Basic math and pre algebra practice problems for dummies

Mantesh Published by John Wiley & Sons, Inc 111 River St Hoboken, NJ 07030-5774 www.wiley.com Copyright © 2013 by John Wiley & Sons, Inc., Hoboken, New Jersey Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions Trademarks: Wiley, the Wiley logo, For Dummies, the Dummies Man logo, A Reference for the Rest of Us!, The Dummies Way, Dummies Daily, The Fun and Easy Way, Dummies.com, Making 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this book may not be included in e-books or in print-on-demand If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com For more information about Wiley products, visit www.wiley.com Library of Congress Control Number: 2013932103 ISBN 978-1-118-44656-0 (pbk); ISBN 978-1-118-44645-4 (ebk); ISBN 978-1-11844653-9 (ebk); ISBN 978-1-118-44654-6 (ebk) Manufactured in the United States of America 10 About the Author Mark Zegarelli is the author of Basic Math & Pre-Algebra For Dummies, Calculus II For Dummies, and five other books on math, logic, and test preparation He holds degrees in both English and math from Rutgers University and is a math tutor and teacher Mark lives in San Francisco, California, and Long Branch, New Jersey Dedication This is for Suleiman Author’s Acknowledgments This is my eighth For Dummies book and, as always, the experience of writing it has been productive and fun Thanks so much to editors Tim Gallan, Christy Pingleton, Lindsay Lefevere, Shira Fass, and Suzanne Langebartels for setting me right as needed And thanks to the folks at Borderlands Café on Valencia Street in San Francisco for the friendly, peaceful, and caffeine-accessible environment that virtually any writer (this one, for example) would find conducive to putting actual words on paper Publisher’s Acknowledgments We’re proud of this book; please send us your comments at http://dummies.custhelp.com For other comments, please contact our Customer Care Department within the U.S at 877762-2974, outside the U.S at 317-572-3993, or fax 317-572-4002 Some of the people who helped bring this book to market include the following: Acquisitions, Editorial, and Vertical Websites Senior Project Editor: Tim Gallan Executive Editor: Lindsay Sandman Lefevere Copy Editors: Suzanne Langebartels, Christine Pingleton Assistant Editor: David Lutton Editorial Program Coordinator: Joe Niesen Technical Editor: Shira Fass Editorial Manager: Michelle Hacker Editorial Assistants: Rachelle S Amick, Alexa Koschier Cover Photos: © Sandra van der Steen/iStockphoto.com Composition Services Senior Project Coordinator: Kristie Rees Layout and Graphics: Carrie A Cesavice, Shawn Frazier, Erin Zeltner Proofreaders: Jacqui Brownstein, Dwight Ramsey Indexer: Potomac Indexing, LLC Publishing and Editorial for Consumer Dummies Kathleen Nebenhaus, Vice President and Executive Publisher David Palmer, Associate Publisher Kristin Ferguson-Wagstaffe, Product Development Director Publishing for Technology Dummies Andy Cummings, Vice President and Publisher Composition Services Debbie Stailey, Director of Composition Services 1,001 Basic Math & Problems For Dummies® Pre-Algebra Practice Visit www.dummies.com/cheatsheet/1001basicmath&pre-algebra to view this book's cheat sheet Table of Contents Introduction What You’ll Find How This Workbook Is Organized Part I: Questions Part II: Answers Beyond the Book What you’ll find online How to register Where to Go for Additional Help Part I: The Questions Chapter 1: The Big Four Operations The Problems You’ll Work On What to Watch Out For Chapter 2: Less than Zero: Working with Negative Numbers The Problems You’ll Work On What to Watch Out For Chapter 3: You’ve Got the Power: Powers and Roots The Problems You’ll Work On What to Watch Out For Chapter 4: Following Orders: Order of Operations The Problems You’ll Work On What to Watch Out For Mantesh Chapter 5: Big Four Word Problems The Problems You’ll Work On What to Watch Out For Chapter 6: Divided We Stand The Problems You’ll Work On What to Watch Out For Chapter 7: Factors and Multiples The Problems You’ll Work On What to Watch Out For Chapter 8: Word Problems about Factors and Multiples The Problems You’ll Work On What to Watch Out For Chapter 9: Fractions The Problems You’ll Work On What to Watch Out For Chapter 10: Decimals The Problems You’ll Work On What to Watch Out For Chapter 11: Percents The Problems You’ll Work On What to Watch Out For Chapter 12: Ratios and Proportions The Problems You’ll Work On What to Watch Out For Chapter 13: Word Problems for Fractions, Decimals, and Percents The Problems You’ll Work On What to Watch Out For Mantesh “FOIL” the left side of the equation; then subtract from both sides Combine like terms and isolate t 952 To begin, cross-multiply to remove the fractions “FOIL” both sides of the equation; then subtract from both sides Simplify and isolate z 953 To begin, cross-multiply to remove the fractions “FOIL” the left side of the equation and distribute the right side; then subtract from both sides Simplify and isolate b 954 18 To begin, add the two terms on the left side of the equation Multiply both sides by and solve for p 955 To begin, use cross-multiplication techniques to add the fractions on the left side of the equation Multiply both sides of the equation by and then isolate d 956 To begin, use cross-multiplication techniques to add the fractions on the left side of the equation Multiply both sides of the equation by and then simplify and isolate s 957 To begin, use cross-multiplication techniques to add the fractions on the left side of the equation Multiply both sides of the equation by 30 and then simplify Isolate r 958 To begin, increase the terms of the first fractions by (so that the common denominator is 4); then multiply both sides of the equation by to eliminate the fractions Isolate j to solve 3=j 959 To begin, change all three fractions so that they have denominators of 8; then multiply both sides of the equation by to eliminate the fractions Isolate k to solve 960 To begin, increase the terms of all three fractions to change all denominators to 12 Then multiply both sides of the equation by 12 to eliminate the fractions Isolate a to solve 961 To begin, increase the terms of all three fractions to change all denominators to 60; then multiply both sides of the equation by 60 to eliminate the fractions Isolate h to solve 11h = 66 h=6 962 –11 Begin by changing all terms to a denominator of 9; then multiply both sides of the equation by to eliminate the fractions Isolate k 963 Begin by changing all terms to a denominator of 8; then multiply both sides of the equation by to eliminate the fractions Distribute to remove parentheses: Isolate y: 14 – 4y = 2y + – 4y = 2y 964 Divide both sides of the equation by Now, divide both sides by x=7 965 Divide both sides of the equation by Next, divide both sides by 45 Now, take the square root of both sides 966 and –5 Isolate x and solve 967 and –9 Begin by factoring the left side of the equation Now, split this equation into two separate equations and solve them x+9=0x–7=0 x = –9 x = 968 and –8 Begin by moving all terms to one side of the equation Now, factor the left side of the equation (x + 8)(x – 1) = Now, split this equation into two separate equations and solve them x+8=0x–1=0 x = –8 x = 969 and Begin by distributing on both sides of the equation to remove the parentheses; then move all terms to one side Factor the left side of the equation (x – 6)(x – 7) = Now, split this equation into two separate equations and solve them x–6=0x–7=0 x=6x=7 970 –3 and –5 Begin by cross-multiplying to remove the fractions Now, distribute on both sides of the equation to remove the parentheses; then move all terms to one side Now, factor the left side of the equation (x + 3)(x + 5) = Now, split this equation into two separate equations and solve them x+3=0x+5=0 x = –3 x = –5 971 2d + 1,000 The amount d doubles to 2d, and then increases by 1,000 to 2d + 1,000 972 3c – 60 The day begins with c chairs Then 20 chairs are removed, bringing the number to c – 20 After that, this number is tripled, which brings the number to 3(c – 20) = 3c – 60 973 p – 234 Penny starts with p pennies She then removes 300 pennies, bringing the total to p – 300 pennies The next day, she adds back in 66 pennies, so the total becomes p – 300 + 66 You can simplify this amount as follows: = p – 234 974 t – The temperature begins at t degrees and then changes as follows: t+5+2–3–6=t–2 975 6w + 12 The puppy’s weight begins at w It triples to 3w, then increases by pounds to 3w + 6, and finally doubles to 2(3w + 6) = 6w + 12 976 2k + 57 Kyle has k baseball cards Randy has half as many, so Randy has Jacob has 57 more cards than Randy, so Jacob has follows: cards And cards Add these up as You can further simplify this by combining the three k terms = 2k + 57 977 0.72s + 425 The school currently has s students The number of graduating students is 0.28s When these students leave, the number of remaining students will be s – 0.28s = 0.72s Additionally, 425 new students will be at the school, so this number will increase to 0.72s + 425 978 5m + 10 Millie walked m miles the first day, m + miles the second day, m + miles the third day, m + miles the fourth day, and m + miles the fifth day The sum of these numbers is m+m+1+m+2+m+3+m+4 Combine like terms to simplify = 5m + 10 979 4n + 12 Every consecutive odd number is exactly two greater than the preceding one So, you can represent the four numbers as n, n + 2, n + 4, and n + Thus, the sum of these numbers is: n+n+2+n+4+n+6 Simplify as follows: = 4n + 12 980 Let x equal the number Then, set up and solve the following equation: 981 Let x equal the number Then, set up and solve the following equation: 982 Let x equal the number Then, set up and solve the following equation: 983 –2 Let x equal the number Then, set up and solve the following equation: 984 Let x equal the number Then, set up and solve the following equation: 985 17 Let x equal the number Then, set up and solve the following equation: 986 23 Let x equal the number Then, set up and solve the following equation: 987 Let x equal the number Then, set up and solve the following equation: 988 7.25 Let x equal the number Then, set up and solve the following equation: 989 –11 Let x equal the number Then, set up and solve the following equation: 990 3.6 Let x equal the number Then, set up and solve the following equation: 991 Let x equal the number Then, set up and solve the following equation: 992 16 Let x equal the number Then, set up and solve the following equation: 993 $11 Let p = the number of dollars that Peter has Then Lucy has p + dollars Together, they have $27, so p + p + = 27 Solve for p 994 $170 Let m = the cost of the MP3 player in dollars Then 2m is the cost of the cellphone and 4m is the cost of the laptop computer So, you can set up the following equation: Simplify and solve for m Therefore, the MP3 player cost $170 995 years old Let j be Jane’s age Then, Cody’s age is j + and Brent’s age is 2j Cody is years older than Brent, so you can set up the following equation: Brent + = Cody Simplify and solve for j Therefore, Jane is years old 996 hours and 20 minutes Let x be the number of minutes that the class takes So, the teacher spends minutes going over homework problems and minutes reviewing for a test Thus, you can set up the following equation: Raise the terms of every term in this equation to a denominator of 10, then drop the denominators Simplify and solve for x Therefore, the class is 140 minutes long, which equals hours and 20 minutes 997 35 Let x be the first number Then the other four numbers are x + 1, x + 2, x + 3, and x + Thus, you can set up the following equation: Simplify and solve for x Thus, the five numbers are 31, 32, 33, 34, and 35 So the greatest is 35 998 78 Let y be the number of yellow marbles in the jar Then, the jar contains 3y orange marbles, y + blue marbles, and 2(y + 6) red marbles So you can set up the following equation: Simplify and solve for y Therefore, the jar contains 22 yellow marbles, so it contains 28 blue marbles and 56 red marbles Therefore, it contains 22 + 56 = 78 yellow and red marbles 999 50 mph Let s be the speed of the southbound train Then, 2s is the speed of the northbound train and 2s – 10 is the speed of the eastbound train Therefore, the southbound train is traveling at 50 mph 1000 $300 Let k equal the number of dollars that Ken has Then Walter has k – 100 dollars So, you can set up the following equation: Simplify on the right and increase the terms of each term to a denominator of 2; then drop the denominators Simplify and solve for k Therefore, Ken has $300 1001 12 Let d be Damar’s age now So Jessica’s age now is 2d Three years ago, Damar’s age was d – and Jessica’s age was 2d – And at that time, Jessica was times as old as Damar, so 2d – = 3(d – 3) Solve for d Thus, Damar is years old right now Jessica is twice his age, so she is now 12 years old To access the cheat sheet specifically for this book, go to www.dummies.com/cheatsheet/1001basicmath&pre-algebra Find out "HOW" at Dummies.com ... of Basic Math & Pre- Algebra For Dummies, Calculus II For Dummies, and five other books on math, logic, and test preparation He holds degrees in both English and math from Rutgers University and. .. for Technology Dummies Andy Cummings, Vice President and Publisher Composition Services Debbie Stailey, Director of Composition Services 1,001 Basic Math & Problems For Dummies Pre- Algebra Practice. .. a bit more basic math information than this book provides, I highly recommend my earlier book Basic Math & Pre- Algebra For Dummies This book gives you a ton of useful information for solving