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.