1) The document discusses various methods for comparing and ordering rational numbers including fractions, decimals, and mixed numbers. 2) Fractions can be compared by finding a common denominator or comparing their equivalent decimal forms. 3) Decimals are compared by lining up their decimal points and comparing digits from left to right. 4) An example shows ordering fractions, decimals, and mixed numbers from least to greatest and representing them on a number line.

1. Comparing and Ordering Rational Numbers

2. Comparing fractions with the same denominator Which is greater, 4/5 or 2/5? = 4/5 = 2/5 Compare numerators! 4/5 > 2/5 because 4 > 2

3. Comparing fractions with unlike denominators Compare 7/8 and 1/2 Make a model 7 8 1 2 This shows that 7 1 8 2 >

4. Comparing fractions with unlike denominators Write equivalent fractions with common denominators. Then compare the numerators. Compare 5/6 and 7/10 The LCM of the denominators 6 and 10 is 30. 5 5 5 25 7 7 3 21 6 6 5 30 10 10 3 30 25 21 , and so, 5 7 6 10 30 30 > > = = = =

5. Compare -3/5 and -5/9 Both fractions can be written with a denominator of 45. -3 -3 9 -27 -5 -5 5 -25 5 5 9 45 9 9 5 45 -27 -25 , 45 45 and so, -3 -5 5 9 < < = = = =

6. Comparing Decimals Line up the decimal points and compare digits from left to right until you find the place where the digits are different. A) Compare 0.73 and 0.78 0.7 3 The tenths are the same. Compare the hundredths: 3 < 8 0.7 8 Since 0.03 < 0.08 , 0.73 < 0.78 http://www.khanacademy.org/video/comparing-decimals?playlist=Developmental Math

7. B) Compare 5.4399 and 5.4398 5.4399 The ones are the same. The tenths are the same. The hundredths are the same. The thousandths are the same. Compare the ten-thousandths: 9 > 8 5.4398 Since 0.0009 > 0.0008, 5.4399 > 5.4398

8. C) Compare -3.6 and -3.8 -3.6 The ones are the same. Compare the tenths: -0.6 > -0.8 -3.8 Since -0.6 > -0.8, then -3.6 > -3.8

9. Compare 6 5/6 and 6 7/10 A) 6 5/6 = 6 25/30 6 7/10 = 6 21/30 6 25/30 > 6 21/30 , so 6 5/6 > 6 7/10 B) 6 5/6 = 41/6 = 205/30 6 7/10 = 67/10 = 201/30 205 > 201, so 6 5/6 > 6 7/10 C) 6 5/6 = 6.834 6 7/10 = 6.700 6.8 > 6.7, so 6 5/6 > 6 7/10

10. Order 4/5, 0.78, -0.3, and 1 1/5 from least to greatest . Graph the numbers on a number line. 4/5 = 0.80 0.78 = 0.78 -0.3 = -0.30 1 1/5 = 1.20 -0.30 < 0.78 < 0.80 < 1.20 Write as decimals with the same number of places. The values on a number line increase as you move from left to right. 1.1 1.2 1.3 -0.30 0.78 4/5 1 1/5 From least to greatest, the numbers are -0.3, 0.78, 4/5, and 1 1/5. http://www.khanacademy.org/video/points-on-a-number-line?playlist=Developmental Math

11. To learn more, visit these websites: Www.ixl.com – click on 6 th grade Www.mathisfun.com --- go to comparing fractions Www.visualfractions.com Www.aaastudy.com – click on 6 th grade; or fractions on the left side bar http://www.mathplayground.com/fractions_compare.html

12. Grade 6 Number Sense 1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.