Multi-Part Lesson 12-1 Rational Numbers - glencoe.com

1 NumbersAMulti-Part Lesson12-1 PARTBCMain IdeaCompare and order fractions , decimals, and Express Rational Numbers as terminating or repeating decimals. compare and order Rational NumbersINSECTS The most common types of insects are shown in the table. 1. Which of the insects is the longest? 2. Is the fire ant or housefly longer? Explain. 3. Are more than or less than half of the insects shown longer than inch? 4. order the lengths from shortest to as positive and negative integers can be represented on a number line, so can positive and negative Rational Numbers . You can use a number line to help you compare and order negative Rational Numbers . compare DecimalsReplace the with <, >, or = to make a true statement. the decimals on a number 0 Since is to the left of , < the decimals on a number is to the right of , > a. b. (in.)Bumble bee 3 _ 4 Cricket 1 _ 1 Fire ant 1 _ 3 Firefly 3 _ 4 Housefly 1 _ 4 Japanese beetle 1 _ 2 Mosquito 5 _ 8 compare FractionsReplace the with <, >, or = to make a true statement.

2 - 7 _ 8 6 _ 8 Since the denominators are the same, compare the numerators by graphing on a number -7 < 6, - 7 _ 8 < 6 _ 8 . - 3 _ 8 - 5 _ 16 Rename the fractions using the least common 3 _ 8 = - 3 2 _ 8 2 = - 6 _ 16 - 5 _ 16 = - 5 1 _ 16 1 = - 5 _ 16 Since -6 < -5, - 6 _ 16 < - 5 _ 16 and - 3 _ 8 < - 5 _ 16 .Check 616-516-416-316-216-116-0 c. 9 _ 16 - 12 _ 16 d. - 7 _ 10 - 4 _ 5 compare Decimals and FractionsReplace the with <, >, or = to make a true statement. - 8 _ 15 Rename - 8 _ 15 as a decimal. Then graph both decimals on a number - 8 _ 15 = 3 Since is to the right of 3 on the number line, > - 8 _ 15 . Replace the with <, >, or = to make a true -3 5 _ 8 f. 3 _ 7 Common Multiple (LCM)Find the LCM of 8 and : 8, 16, 2416: 16, 32, 48 The LCM is order Rational Numbers , first write them in the same form and then order the Numbers .

3 order Rational Numbers SCIENCE Mr. Plum s science class is Difference fromAverage Plant GrowthStudentDifference(in.)Ricky3 1 _ 4 7 _ 10 growing plants under different conditions. The average plant growth during a week was inches. The table shows the difference from the average for some students plants. order the differences from least to each number as a decimal. Ricky s plant: 3 1 _ 4 = Debbie s plant: Suni s plant: Leonora s plant: -1 7 _ 10 = each number on a number least to greatest, the differences are , -1 7 _ 10 , , and 3 1 _ 4 . g. OCEANS The average depths of the three deepest oceans are miles, miles, and miles. order the depths from least deep to deepest. Real-World LinkThe longest species of seaweed measures 197 feet. This kelp is the fastest growing species, growing more than 13 inches per day. Replace the with <, >, or = to make a true 1 5(pp.)

4 677 678) 1. 2. 3. 5 _ 8 - 3 _ 8 4. - 7 _ 12 5 _ 12 5. -6 7 _ 10 6. - 5 _ 6 Example 6(p. 679) 7. MONEY Stephen recorded the following amounts in his checkbook: -$ , $ , -$ , and $ order these amounts from least to greatest. order the following Numbers from least to greatest. 8. -3 1 _ 3 , , -3 3 _ 4 , 99 , -2 3 _ 4 , 3 1 _ 8 , -2. 2 = Step-by-Step Solutions begin on page R31. Extra Practice is on page the with <, >, or = to make a true 1 5(pp. 677 678) 10. 11. 12. 13. - 4 _ 9 - 5 _ 9 14. 5 _ 4 - 1 _ 4 15. - 3 _ 7 - 2 _ 5 16. -6 1 _ 3 17. - 3 _ 5 18. -9 2 _ 7 Example 6(p. 679) 19. STOCK MARKET The change in four stocks during CompanyChangeA-4 1 _ 2 3 _ 8 day are shown.

5 order the changes from least to greatest. 20. IN-LINE SKATING The average amount of time Brent spent in-line skating for one week was 34 minutes. During the next week, the difference between the average time and actual time spent skating was minutes, -5 1 _ 3 minutes, -2 1 _ 2 minutes, and minutes. order these differences from least to greatest. Replace the with <, >, or = to make a true statement. B 21. -0. 4 -0. 45 22. -2. 21 -2. 212 23. -6. 4 -6 4 _ 9 order the following Numbers from least to greatest. 24. 2. 1 , , 2 1 _ 11 , -2 25. 1 _ 8 , 5 , , - 1 _ 7 26. 2 _ 3 , 60%, , 4 _ 5 27. 125%, 1 3 _ 4 , 5 , 1 1 _ 5 28. SNACKS The bar graph shows the LossProfit$ $ $ $ $ $ $ $ $ or Lossprofit or loss of the after-school snack stand.

6 A. Write each profit as a positive number and each loss as a negative number. b. order the Numbers from least to greatest. 2929 MODEL ROCKETS For a technology TrialsDifference BetweenAverage Height andActual Height (ft) , Julienne constructed a model rocket. The average height the rocket can reach is 545 feet. The table shows the differences between the average height and the actual height reached. order the differences from least to greatest. Determine whether the following statement is always, sometimes, or never true. Give examples to justify your answer. If x and y are both greater than zero and x > y, then -x < -y. SENSE Determine whether the fractions - 4 _ 5 , - 4 _ 6 , - 4 _ 7 , and - 4 _ 8 are arranged in order from least to greatest. Explain. 32. Explain why is greater than -0. 33 . Write each fraction as a decimal.

7 ( Lesson 12-1B) 37. 5 _ 9 1 _ 8 39. 2 _ 3 40. Find the value of x y if x = -15 and y = -3.( Lesson 11-3E) 41. BUSINESS The table shows the results of a company s MonthProfitLossApril$15,000 May$19,000 June$12,000operations over a period of three months. Find the company s overall profit or loss over this time period. ( Lesson 11-2B) , NGSSS 33. Which point shows the approximate location of - 1 _ 3 ? "#$% A. point A B. point B C. point C D. point D 34. GRIDDED RESPONSE Which of the following Numbers is the greatest? , , , 35. SHORT RESPONSE Student Council s goal was to raise $50 each week for 4 weeks to have enough money for the school dance. The table shows the difference between the goal and the actual amount raised. order these amounts from least to ($) 36. Which of the following Numbers is less than - 2 _ 3 ? F. H. 0. 6 G.

8 1 _ 3 I. - 5 _ 6