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Comparing & Ordering Rational Numbers

Learn to compare and order positive and negative rational numbers written as fractions, decimals, and integers. Practice problems included.

carolhartman
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Comparing & Ordering Rational Numbers

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  1. AGENDA – August 11th – 15th Monday- 2-2 Comparing & Ordering Rational Numbers-NOTES – HW Practice B #’s 1-5 Tuesday – 2-2 Practice, Short Quiz HW – Study for 2-1 & 2-2 Test Wednesday – TEST 2-1 & 2-2 Thursday – Integer Review Notes HW- Textbook page 57-58 #'s 28, 29, 32, 35, 36, 43, 46 (Write out the problems) Friday – 2-7 Solving Equations with Rational Numbers – HW p.98 #’s 1-12 EVEN

  2. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  3. Write the question and show the work

  4. 0.3 0.6 Warm Up Write each fraction as a decimal. 1 3 45 2. 0.8 1. 3 4 23 3. 0.75 4.

  5. Problem of the Day How much pie do you have if you take 2 of 5 total pieces? 0.4 pie

  6. Learn to compare and order positive and negative rational numbers written as fractions, decimals, and integers.

  7. Vocabulary least common denominator (LCD)

  8. To compare or order rational numbers, first write them in the same form. To compare fractions, find a common denominator. This could be the least common denominator (LCD), which is the least common multiple of the denominators.

  9. Remember! The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.

  10. 50 60 42 60 10 10 6 6 7 10 5 6 7  6 10  6 5  10 6  10   = = = = 50 60 42 60 5 6 7 10 > ,so > Additional Example 1A: Comparing Fractions by Finding a Common Denominator Compare. Write <, >, or =. 5 6 7 10 > Method 1: Multiply to find a common denominator. Multiply 6 and 10 to find a common denominator. 6  10 = 60 Write the fractions with a common denominator. Compare the fractions.

  11. 10 15 12 15 5 5 3 3 4 5 2 3 4  3 5  3 2  5 3  5   = = = = 10 15 12 15 2 3 4 5 < ,so < Additional Example 1B: Comparing Fractions by Finding a Common Denominator Compare. Write <, >, or =. 2 3 4 5 > Method 2: Find the least common denominator. List multiples of 3 and 5. The LCM is 15. 3; 3, 6, 9, 12, 15… 5; 5, 10, 15 Write the fractions with a common denominator. Compare the fractions.

  12. 5 10 4 10 5 5 2 2 2 5 1 2 2  2 5  2 1  5 2  5   = = = = 5 10 4 10 1 2 2 5 > ,so > Check It Out: Example 1A Compare. Write <, >, or =. 1 2 2 5 > Method 1: Multiply to find a common denominator. Multiply 2 and 5 to find a common denominator. 2  5 = 10 Write the fractions with a common denominator. Compare the fractions.

  13. 8 12 9 12 4 4 3 3 3 4 2 3 3  3 4  3 2  4 3  4   = = = = 8 12 9 12 2 3 3 4 < ,so < Check It Out: Example 1B Compare. Write <, >, or =. 2 3 3 4 > Method 2: Find the least common denominator. List multiples of 3 and 4. The LCM is 12. 3; 3, 6, 9, 12, … 4; 4, 8, 12… Write the fractions with a common denominator. Compare the fractions.

  14. _ _ _ _ _ 2 9 2 9 2 7 2 7 2 9 _ 5 = 5.2 and 5 = 5.285714… _ 5.2 < 5.285714…, so 5 < 5 Additional Example 2A: Comparing by Using Decimals Compare. Write <, >, or =. _ 2 7 < A. 5 5 Write the fractions as decimals. Compare the decimals.

  15. _ _ _ _ _ _ _ _ 1 9 2 5 2 5 1 9 2 5 2 5 1 9 1 9 Write - as decimal. Write as decimal. – = –0.4 –0.44 < –0.4, so –0.44 < – = 0.1 0.1 > 0.1, so > 0.1 Additional Example 2B & 2C: Comparing by Using Decimals Compare. Write <, >, or =. < B. –0.44 – Compare the decimals. C. 0.1 > Compare the decimals.

  16. _ _ _ _ _ 2 9 3 5 3 5 2 9 2 9 _ 4 = 4.2 and 4 = 4.6 4.2 < 4.6, so 4 < 4 Check It Out: Example 2A Compare. Write <, >, or =. _ 3 5 < A. 4 4 Write the fractions as decimals. Compare the decimals.

  17. _ _ _ _ _ _ _ _ 5 6 4 5 4 5 5 6 5 6 5 6 4 5 4 5 Write – as decimal. Write as decimal. – = –0.8 –0.80 = –0.8, so –0.80 = – = 0.83 _ 0.83 > 0.8, so > 0.8 Check It Out: Example 2B & C Compare. Write <, >, or =. = B. –0.80 – Compare the decimals. C. 0.8 > Compare the decimals.

  18. To order fractions and decimals, you can either write them all in the same form and then compare them, or place them on a number line.

  19. The numbers , –3.4, 6.0, and –2.5 represent the percentage of change in populations for four states. List these numbers in order from least to greatest. Place the numbers on a number line and read them from left to right. The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0. 14 4 __ –3.4 14 4 __   –4 –3 –2 –1 0 1 2 3 4 5 6 __ 14 4 Additional Example 3: Social Studies Application 6.0  –2.5 

  20. The numbers , 3.0, –2.2, and –3.9 represent the percentage of change in populations for four states. List these numbers in order from least to greatest. Place the numbers on a number line and read them from left to right. 7 2 __ 7 2 __ –3.9   –5 –4 –3 –2 –1 0 1 2 3 4 5 The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and . __ 7 2 Check It Out: Example 3 3.0  –2.2 

  21. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  22. 9 11 7 8 6 7 2 9 1 4 8 9 < Lesson Quiz Compare. Write <, >, or =. 1 3 1. > 2. – –0.29 > 3. –2 –2 4.Leeanne competed in a long-jump contest. Her first jump was 3.75 m, her second jump was 3 m, and her third jump was 3 m. Which jump was the longest? second jump

  23. Lesson Quiz for Student Response Systems 1. Identify the correct sign to compare. A. < B. = C. > D. ≤ 1 7 1 5

  24. Lesson Quiz for Student Response Systems 2. Identify the correct sign to compare. – –0.498 A. < B. > C. = D. ≤ 3 7

  25. Lesson Quiz for Student Response Systems 3. Identify the correct sign to compare. –3 –3 A. < B. ≥ C. > D. = 4 9 5 8

  26. Lesson Quiz for Student Response Systems 4. Dalton competed in a shot put contest. His first throw was 6 m, his second throw was 6.78 m, his third throw was 6 m, and his fourth throw was 6.59 m. Which was his longest throw? A. first B. second C. third D. fourth 4 9 8 9

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