Multiplying and Dividing Decimals

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Multiplying and Dividing Decimals

• Section 1-3 (Pages 17-22)

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Review

• Estimate each quotient using compatible numbers.
• 1. 24.8 4.9
• 2. 103.8 13.2
• 3. 128.62 9.86
• 4. 41.77 6.07

About 5 About 8 About 13 About 7
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Properties of Multiplication

• Identity Property
• The product of 1 and a is a.
• 5 x 1 5 1 x 5 5

Zero Property The product of 0 and any number is
0. 5 x 0 0 0 x 5 0
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Properties of Multiplication

• Commutative Property
• Changing the order of factors does not change the
  product.
• 5 x 2 2 x 5

Associative Property Changing the grouping of
factors does not change the product. (3 x 2) x 5
3 x (2 x 5)
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To multiply decimals

• Step 1 Multiply as if the factors are whole
  numbers.

• Step 2 Add the number of the decimal places in
  both factors to find the number of decimal places
  in the product.

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Example

• Find the product of 0.2 x 0.7

Step 1 Multiply as with whole numbers. 2
x 7 14
Step 2 Locate the decimal point. 0.2
x 0.7 0.14
1 decimal place
1 decimal place
2 decimal places
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Example

• Find the product of 1.45 x 2.6.

Step 1 Multiply as with whole numbers.
Step 2 Locate the decimal point.
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Example

• Find the product of 1.02 x 3.6.

Step 1 Multiply as with whole numbers.
Step 2 Locate the decimal point.
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Multiplying using the Properties

• Use mental math to find 2 x 4.097 x 0.5

We know that 2 x 0.5 will give us 1 and then the
product of 1 and 4.097 is 4.097.
2 x 4.097 x 0.5 2 x 0.5 x 4.097
Commutative Property
Associative Property
(2 x 0.5) x 4.097
1 x 4.097
Simplify
4.097
Identity Property
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Example

• Use mental math to find the product of 1.09 x
  23.6 x 0.

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Example

• Use mental math to find the product of 2.5 x 6.3
  x 4.

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Additional Problems

• 1. 1.45 x 2.6
• 2. 1.3 x 0.005
• 3. 41 x 7.5
• 4. 0 x 2.78 x 1
• 5. 5 x (4.3 x 1)