1. Multiplying and Dividing Decimals
Section 1-3 (Pages 17-22)

2. Review… Estimate each quotient using compatible numbers. 1. 24.8 ÷ 4.9
÷ 4.9
÷ 13.2
÷ 9.86
÷ 6.07
About 5
About 8
About 13
About 7

3. 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

4. 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)

5. 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.

6. 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

7. Example Find the product of 1.45 x 2.6.
Step 1: Multiply as with whole numbers.
Step 2: Locate the decimal point.

8. Example Find the product of 1.02 x 3.6.
Step 1: Multiply as with whole numbers.
Step 2: Locate the decimal point.

9. Multiplying using the Properties…
Use mental math to find 2 x x 0.5
We know that 2 x 0.5 will give us 1 and then the product of 1 and is
2 x 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

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

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

12. Additional Problems 1. 1.45 x 2.6 2. 1.3 x 0.005 3. 41 x 7.5