Multiplying Whole Numbers and Decimals

Lesson 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

Strategy #1405 • 59 = x

405

x 59or

405

x 50

405

x 9+

45

5 x 9 = 45Put 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 = 25Put 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

Strategy #1405 • 59 = x

405

x 59or

405

x 50

405

x 9+

45436 02502 2

23,895The final answer is:

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…

Strategy #2The Lattice

405

x 59

3 digits

2 digits

Strategy #2The Lattice

405

x 59

4 0 5

5

9

x

Put diagonal lines in each of the windows.

Strategy #2The Lattice

405

x 59

4 0 5

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

20

Strategy #2The Lattice

405

x 59

4 0 5

5

9

x

5 x 0 = 0

20

00

Strategy #2The Lattice

405

x 59

4 0 5

5

9

x

5 x 5 = 25

20

00 2

5

Strategy #2The Lattice

405

x 59

4 0 5

5

9

x

4 x 9 = 36

20

00 2

5

36

Strategy #2The Lattice

405

x 59

4 0 5

5

9

x

0 x 9 = 0

20

00 2

5

36 0

0

Strategy #2The Lattice

405

x 59

4 0 5

5

9

x

5 x 9 = 45

20

00 2

5

36 0

04

5

Strategy #2The Lattice

405

x 59

4 0 5

5

9

x

20

00 2

5

36 0

04

5

Now we will add numbers diagonally from right to left…

Strategy #2The Lattice

405

x 59

4 0 5

5

9

x

20

00 2

5

36 0

04

5

598322

3 8 9 5

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.

If my problem has decimals…

4.05

x 5.923,89

5

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.

Let’s try one more…

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…

Strategy #2The Lattice

3 digits

2 digits

395

x 84

Strategy #2The Lattice

3 9 5

8

4

x

Put diagonal lines in each of the windows.

395

x 84

Strategy #2The Lattice

3 9 5

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

24

395

x 84

Strategy #2The Lattice

3 9 5

8

4

x

8 x 9 = 72

24

72

395

x 84

Strategy #2The Lattice

3 9 5

8

4

x

8 x 5 = 40

24

72 4

0 395

x 84

Strategy #2The Lattice

3 9 5

8

4

x

4 x 3 = 12

24

72 4

0

12

395

x 84

Strategy #2The Lattice

3 9 5

8

4

x

4 x 9 = 36

24

72 4

0

12 3

6

395

x 84

Strategy #2The Lattice

3 9 5

8

4

x

4 x 5 = 20

24

72 4

0

12 3

62

0

395

x 84

Strategy #2The Lattice

3 9 5

8

4

x

24

72 4

0

12 3

62

0

Now we will add numbers diagonally from right to left…

395

x 84

Strategy #2The Lattice

3 9 5

8

4

x

24

72 4

0

12 3

62

0

081333

3 8 0

395

x 84

111

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.

If my problem has decimals…

39.5

x 8.4

33180

39.5

x 8.4331.8

0

.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

Let’s Practice…

78.6 x 983

7

9

8

8 6

3

63

72

54

56

64

48

21

24

18

83

1

6

1

2

2

7

17

77263.8

There is one digit after a decimal point.

772638

.392 x .008

3

0

0

9 2

8

00

00

00

00

00

00

24

72

16

631

1

3

0

0

.003136

There are 6 digits after a decimal point.

003136

9358 x .3

2807.4

115.6 x .004

.4624

.0018 x 7

.0216