1. Comparing and Ordering Rational Numbers Coach Lesson 5 Also see textbook pages 108 - 110 Jeff Rhodus 6th Grade Elsanor Elementary Coach Lesson 5 Also see textbook pages 108 - 110 Jeff Rhodus 6th Grade Elsanor Elementary

2. Getting the Idea! Sometimes, you need to order numbers that are in different forms. For example, you may need to order a set of numbers that includes whole numbers and decimals. A good strategy to use to order whole numbers and decimals is to first compare the whole-number parts of all the numbers. Then compare the decimal parts if necessary. Example: 10 > 9.25 > 8.1 because 10 > 9 > 8

3. You can use the same strategy to order whole numbers and mixed numbers. First, compare the whole number parts. Then compare the fractional parts if necessary. Example: 5 > 4 > 3 because 5 > 4 > 3 1 2 1 2

4. Example 1: Order these numbers from least to greatest. Strategy: Compare the whole-number parts. Then compare the fractional parts if needed. 2 3 4 1.5 Compare the whole-number parts first. 2 is a whole number. 3/4 is the same as 0 +,so its whole number part is 0. 3 4 1.5 has 1 as its whole-number part 0 < 1 < 2, so < 1.5 < 2 3 4 Solution: The numbers in order from least to greatest are: 3 4, 1.5, 2

5. Example 2: Order these numbers from greatest to least. 3 2 2 5 6 1 4 Strategy: Compare the whole number parts. Then compare the fractional parts. Step 1: Compare the whole number parts first. 3 > 2 so 3 is greater than both 2 and 2 5 6 1 4 2 and 2 each have the same whole number part, 2, so compare the fractional parts. 5 6 1 4 Step 2: Compare the fractional parts of the remaining numbers. Just look at the fractional parts: 5/6 and 1/4 The least number that is a multiple of both 6 and 4 is 12.

6. Rewrite each fraction as an equivalent fraction with a denominator of 12. 5 6 = 5 x 2 6 x 2 = 10 12 1 4 = 1 x 3 4 x 3 = 3 12 10 12 > 3 so 5 6 > 1 4 Solution: The numbers in order from greatest to least is: 3, 2 2 5 6 1 4 Sometimes ordering numbers requires you to compare fractions, decimals, and percents. A good strategy for doing this is to put all the numbers into the same form. That means converting all numbers to fractions or converting all numbers to decimals.

7. Coached Example: Order these numbers from greatest to least. 72% 1 1.78 7 10 7 25 Thinking it Through: Convert all the numbers to decimals with two places after the _______. 72%= ______ 1 = ______ 1.78 = ______ 7/25 = ______ Order the decimals from greatest to least: _____ > _____ > _____ > _____ The numbers ordered from greatest to least are: _____, _____, _____, _____