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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. or. Strategy #1.

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things you need to know
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 1

or

Strategy #1

405 • 59 = x

405

x 59

405

x 9

405

x 50

+

3

6

4

4

5

2

0

2

2

5

0

(5 x 4) = 20

Since there are no other numbers to multiply, write down the 20.

(5 x 0) + 2 = 2

Write down the 2.

Zero is a place holder. Put a zero in your answer to hold its place.

(9 x 0) + 4 = 4

Write down the 4.

5 x 9 = 45

Put the 5 in the answer and carry the 4 (it’s really 40) to the next place value (tens)

5 x 5 = 25

Put the 5 in the answer and carry the 2 (it’s really 20) to the next place value (tens)

(9 x 4) = 36

Since there are no other numbers to multiply, write down the 36.

strategy 11

or

Strategy #1

405 • 59 = x

405

x 59

405

x 9

405

x 50

+

3

6

4

4

5

2

0

2

2

5

0

23,895

The final answer is:

strategy 2 the lattice
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 2 the lattice1
Strategy #2The Lattice

3 digits

405

x 59

2 digits

strategy 2 the lattice2
Strategy #2The Lattice

x

4

0

5

405

x 59

5

9

Put diagonal lines in each of the windows.

strategy 2 the lattice3
Strategy #2The Lattice

x

4

0

5

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.

strategy 2 the lattice4
Strategy #2The Lattice

x

4

0

5

0

405

x 59

2

5

0

0

9

5 x 0 = 0

strategy 2 the lattice5
Strategy #2The Lattice

x

4

0

5

0

405

x 59

2

2

5

0

0

5

9

5 x 5 = 25

strategy 2 the lattice6
Strategy #2The Lattice

x

4

0

5

0

405

x 59

2

2

5

0

0

5

3

9

6

4 x 9 = 36

strategy 2 the lattice7
Strategy #2The Lattice

x

4

0

5

0

405

x 59

2

2

5

0

0

5

3

0

9

6

0

0 x 9 = 0

strategy 2 the lattice8
Strategy #2The Lattice

x

4

0

5

0

405

x 59

2

2

5

0

0

5

3

0

4

9

6

0

5

5 x 9 = 45

strategy 2 the lattice9
Strategy #2The Lattice

x

4

0

5

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…

strategy 2 the lattice10
Strategy #2The Lattice

x

4

0

5

0

405

x 59

2

2

5

0

0

5

3

0

4

9

6

0

5

2

2

3

3

8

8

9

9

5

5

what if i have a decimal point in my problem
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
If my problem has decimals…

405

x 59

4.05

x 5.9

4.05

x 5.9

.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.

strategy 2 the lattice11
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 2 the lattice12
Strategy #2The Lattice

3 digits

395

x 84

2 digits

strategy 2 the lattice13
Strategy #2The Lattice

x

3

9

5

395

x 84

8

4

Put diagonal lines in each of the windows.

strategy 2 the lattice14
Strategy #2The Lattice

x

3

9

5

395

x 84

2

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.

strategy 2 the lattice15
Strategy #2The Lattice

x

3

9

5

7

395

x 84

2

8

2

4

4

8 x 9 = 72

strategy 2 the lattice16
Strategy #2The Lattice

x

3

9

5

7

395

x 84

2

4

8

2

4

0

4

8 x 5 = 40

strategy 2 the lattice17
Strategy #2The Lattice

x

3

9

5

7

395

x 84

2

4

8

2

4

0

1

4

2

4 x 3 = 12

strategy 2 the lattice18
Strategy #2The Lattice

x

3

9

5

7

395

x 84

2

4

8

2

4

0

1

3

4

2

6

4 x 9 = 36

strategy 2 the lattice19
Strategy #2The Lattice

x

3

9

5

7

395

x 84

2

4

8

2

4

0

1

3

2

4

2

6

0

4 x 5 = 20

strategy 2 the lattice20
Strategy #2The Lattice

x

3

9

5

7

395

x 84

2

4

8

2

4

0

1

3

2

4

2

6

0

Now we will add numbers diagonally from right to left…

strategy 2 the lattice21
Strategy #2The Lattice

x

3

9

5

7

395

x 84

2

4

8

2

4

0

1

3

2

4

2

6

0

3

3

1

3

3

1

1

1

8

8

0

0

what if i have a decimal point in my problem1
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 decimals1
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.

78 6 x 983

7

8

6

6

7

5

9

3

2

4

4

5

6

8

8

6

4

2

2

1

3

1

4

8

78.6 x 983

1

2

There is one digit after a decimal point.

1

1

7

7

2

6

3

8

77263.8

772638

392 x 008

3

9

2

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2

7

1

8

4

2

6

.392 x .008

1

There are 6 digits after a decimal point.

0

0

3

1

3

6

.003136

003136

9358 x 3
9358 x .3

2807.4