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- 1 / 3 -0 . 08. Math 8 Compar ing and Ordering Rational Numbers. Comping Numbers Decimals and Fractions. There are 4 simple principles you can use to compare and order fractions and decimal numbers: Use points of reference Use common denominators Use common numerators

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  1. -1/3-0.08 Math 8Comparing and Ordering Rational Numbers

  2. Comping Numbers Decimals and Fractions There are 4 simple principles you can use to compare and order fractions and decimal numbers: • Use points of reference • Use common denominators • Use common numerators • Convert to fractions or decimal numbers.

  3. Reference Points When we speak of reference points (benchmarks) be familiar with common fractions and their decimal equivalents as good reference points: 1/8 = 0.125 1/3 = 0.3333…1/5 = 0.20 3/4 = 0.751/4 = 0.25 2/3 =0.6666… 1/2 = 0.5 1/10 = 0.1

  4. A special pattern with denominator of « 9 » _ __ ___ 1/9 = 0.1 1/99 = 0.01 1/999 = 0.001 _ __ ___2/9 = 0.2 2/99 = 0.02 31/999 = 0.031 _ __3/9 = 0.3 3/99 = 0.03 _ __ 4/9 = 0.4 11/99 = 0.11 etc…… __12/99 = 0.12

  5. What is the decimal value of this fraction? 1.25

  6. What is the decimal value of this fraction? -2,333…

  7. What is the decimal value of this fraction? 8.75

  8. What is the decimal value of this fraction? -3.666…

  9. What fraction is greater? If the 2 fractions are converted to decimals, it’s easy… 2/3 = 0.666… 3/4 = 0.75 Then 3/4 is greater.

  10. What fraction is greater? Reference Points! 3/4 = 0.75 9/10 is closer to 1 So 9/10 is greater.

  11. What fraction is greater? We can use ½ as a reference point. 3/7 < 1/2 5/8 > 1/2 So 5/8 is greater.

  12. Comparing negative numbers If the numbers are negative, the numbers further left are smaller than numbers to the right on a number line. -0.5 is closer to zero so it is greater Example: What number is greater? -0.56 ou -0.5?

  13. -1 0 +1 What number is greater? - 3/4 is closer to zero so it is greater

  14. 0 +1 -1 Comparing with common denominators. If you compare - 4/7and - 3/7 you see - 3/7 is closer to zero so it is greater.

  15. Comparing with common denominators. You can also change the fraction to have common denominators to compare: Example: What fraction is greater?

  16. 0 +1 -1 What fraction is greater? When you find equivalent fractions - 7/21 is closer to zero so it is greater.

  17. Use common numerators to compare fractions. • If the numerators are the same, the fraction with the smaller denominator is the greater absolute value.

  18. What fraction is greater?

  19. -1 0 +1 What fraction is greater? • 6/8 is greater because it is closer to zero

  20. Compare fractions by converting to decimal numbers Example: What fraction is greater? So 1/8 is greater.

  21. What fraction is greater? So, 1/13 is the greater fraction.

  22. Place the row of numbers in order from least to greatest:

  23. Place the row of numbers in order from least to greatest:

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