Chapter 6 Rational Number Operations and Properties

1
Chapter 6Rational Number Operations and
Properties

• Section 6.4
• Operations with Decimals

2
Procedure for Adding and Subtracting Rational
Numbers Represented by Decimals

• Align the place-value positions by aligning the
  decimal points and apply the algorithms for
  addition or subtraction of whole numbers.
• Demonstrate the Standard Procedure, then Verify
  using Fractions. (see page 324)

3
Multiplying Rational Numbers in Decimal Form

• Multiply factors as if they are whole numbers,
  then place the decimal point in the appropriate
  place in the product.
• The product of a factor with m places to the
  right of the ones place and a factor with n
  places to the right of the ones place will have m
  n decimal places to the right of the ones place.

4
Examples

• Find the following products.
• 1.) 6.14 x 1.3
• 2.) 0.85 x 2.9
• 3.) Find the product of 2.75 x 0.2 using the
• standard procedure for multiplying
• decimals. Verify using fractions .

5
Procedure for Dividing Rational Numbers in
Decimal Form

• Based on the Fundamental Law of Fractions.
• Consider 0.125 0.05
• 0.125 (100) 0.05 (100)
• 12.5 5
• 2.5
• How would we solve this using the standard
  algorithm for division?
• How could we check our answer?

6
Modeling with Decimals

• Using base-ten blocks.
• Let 1 flat 1 and 1 long 1/10
• Using a number line or metric ruler.
• Divide each unit into tenths, etc.
• Using an area model.
• Let one square 1 and divide into tenths.

7
Modeling Examples

• From page 331 in textbook
• 1c.) Model 1.6 1.5 using base-ten blocks.
• 2b.) Model 0.6 0.3 using a number line
• (or metric ruler).
• 3a.) Model 0.6 x 0.5 using an area model.