
115.6 x .004
.4624
37
.0018 x 7
.0216