Multiply and Divide Decimals

1
Multiply and Divide Decimals

• Using Models

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Multiply Decimals by Building Rectangles
1
0.1
0.01
You can model the multiplication of decimals by
building a rectangle.
Lets try 3.2 x 2.4
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Multiply Decimals by Building Rectangles
3.2

1. Model 3.2 as the length of your rectangle.

1. Model 2.4 as the width of your rectangle.

2.4

1. Use blocks to fill in the rectangle.

3.2 x 2.4 7.68
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What Does This Method Do For Students?

• Builds an understanding of the size of numbers.
• Relates the idea of place value to something
  tangible.
• Creates a deeper understanding of the
  multiplication algorithm.
• Enforces the concept of area.
• Builds prior knowledge for the use of algebra
  tiles with polynomials.

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Your Turn

1. Find 2.8 x 2.3
2. Find 3.1 x 2.7

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Work Backwards
What multiplication problem is modeled by the
blocks shown below?
2.4 x 2.4 5.76
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What Are Some Disadvantages To Using This Model?

• Students are used to relating the blocks to
  different numbers.

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Modeling Decimal Division
The blocks are still the same!
1
0.1
0.01
We can divide decimals by separating blocks into
equal groups.
Lets divide 0.4 by 0.02
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Divide Decimals by Grouping
20
You will have 40 hundredths pieces.

1. Model 0.4

1. Divide the 40 pieces into groups of 0.02

How many equal groups are there?
10
Lets Try Another
4
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Drawing Conclusions

• Find 36 divided by 12. How does this problem and
  its quotient compare to 3.6 divided by 1.2?
• Could you use base-ten pieces to find the
  quotient of 2.3 divided by 0.3? Justify your
  answer.