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Transcript
Lesson 1 TAKS Grade 8 Objective 1 (8.1)(A) Comparing and Ordering Rational Numbers The set of whole numbers and their opposites is called the set of integers. Examples: 5, 3, 0, 6, 11 New Vocabulary Comparing and Ordering Integers • integers • rational numbers Use a number line to compare integers. As you move to the right on a horizontal number line, numbers increase in value. 4 2 0 2 4 2 is to the right of 4, so 2 is greater than 4. EXAMPLE 1 Use a number line to compare and order these integers: 4, 1, 5, 1. Step 1 Use a number line to represent the integers. 5 1 1 4 a < b < c < d means: “a is less than b, b is less than c, and c is less than d.” Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Step 2 Compare the integers two at a time using the number line. 5 is to the left of 1, so 5 1. 1 is to the left of 1, so 1 1. 1 is to the left of 4, so 1 4. Step 3 Order the integers using inequality signs. 5 1 and 1 1 and 1 4, so 5 1 1 4. Quick Check 1 1a. Use a number line to order these integers: 3, –1, –2. TAKS Review and Preparation Workbook 1b. Order these integers from least to greatest: 2, 0, 6, 1, 3. LESSON 1 ■ Comparing and Ordering Rational Numbers 1 TAKS Objective 1 (8.1)(A) LESSON 1 The set of rational numbers consists of all numbers that can be expressed in the form ba , where a and b are integers and b 0. Examples: 35, 0.54, 25% Comparing and Ordering Rational Numbers To order a set of rational numbers in which some are fractions or percents and some are decimals, convert them all to decimals. Then line up the numbers on the decimal point, use trailing zeros to fill out each number to the same number of decimal digits, and then compare. EXAMPLE 2 Order 31, 0.41, 0.35, 45, 30%, and 1.2 from least to greatest. To order a set of rational numbers in which some are fractions and some are decimals, write each fraction as a decimal: 13 0.333. . . and 45 0.8. Add trailing zeros and order the decimals from least to greatest. 1.20, 0.80, 0.41, 0.30, 0.333. . ., 0.35. 1.2 45 30% 0.41 1 1 12 1 2 0 1 3 0.35 1 2 1 1 12 2a. Order 23, 1.5, 0.2, 35, 9%, and 0.95 from least to greatest. 2b. Jason worked 23 of an hour and Tara worked from 6:05 P.M. to 6:50 P.M. Who worked longer? 2 LESSON 1 ■ Comparing and Ordering Rational Numbers TAKS Review and Preparation Workbook Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Quick Check 2 Name__________________________Class____________Date________ 1 A random group of students from four different classes was asked how many preferred dogs. Which class had the greatest fraction that preferred dogs? A Science class: 94 4 Which fraction below is between 53 and 45? F 23 G 56 H 87 5 B Math class: 12 J 43 C English class: 87 D History class: 56 5 Which of the following lists of rational numbers is ordered from greatest to least? 2 Which point on the number line best represents 256? 0 1 W XY 2 3 Z 4 F W A 7, 6.5, 781, 7.05 B 815, 8.95, 8.02, 8 C 6, 5.95, 5.9, 554 D 5.001, 5.01, 5, 478 G X Copyright © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. H Y J Z 6 Which list correctly places these rational numbers in order from least to greatest? 8, 8.01, 813, 8.1, 883 3 A librarian arranged some books on the shelf using the Dewey decimal system. Choose the group of book numbers that is listed in order from least to greatest. A 96.1, 96.11, 96.01, 96.001 B 240.12, 204.12, 420.12, 240.21 F 813, 8.01, 8, 8.1, 883 G 838, 8.1, 8, 8.01, 831 H 831, 8.01, 883, 8.1, 8 J 8, 8.1, 883, 8.01, 813 C 855, 855.6, 855.61, 855.601 D 531, 531.9, 531.902, 531.92 TAKS Review and Preparation Workbook LESSON 1 ■ Comparing and Ordering Rational Numbers 3