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Multiply and Divide Decimals

- Using Models

Multiply Decimals The Area Model

1

0.1

0.01

You can model the multiplication of decimals by

using an area model.

Lets try 0.2 x 0.6

Multiply Decimals The Area Model

0.2 x 0.6

0.12

- Model 0.2 on the grid.

- Model 0.6 on the grid.

- Your answer is the sum of the overlapped squares.

Multiply Decimals The Area Model

- But what if we have whole numbers???

We could use a bigger grid!

1.4 x 0.5

OR

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

Multiply Decimals by Building Rectangles

3.2

- Model 3.2 as the length of your rectangle.

- Model 2.4 as the width of your rectangle.

2.4

- Use blocks to fill in the rectangle.

3.2 x 2.4 7.68

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.

Your Turn

- Find 2.8 x 2.3
- Find 3.1 x 2.7

Work Backwards

What multiplication problem is modeled by the

blocks shown below?

2.4 x 2.4 5.76

What Are Some Disadvantages To Using This Model?

- Students are used to relating the blocks to

different numbers.

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

Divide Decimals by Grouping

20

You will have 40 hundredths pieces.

- Model 0.4

- Divide the 40 pieces into groups of 0.02

How many equal groups are there?

Lets Try Another

4

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.

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