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UNIT 1 Study Guide MODULE ? 1 Review Integers Key Vocabulary ESSENTIAL QUESTION How can you use integers to solve real-world problems? EXAMPLE 1 James recorded the temperature at noon in Fairbanks, Alaska, over a week in January. Day Mon Tues Wed Thurs Fri 3 2 7 -3 -1 Temperature absolute value (valor absoluto) inequality (desigualdad) integers (entero) negative numbers (número negativo) opposites (opuestos) positive numbers (número positivo) Graph the temperatures on the number line, and then list the numbers in order from least to greatest. Graph the temperatures on the number line. Th F -10-9 -8 -7 -6 -5 -4 -3 -2 -1 Tu M W 0 1 2 3 4 5 6 7 8 9 10 Read from left to right to list the temperatures in order from least to greatest. The temperatures listed from least to greatest are -3, -1, 2, 3, 7. EXAMPLE 2 Graph the following numbers on the number line. Then use the number line to find each absolute value. © Houghton Mifflin Harcourt Publishing Company -4 0 -4 -1 2 -1 -5 -4 -3 -2 -1 0 1 2 4 0 1 2 3 4 5 | -4 | = |0| = |2| = | -1 | = EXERCISES 1. Graph each number on the number line. (Lesson 1.1) 7, -2, 5, 1, -1 -10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 Unit 1 51 Write the opposite of each number . (Lesson 1.1) 3. -3 2. 8 List the numbers from least to greatest. (Lesson 1.2) 4. 4, 0, -2, 3 5. -3, -5, 2, -2 Use a number line to help you compare the numbers. Use < or >. (Lesson 1.2) 6. 4 1 8. -3 -5 7. -2 2 9. -7 2 Find each absolute value. (Lesson 1.3) 10. |6| MODULE ? 2 11. | -2 | Rational Numbers ESSENTIAL QUESTION How can you use rational numbers to solve real-world problems? Key Vocabulary rational number (número racional) Venn digram (diagrama de Venn) EXAMPLE 1 Use the Venn diagram to determine in which set or sets each number belongs. -5 1 2 Integers 4 Whole Numbers A. _12 The number _12 belongs in the set of rational numbers. 52 B. -5 The number -5 belongs in the sets of integers and rational numbers. C. 4 The number 4 belongs in the sets of whole numbers, integers, and rational numbers. D. 0.2 The number 0.2 belongs in the set of rational numbers. Unit 1 © Houghton Mifflin Harcourt Publishing Company Rational Numbers 0.2 EXAMPLE 2 1 _3 A. Order __ 10 , 0.9, 0.2, 5 , and 0.35 from least to greatest. 3 _ = 0.6 5 1 = 0.1 Write the fractions as equivalent decimals. __ 10 Use the number line to write the decimals in order. 0.1 0.2 0.35 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.6 0.9 0.8 1 0.1 < 0.2 < 0.35 < 0.6 < 0.9 1 The numbers in order from least to greatest are __ , 0.2, 0.35, _35 , 0.9. 10 B. 4 Order _25 , 0.2, and __ 15 from greatest to least. 2 Write the decimal as an equivalent fraction. 0.2 = __ = _15 10 Find equivalent fractions with 15 as the common denominator. 2 ×3 6 ____ = __ 15 5×3 1 ×3 3 ____ = __ 15 5×3 4 4 __ = __ 15 15 Order fractions with common denominators by comparing the numerators. 6>4>3 6 4 3 __ > __ > __ 15 15 15 4 The numbers in order from greatest to least are _25 , __ 15 , 0.2. EXERCISES Classify each number by indicating in which set or sets it belongs. (Lesson 2.1) 1. 8 2. 0.25 © Houghton Mifflin Harcourt Publishing Company Find the absolute value of each rational number. (Lesson 2.2) 3. 4. |-_23 | | 3.7 | Graph each set of numbers on the number line and order the numbers from greatest to least. (Lesson 2.1, 2.3) 5. -0.5, -1, -_14 , 0 -1.5 -1 -0.5 0 0.5 Unit 1 53 Don't use example 3 when solving the problems below. It has not been covered in class. You will learn that during 2nd semester.