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Properties of Real Numbers 1-2 Vocabulary Review 1. Circle the pairs of numbers that are opposites. 7 and 17 24 and 4 5 and 25 1.2 and 2.1 4 and u 4 u 2. Write the opposite of each number. u 23 u 1 217 1 2 !16 0 Vocabulary Builder Real Numbers real numbers (noun) reel NUM burz 1 , 8, 0, 3 6 1.55, and 4 Definition: The set of real numbers includes all rational and irrational numbers. Related Words: natural numbers, whole numbers, integers, rational numbers, irrational numbers Use Your Vocabulary 3. Circle the real numbers. 23 !5 !21 0 7 8 !21 0 7 8 4. Circle the real numbers that are integers. 23 !5 5. How does the set of real numbers differ from the set of integers? _______________________________________________________________________ _______________________________________________________________________ Chapter 1 6 Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. 5, Problem 1 Classifying a Variable Got It? Your school is sponsoring a charity race. If each participant made a donation d of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised? 6. Circle the values below that could represent the number of participants making a donation. !5 3 8 0 2.7 10 150 7. Circle the set of numbers that best describes the numbers you chose in Exercise 6. counting numbers rational numbers real numbers whole numbers Problem 2 Graphing Numbers on the Number Line Got It? What is the graph of the numbers !3, 21.4, and 13 ? 8. Find the integers each number is between. Use a calculator and round to one decimal place: Because !3 < , !3 is between 1 and 2. Think of the fraction form: 21.4 < 21.4 < so 21.4 is between and Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. Think: 13 is between and , . . 9. How can you estimate !3 without using a calculator? _______________________________________________________________________ 10. Graph the numbers !3, 21.4, and 13 on the number line. 3 2 1 0 1 2 3 Problem 3 Ordering Real Numbers Got It? How do !26 and 6.25 compare? Use S or R. 11. Find a perfect square close to 26. 2 5 12. Find a square root of a perfect square close to 6.25. " 5 7 Lesson 1-2 13. Use , or . twice to compare your answers to Exercises 11 and 12. " " 6.25 14. Now write . or , to compare !26 and 6.25. !26 6.25 Key Concept Properties of Real Numbers Let a, b, and c represent real numbers. Property Addition Multiplication Closure a b is a real number. ab is a real number. Commutative abba ab ba Associative (a b) c a (b c) (ab)c a(bc) Identity a 0 a, 0 a a 0 is the additive identity a ∙ 1 1, 1 ∙ a a 1 is the multiplicative identity Inverse a (a) 0 1 1, a 0 a ∙ a a(b c) ab bc Distributive Column A Column B 2(3x 1 7) 5 (3x 1 7)(2) Inverse Property of Addition (x 1 y) 1 5 5 x 1 (y 1 5) Commutative Property of Multiplication x105x Associative Property of Addition x?15x Distributive Property 8 1 (28) 5 0 Identity Property of Multiplication 5(2x 1 1) 5 5 ? 2x 1 5 ? 1 Identity Property of Addition Problem 4 Identifying Properties of Real Numbers Got It? Which property does the equation 3(g 1 h) 1 2g 5 (3g 1 3h) 1 2g illustrate? 16. Circle the operations used in the equation. division addition multiplication subtraction 17. Circle the algebraic equation that models 3(g 1 h) 5 3g 1 3h. hg 5 gh h1g5g1h a(g 1 h) 5 ag 1 ah a 1 (g 2 h) 5 (g 2 h) 1 a 18. The equation 3(g 2 h) 1 2g 5 3g 2 3h 1 2g illustrates the 9 Property. Chapter 1 8 Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. 15. Draw a line from the expression in Column A to the property that it illustrates in Column B. Lesson Check • Do you UNDERSTAND? Reasoning There are grouping symbols in the equation (5 1 w) 1 8 5 (w 1 5) 1 8, but it does not illustrate the Associative Property of Addition. Explain. 19. Circle the equation below that illustrates the Associative Property of Addition. a1b1c5b1a1c a 1 (b 1 c) 5 ab 1 ac (a 1 b) 1 c 5 a 1 (b 1 c) 20. The Associative Property of Addition is a rule about the order / grouping of the terms of an addition statement. 21. Write the terms grouped on each side of the equation. Left side: and Right side: and 22. Now explain why (5 1 w) 1 8 5 (w 1 5) 1 8 does NOT illustrate the Associative Property of Addition. _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ 23. Circle the property that the equation illustrates. Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. Closure Property of Addition Commutative Property of Addition Inverse Property of Addition Distributive Property Math Success Check off the vocabulary words that you understand. additive inverse multiplicative inverse opposite reciprocal squares Rate how well you understand the properties of real numbers. Need to review 0 2 4 6 8 Now I get it! 10 9 Lesson 1-2