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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

405x 59

or 405x 50

405x 9

+

455 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.

0255 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

Strategy #1405 • 59 = x

405x 59

or 405x 50

405x 9

+

45436 02502 2

23,895The final answer is:

Strategy #2The Lattice

405x 59

There are 3 digits in this number


We will start by making a 3 x 2 window…


405x 59

3 digits

2 digits


405x 59

4 0 5

5

9

x

Put diagonal lines in each of the windows.


405x 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

2 0


405x 59

4 0 5

5

9

x

5 x 0 = 0

2 00 0


405x 59

4 0 5

5

9

x

5 x 5 = 25

2 00 0 2 5


405x 59

4 0 5

5

9

x

4 x 9 = 36

2 00 0 2 5

3 6


405x 59

4 0 5

5

9

x

0 x 9 = 0

2 00 0 2 5

3 6 0 0


405x 59

4 0 5

5

9

x

5 x 9 = 45

2 00 0 2 5

3 6 0 0 4 5


405x 59

4 0 5

5

9

x2 0

0 0 2 53 6 0 0 4 5

Now we will add numbers diagonally from right to left…


405x 59

4 0 5

5

9

x2 0

0 0 2 53 6 0 0 4 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…

4.05x 5.9

23,895

4.05x 5.9

405x 59

23.895

.405x .059

.405x .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…


395x 84



We will start by making a 3 x 2 window…


3 digits

2 digits

395x 84


3 9 5

8

4

x

Put diagonal lines in each of the windows.

395x 84


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

2 4 395x 84


3 9 5

8

4

x

8 x 9 = 72

2 47 2 395

x 84


3 9 5

8

4

x

8 x 5 = 40

2 47 2 4 0 395

x 84


3 9 5

8

4

x

4 x 3 = 12

2 47 2 4 0

1 2

395x 84


3 9 5

8

4

x

4 x 9 = 36

2 47 2 4 0

1 2 3 6

395x 84


3 9 5

8

4

x

4 x 5 = 20

2 47 2 4 0

1 2 3 6 2 0

395x 84


3 9 5

8

4

x2 4

7 2 4 01 2 3 6 2 0

Now we will add numbers diagonally from right to left…

395x 84


3 9 5

8

4

x2 4

7 2 4 01 2 3 6 2 0

081333

3 8 0

395x 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…

39.5x 8.4

33180

39.5 x 8.4331.8

0

.395x .084

.395x .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.

395x 84

Let’s Practice…

78.6 x 9837

9

8

8 6

3

6 3 7 2 5 45 6 6 4 4 82 1 2 4 1 8

83

1

6

1

2

2

7

17

77263.8

There is one digit after a decimal point.

772638

.392 x .0083

0

0

9 2

8

0 0 0 0 0 00 0 0 0 0 02 4 7 2 1 6

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