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Algebra PDF

66 Pages·2005·6.567 MB·English
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MP4050 MILLIKEN PUBLISHING CO. • ST. LOUIS, MISSOURI Algebra Grades 7–9 What does X stand for, anyway? Let X stand for prevention! Prevent: errors confusion disorganization misinformation anxiety Let X stand for prescription! Prescribe: tips procedures hints directions strategies Author: Let X stand for performance! Beverly Nance Perform: games puzzles Artists: challenges Elizabeth Adams Kisling There are certain mistakes that students frequently make while Cover Art: learning algebra. This workbook clearly explains these mistakes Joe Gray Graphic Design so the student can avoid them. Examples then illustrate the Elizabeth Adams Kisling correct way of working an algebra problem, and practice problems are provided. Puzzles and games based on scientific formulas and interesting facts challenge students to think Editor: Amy Taplin creatively. Self-checking exercises motivate students to finish each page while acquiring valuable algebraic skills. © Copyright 1991 Milliken Publishing Company 11643 Lilburn Park Drive St. Louis, MO 63146 www.millikenpub.com The purchase of this book entitles the individual purchaser to reproduce copies by duplicating master or by any photocopy process for single classroom or home use.The reproduction of any part of this book for commercial resale or for use by an entire school or school system is strictly prohibited. Storage of any part of this book in any type of Printed in the USA. networked electronic retrieval system is prohibited unless purchaser receives written All rights reserved. authorization from the publisher. Reading Mathematics 3 2 = 6 3 2 = 3⋅3 = 9 Tip Recognizing mathematical symbols will make understanding mathematics much easier. Find the symbol, unit of measurement, or prefix that matches each expression. Shade the answers to find the symbolic expression for the circumference of a circle. 1. is an element of 11. the set containing 2. absolute value of y 12. one million 3. milligram 13. equivalent to 25% 4. pi 14. 4 ⋅3⋅2⋅1 5. least common multiple 15. kilometer 6. is a subset of 16. cube root 7. alpha 17. ray AB 8. is greater than 18. right angle in degrees 9. is not equal to 19. ratio of 2 to 5 10. measure of angle C 20. brackets Circumference of a circle C = __________ . © Milliken Publishing Company 1 MP4050 Algebra Word Search There are 20 words here. Can you find them? N O G C Y L F I W U G E I E P Y T O O T J F P S T A E A N E W I N D V B T A I G W A C E I N M A C D N Z V W O Y X P D W X R A U L O N S I T L A E N L B T J W K J B S F A I F A E B O Z R M F I U H I I N E X Z U T U G P M S R S H O N H S U R N G J B Q A E J N A S G E F F O F C T X L L I J E R V H T X J E F A X M D T C H A A N K N R T N E I T O U Q I I V T U Z I I M O I I C M F A V X Y C J A Q T D F M M L U I E C N E R E F F I D L Z R O J O O L A S T V R E C I P R O C A L I R J N N U U N A A X T E S B U S D V P N P P Y O J P Y O P U C G K T B U I M H O B E L M N L F O I Q Q N A T U R A L R M O L O A J L N V X T M E R A M O Q E Y I L Q P U F E U Q U T A K O I F Z L H J A T R E D N I O K K K V R A O Z A I J R L Y X I T A Z K S V E F X P K F A G R S T F C O U W B W P Z G C Q O Q Y U O A S U Z I Here are the words to look for: algebra monomial binomial natural difference polynomial equation product exponent quotient factor rational inequality reciprocal integer subset inverse sum irrational trinomial © Milliken Publishing Company 2 MP4050 Order of Operations with Integers 8÷4⋅−2+2 = 8÷4⋅−2+2 = 8÷−8+2 = 2⋅−2+2 = −1+2 = −4+2 = 1 −2 n o n ultiplic vaitsiio n d ditio n u b tr a c tio i M D A S Y EAR UNT ALLY Tip Do multiplication and division from left to right. Division may come before multiplication. Then do addition and subtraction from left to right. Solve the problems. Write the answers in the cross-number puzzle. Across 1. −6⋅2 + 32 = 2. −6 − 7⋅8 = 3. −19 + −4⋅−9 = 4. 300 ÷ −15 + 36 = 5. 150 ÷ 6 − −4 = 6. −14 + −3⋅4 = 8. −32⋅−5 − 2 = 9. −35 + −4⋅−55 = 1 0. 85 ÷ −17 + −15 = Down 1. −25⋅−9 −13 = 2. −12 +18⋅−3 = 3. −2 − 34 ÷ −2 = 6. −28 ÷ 7⋅7 = 7. −16 − −4⋅−5 = 8. 76 − −4⋅19 = 9. 8⋅−3 − −40 = 10. −18 + −3 − 2⋅4 − 3 ÷ −3 = © Milliken Publishing Company 3 MP4050 Properties of Real Numbers a −b = b −a a −b = b −a a +−b = −b +a 6−2 = 2−6 6+−2 = −2+6 4 = −4 4 = 4 Tip Understanding the properties of real numbers helps prevent careless errors. Each of the following equations is an example of a real number property. Match the equation with the appropriate property. Use the code to uncover the name of one method of solving second degree equations. 1. a +b = b +a D Symmetric Property 2. a =a T Additive Identity 3. (a⋅b)⋅c =a⋅(b⋅c) O Associative Property of Addition 4. If a = b, then b =a M Multiplicative Identity 5. If a = b, and b =c, then a =c I Additive Inverse 6. a +0 = 0+a =a C Commutative Property of Addition 7. a +(−a) = 0 F Multiplicative Inverse 8. ab +ba U Transitive Property 1 9. a⋅ =1; a ≠ 0 L Multiplicative Property of Zero a 10. a +(b +c) = (a +b)+c R Reflexive Property 11. a⋅1=1⋅a =a Q Commutative Property of Multiplication 12. a⋅0 = 0⋅a = 0 A. Associative Property of Multiplication © Milliken Publishing Company 4 MP4050 Using Properties 3⋅4⋅−2⋅0⋅1= 3⋅4⋅−2⋅0⋅1= 3⋅4⋅−2⋅1⋅0 = 12⋅−2 = −24⋅0 = −24 0 Tip Use the properties of real numbers to simplify problems. Simplify the following problems. Follow the answers to the treasure. 1 1. a ⋅ = a 2. b + −b +y = 3. 0 ÷c = 4. x + 0⋅d = 5. 1⋅e = 6. 2x ÷ x = 7. −17a + 4a +17a = 1 8. 6a ⋅8x ⋅ = 6a a c b d 9. ⋅ ⋅ ⋅ = b d a 1 10. 5 ( x + 3x ) = 11. ab +cd + −ab = a 12. ⋅x2 = a 13. ( 3x + 5x − 8x )⋅4y = 14. 37x2 + 52x2 + −37x2 = 15. xyz ÷ xyz = 1 1 16. 5a ⋅( 2a ⋅ ⋅ ) = 5 a 17. 6y2 + 5y2 − 6y2 = 18. ( −14x2y + 42xy2 −17x )⋅0 + 7 = 19. 2⋅3a + 2⋅4a = 1 1 20. −a ⋅ ⋅−b ⋅ ⋅4 = a b © Milliken Publishing Company 5 MP4050 Application Word Problems Solve the word problems. 1. Last week Calvin scored twice as many baskets as Joel. If Calvin scored 36 baskets, how many did Joel score? 2. A chocolate brownie has four times as many calories as an apple. If an apple has 70 calories how many does a brownie have? 3. Jan bought a motorcycle for $3500. Julie bought a bicycle. The motorcycle cost seven times as much as the bicycle. How much was Julie’s bicycle? 4. Sam emptied his bank and counted 105 coins. If 37 are dimes, 42 are nickels, and the rest are quarters, how many quarters are there? 5. Jeff has 4 more than twice the number of compact discs that Ryan has. If Jeff has 34, how many compact discs does Ryan have? 6. For $18 Becky can order 24 cupcakes for her party. How much does one cupcake cost? 7. Nineteen-year-old Wendell is one more than three times his brother’s age. How old is Wendell’s brother? 8. A leather jacket costing $300 is priced at $60 less than four times a wool jacket. How much is the wool jacket? 9. The Tigers scored 84 points in their last game. They made 34 two-point baskets. How many points came from free-throws? 10. Cynthia paid $7 less than twice what Shantel paid for her sweater. If Shantel paid $28 for her sweater, how much did Cynthia pay for her’s? © Milliken Publishing Company 6 MP4050 Prime Factor Trees Tip Using prime factor trees will help you find greatest common factors (GCF) and least common multiples (LCM). Express each number as a product of primes. Then shorten the expression using exponents (e.g., 2 ⋅2⋅3⋅3 = 22⋅32). Shade your answers to uncover the name of the man who first defined primes in 300 B.C. 1. 24 = 9. 12 = 17. 36 = 2. 45 = 10. 48 = 18. 160 = 3. 54 = 11. 135 = 19. 96 = 4. 108 = 12. 8 = 20. 40 = 5. 21= 13. 72 = 21. 98 = 6. 30 = 14. 18 = 22. 275 = 7. 121= 15. 66 = 23. 84 = 8. 50 = 16. 27 = 24. 324 = © Milliken Publishing Company 7 MP4050 Reducing Square Roots 2448 = 2448 = 4⋅36⋅17 = 50 ? 48 ? 2⋅6 17 = 116 ? 12 17 Tip Use prime factor trees to help find perfect squares. Reducing radicals is much easier then. Find the missing radicand by factoring out perfect squares. Write the answers in the cross-number puzzle. Across 1. 468 = 6 2. 207 = 3 3. 270 = 3 4. 496 = 4 5. 1216 = 8 6. 891= 9 8. 456 = 2 9. 7525 = 5 10. 1377 = 9 11. 1188 = 6 Down 1. 404 = 2 2. 525 = 5 3. 1715 = 7 6. 56 = 2 7. 801= 3 8. 1808 = 4 9. 2496 = 8 10. 1000 =10 © Milliken Publishing Company 8 MP4050

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