Multiplying and Dividing Decimals

Section 1-3 (Pages 17-22)

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

Properties of Multiplication

Identity Property

The product of 1 and “a” is “a”.

5 x 1 = 5 1 x 5 = 5

Zero PropertyThe product of 0 and any number is 0.5 x 0 = 0 0 x 5 = 0

Properties of Multiplication

Commutative Property

Changing the order of factors does not change the product.

5 x 2 = 2 x 5

Associative PropertyChanging the grouping of factors does not change the product.(3 x 2) x 5 = 3 x (2 x 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.

ExampleFind the product of 0.2 x 0.7

Step 2: Locate the decimal point. 0.2 x 0.7

0.14

Step 1: Multiply as with whole numbers. 2 x 7 14

1 decimal place

1 decimal place

2 decimal places

ExampleFind the product of 1.45 x 2.6.

Step 2: Locate the decimal point.

Step 1: Multiply as with whole numbers.

ExampleFind the product of 1.02 x 3.6.

Step 2: Locate the decimal point.

Step 1: Multiply as with whole numbers.

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

= (2 x 0.5) x 4.097

= 1 x 4.097

= 4.097

Commutative Property

Associative Property

Simplify

Identity Property

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

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

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)