5-3 Compare and Order Integers. with <, >, or = to make a true statement. 1. SOLUTION: Graph and on a number line. Then compare.

Transcription

1 Fill in the with <, >, or = to make a true statement. 1. Graph and on a number line. Then compare. Since is to the right of, Compare the signs. Since 1 is a positive number, and is negative, then Graph 5 and 0 on a number line. Then compare. Since 5 is to the right of 0, 5 > Amy is building a house. The basement floor is at feet. The roof of the house is above the ground 25 feet. Write an inequality to compare the heights. Explain the meaning of the inequality. Compare and 25. Since is a negative number and 25 is a positive number,. 5. The low temperature in Anchorage, Alaska, one day was F. On the same day, the low temperature in Flagstaff, Arizona, was 26 F. Write an inequality to compare the temperatures. Explain the meaning of the inequality. Compare and 26. Since is negative and 26 is positive,. Order the set of integers from least to greatest. 6. {15, 17, 21, 6, 3} Graph the numbers on a number line. The order from left to right is 3, 6, 15, 17, and 21. esolutions Manual - Powered by Cognero Page 1

2 7. { 55, 143, 18, 79, 44, 101} Compare negative numbers. Then compare positive numbers. The negative integers are and. The positive integers are 143, 18, 44, < 44 < 101 < 143 So, the order from least to greatest is 79, 55, 18, 44, 101, The table indicates Xavier s cell phone use over the last four months. Positive values indicate the number of minutes he went over his allotted time, and negative values indicate the number of minutes he was under. Arrange the months from least to most minutes used. Compare the negative numbers. Then compare the positive numbers. The negative integers are and. The positive integers are 12 and > 0 So, the order from least to greatest is. The months in order are February, May, April, March. esolutions Manual - Powered by Cognero Page 2

3 9. Use Math Tools Refer to the table and the following information. The apparent magnitude of an object measures how bright the object appears to the human eye. A negative magnitude identifies a brighter object than a positive magnitude. a. Which object appears the brightest to the human eye? b. Order the objects from the brightest to the faintest. c. Find the least apparent magnitude of this data set. a. The least approximate apparent magnitude in the table is 27 which represents the Sun. b. Compare the negative numbers. Then compare positive numbers. The negative numbers are 19, 13, 27, and < 19 < 13 < 5 The positive numbers are 4 and 0. 4 > 0 The numbers from least to greatest are 27, 19, 13, 5, 0, 4. The objects from brightest to faintest are Sun, 100-Watt Bulb, Full Moon, Venus, Andromeda Galaxy, Alpha Centauri. c. The least apparent magnitude is the least value, or 27. esolutions Manual - Powered by Cognero Page 3

4 10. Justify Conclusions Refer to the graphic novel frame below for exercises a c. a. The memory card holds 65,536 kilobytes. If each picture is about 760 kilobytes, about how many more pictures can they take? b. Write an inequality to compare the number of pictures taken during school to the number of pictures taken after school. c. Explain the meaning of the inequality. a. Each picture takes about 760 kilobytes. To find how many more pictures they can take, divide 65,536 by , The camera holds about 86 picture. Subtract 43 from 86 to find how many more they can take = 43 pictures b. 19 pictures were taken during school and 24 pictures were taken after school. 19 < 24. c. More pictures were taken after school. 11. Model with Mathematics Write a real-world situation to explain the inequality $15 < $7. To represent $15 in a real-world situation, use a situation in which money is being lost or borrowed. Since $7 is positive, use a situation where money is gained or in an account. 12. Reason Abstractly Explain why 11 is less than 7, but is greater than. Sample answer: Since 11 is to the left of 7 on a number line, 11 < 7. But since 11 is a greater distance from zero than 7,. esolutions Manual - Powered by Cognero Page 4

5 13. Persevere with Problems Order the fractions from least to greatest. To order the fractions, rename each fraction with a common denominator, then order based on the numerators. The denominators are 2, 4, 6, and 8, so the least common denominator is 24. The numerators are 12, 60, 72, 4, and 21.From least to greatest, the numerators are 72, 12, 4, 21, and 60. So, the fractions from least to greatest are. 14. Persevere with Problems Find all the integers that make a true statement. Then graph the integers on the number line. Absolute value is the distance from zero. Find all the integers that have a distance of less than 3 from zero. Use a number line to help. So the integers that make the statement true are -2, -1, 0, 1 and 2. Fill in the with <, >, or = to make a true statement Since 2 is to the left of 4, 2 < 4. esolutions Manual - Powered by Cognero Page 5

6 Since 6 is to the left of 3, 6 < Since 3 is to the left of 2, 3 < The elevation of Driskill Mountain, Louisiana, is 163 meters above sea level. Death Valley has an elevation of 86 meters. Write an inequality to compare the elevations. Explain the meaning of the inequality. Since 163 is positive and 86 is negative, 163 > Yvonne owes her sister $25. Michael s checking account balance is $20. Write an inequality to compare the amounts. Explain the meaning of the inequality. If Yvonne owes money, the integer is 25. Use a number line to compare 25 and 20. Since 20 is to the right of 25, 20 > 25. Order the set of integers from least to greatest. 20. {14, 1, 6, 23, 7, 5} Graph each number on a number line. From left to right, the values are 1, 5, 6, 7, 14, 23. esolutions Manual - Powered by Cognero Page 6

7 21. { 221, 63, 54, 89, 71, 10} Order the negative numbers. Then order the positive numbers. The negative numbers are 221, 89, 71, and 10. From least to greatest, the order is 221, 89, 71, and 10. The positive numbers are 63 and < 63. So, the order from least to greatest is 221, 89, 71, 10, 54, and Gary, Sindhu, and Beth are all waiting for their trains to arrive. Gary s train leaves at 5 minutes before noon, Sindhu s leaves at 25 minutes after noon, and Beth s leaves 5 minutes before Sindhu s train. Order the three by who will leave first. Since Gary's train leaves at 5 minutes before noon, his train leaves at 11:55. Sindhu's train leaves at 25 minutes after noon, or 12:25. Beth's train leaves 5 minutes before Sindhu's train, or 12:20. The order that the three leave is Gary, Beth, Sindhu. 23. Use Math Tools Use the bar graph and the information below. The bar graph gives the scores of four golfers (A, B, C, and D). The numbers indicate scores above and below par. a. Order the scores on a number line. b. Which player had the worst score? a. Graph the scores on the number line. b. The worst score in golf is the greatest number. Player D had the greatest number, so player D had the worst score. esolutions Manual - Powered by Cognero Page 7

8 24. Verónica (V) was 12 minutes early to class, Deshawn (D) was right on time, and Kendis (K) was 3 minutes late. Which time line represents the students arrival to class? Since Verónica was 12 minutes early, the integer is 12. Deshawn was right on time, so the integer for D is 0. Kendis was 3 minutes late, so K is at 3. The second choice is correct. esolutions Manual - Powered by Cognero Page 8

9 25. The table shows the scores for a game of miniature golf. The integer 0 represents par. Sort the players from least shots taken to most shots taken. Compare negative numbers. Then compare positive numbers. The negative integers are 6 and 3. 6 < 3. The positive integers are 2 and 5. 2 < 5. So the numbers from least to greatest are 6, 3, 2, and 5. The players in order are Cristian, Liam, Bailey, and Marisol. 26. Write the fraction as a decimal. Find equivalent fractions. By multiplying both the numerator and denominator by 25, an equivalent fraction with 100 as a denominator can be found. Seventy-five hundredths can be written as esolutions Manual - Powered by Cognero Page 9

10 27. Find equivalent fractions. By multiplying the numerator and denominator by 2, an equivalent fraction with 10 as the denominator can be found. Two tenths can be written as Write an equivalent fraction. By multiplying the numerator and denominator by 5, a fraction with 100 as the denominator can be found. Fifteen hundredths can be written as The table shows the heights of Sonya s siblings. Who is taller, Frieda or Julio? Compare their heights using the symbol >. Since the whole numbers are the same, compare the fractions. To compare the fractions, rename each fraction using a common denominator. The denominators are 4 and 6, so the least common denominator is 12. Since 3 < 10,. So,. 30. Kristen and Mitchell were given the same math assignment. Kristen completes 0.8 of her work in class. Mitchell completes 0.75 of his work during class. Who has more homework remaining after class? Compare 0.8 and Rename 0.8 as Since 0.80 > 0.75, that means Kristen has done more work than Mitchell. So, Mitchell has more homework remaining after class. esolutions Manual - Powered by Cognero Page 10