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T TABLE OF CONTENTS UNIT 1 – BUILDING THE FOUNDATION CHAPTER 1 PLACE VALUE ALGEBRA TIPS TO WIN! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 ALGEBRA TIPS TO WIN! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 WORDS ARE POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 THE POWER IS YOURS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 START WITH PLACE VALUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 CHAPTER 2 READING NUMBERS USING THE PLACE VALUE TABLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 READING THE NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 READING REALLY BIG NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 LET'S DO IT AGAIN! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 FILL IT IN! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 E CHAPTER 3 COMPARING AND ROUNDING MORE OR LESS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 LESS OR MORE? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12 ROUNDING OFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13 ROUND! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14 THE DATE! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 PL CHAPTER 4 NUMBER EXPRESSIONS EATING OUT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 IMPORTANT WORDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 USE THOSE WORDS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18 OPERATION DIVISION! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 LET'S EXERCISE THOSE MATH SKILLS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 SA M CHAPTER 5 ORDER OF OPERATIONS AND EXPONENTS MEET AUNT SALLY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 HEY, AUNT SALLY! HELP! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 WHAT'S AN EXPONENT? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 PUSH IT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 MORE PRACTICE WITH EXPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 CHAPTER 6 EQUAL AND NONEQUAL EXPRESSIONS HIT IT HARD! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 GO AFTER IT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 ARE THEY THE SAME? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28 THE SAME? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 E = MC2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 UNIT 2 – PROPERTIES, VARIABLES, AND SUBSTITUTION CHAPTER 7 ADDITION PROPERTIES ADD 'EM UP! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31 CANDY IS CANDY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32 I.D. THE PROPERTY WITH ZERO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33 YOU ARE THE DETECTIVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34 ADDITION WORKOUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35 CHAPTER 8 MULTIPLICATION PROPERTIES MULTIPLICATION PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36 YOU ARE ON EASY STREET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37 MULTIPLICATION WITH ZERO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38 YOU ARE THE TEACHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 EASY AS PIE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .40 CHAPTER 9 DISTRIBUTIVE PROPERTY DISTRIBUTING NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 USE THE RIGHT STEPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42 DISTRIBUTION TRAINING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .43 USE A LETTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44 HOW DO WE USE VARIABLES? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45 © Copyright 2009 www.firelightbooks.com TCHAPTER 10 IDENTIFYING TERMS WHAT IS A TERM? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 WHAT IS A CONSTANT? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47 WHAT IS A COEFFICIENT? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 LIKE TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 UNLIKE TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 CHAPTER 11 COMBINING TERMS VARIABLES WITH THE SAME EXPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 PUTTING LIKE TERMS TOGETHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 EVERYONE LOVES DOGS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53 WHAT IF THEY ARE NOT LIKE TERMS? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 DON'T FORGET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 CHAPTER 12 SUBSTITUTING TO SOLVE PROBLEMS COACH, I NEED A SUB! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 PLUG IT IN, PLUG IT IN! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 YOU GO! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58 MOVING ON UP! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .59 TO THE TOP! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 E UNIT 3 – VARIABLE AND EQUIVALENT EQUATIONS PL CHAPTER 13 ORDERING WITH VARIABLES WHERE DO THEY GO? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 MORE THAN ONE LETTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 FOLLOW THE STEPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 VARIABLE EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 VARIABLE SOLUTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 SA M CHAPTER 14 VARIABLE EQUATIONS NAIL IT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66 SOLVING VARIABLE EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67 WHERE'S MY CHANGE? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68 BOX OF CHOCOLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69 PEANUTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70 CHAPTER 15 EQUIVALENT EQUATIONS E IS FOR EQUAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .71 ARE THEY EQUAL? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .72 EASY EQUIVALENT EQUATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 STEP IT UP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74 BOTH SIDES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 CHAPTER 16 PROPERTIES OF EQUALITY PROPERTIES OF EQUALITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76 EQUALITY WITH MULTIPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77 COUNTING CASH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78 EQUALITY WITH DIVISION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .79 TIME TO EAT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80 CHAPTER 17 INVERSE OPERATIONS REVERSE, REVERSE! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .81 FOR REAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82 GIVE IT A GO! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83 UNDO IT WITH DIVISION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .84 UNDO WITH MULTIPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .85 CHAPTER 18 UNDOING OPERATIONS UNDOING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86 SOLVING EQUATIONS BY SUBTRACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .87 PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .88 UNDO SUBTRACTION WITH ADDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89 GET THE VARIABLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90 © Copyright 2009 www.firelightbooks.com UNIT 4 – ORDER OF OPERATIONS CHAPTER 19 USING MULTIPLICATION AND DIVISION USING MULTIPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91 PUPPIES! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92 ON THE JOB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93 USING DIVISION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94 SOLVING PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95 CHAPTER 20 OPERATION PRACTICE USING PARENTHESES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96 AUNT SALLY IS BACK! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97 THE OTHER SIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98 OPERATION PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .99 POTATOES! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .100 E CHAPTER 21 IDENTIFYING AND WRITING EXPONENTS SHORTCUT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101 FIND THE POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102 EXPONENTS IN ACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103 WHAT TIMES WHAT? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104 EXPONENTS FOR REAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105 PL CHAPTER 22 ORDER OF OPERATIONS ORDER OF OPERATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106 KEEP THE ORDER! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107 WHO'S FIRST? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 LIKE A DOCTOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109 DOCTOR KNOW-IT-ALL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110 SA M CHAPTER 23 ORDERING WITH PARENTHESES AND EXPONENTS PARENTHESES RULE! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111 MORE PARENTHESES PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .112 OPERATIONS WITH EXPONENTS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113 THE NEXT STEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .114 AWAY YOU GO! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .115 CHAPTER 24 COMPARING INTEGERS ON A NUMBER LINE THE NUMBER LINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .116 GRAPHING IS FUN! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 HOW DO YOU COMPARE? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118 COMPARING WITH A NUMBER LINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119 COMPARING POSITIVE AND NEGATIVE NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120 UNIT 5 – ABSOLUTE VALUE AND SIMPLIFYING CHAPTER 25 ABSOLUTE VALUE ABSOLUTELY! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121 OPPOSITES ARE THE SAME! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .122 YOU ARE ABSOLUTELY RIGHT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .123 GET THE ABSOLUTE VALUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .124 FOR REAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125 CHAPTER 26 NUMBER LINE SKILLS ADDING ON A NUMBER LINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .126 ABSOLUTE ADDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127 ADD THEM UP! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128 SUBTRACTING NUMBERS USING A NUMBER LINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129 MEASURE TWICE, CUT ONCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130 CHAPTER 27 MULTIPLYING INTEGERS MULTIPLYING INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .131 MULTIPLYING INTEGER RULES (RULE #1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132 RULE #2: MULTIPLYING NEGATIVE INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .133 RULE #3: MULTIPLYING INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .134 MULTIPLY THOSE INTEGERS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .135 © Copyright 2009 www.firelightbooks.com CHAPTER 28 DIVIDING INTEGERS DIVIDING INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136 RULE #1: DIVIDING POSITIVE INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137 RULE #2: DIVIDING NEGATIVE INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138 RULE #3: DIVIDING INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139 DIVIDE THOSE INTEGERS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140 CHAPTER 29 SIMPLIFYING WITH ADDITION SIMPLIFYING ADDITION EXPRESSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141 ADDING POSITIVE INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .142 ADDING NEGATIVE INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143 SIMPLIFYING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .144 YOU SIMPLIFY! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145 CHAPTER 30 SIMPLIFYING INTEGERS SIMPLIFYING SUBTRACTION PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .146 SUBTRACTING POSITIVE INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .147 SUBTRACTING NEGATIVE INTEGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .148 SIMPLIFYING PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .149 SUBTRACTING NEGATIVES AGAIN! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .150 E UNIT 6 – PERFORMING OPERATIONS PL CHAPTER 31 GROUPING GROUPING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .151 GROUPING PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .152 PRACTICE SUBTRACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153 ORDER IS IMPORTANT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .154 DRILL TIME! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155 SA M CHAPTER 32 EXPONENTS EXPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156 NEGATIVE EXPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157 A TRICK! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158 EXPRESSIONS ARE POWERFUL! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159 YOU HAVE THE POWER! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160 CHAPTER 33 ADDITION PROPERTIES ADDITION PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .161 ASSOCIATIVE PROPERTY OF ADDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .162 IDENTITY PROPERTY OF ADDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163 ADDITION PROPETY OF OPPOSITES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164 ADDITION PROPERTY PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165 CHAPTER 34 MULTIPLICATION PROPERTIES MULTIPLICATION PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166 ASSOCIATIVE PROPERTY OF MULTIPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .167 IDENTITY PROPERTY OF MULTIPLICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168 MULTIPLICATION PROPERTY OF ZERO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169 MULTIPLICATION PROPERTIES COMBINED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .170 CHAPTER 35 THE DISTRIBUTIVE PROPERTY THE DISTRIBUTIVE PROPERTY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171 DISTRIBUTING EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .172 WHICH NUMBER TO DISTRIBUTE? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .173 DISTRIBUTION WITH SUBTRACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174 MOVING WITH DISTRIBUTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175 CHAPTER 36 REVIEW MULTIPLY AND DIVIDE INTEGERS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .176 MORE POWER! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .177 ADDITION PROPERTIES PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178 MULTIPLICATION PROPERTIES PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .179 PRACTICE DISTRIBUTING AGAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180 IMPORTANT WORDS TO KNOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181 © Copyright 2009 wwwfirelightbooks.com UNIT 1 ALGEBRA TIPS TO WIN! PRACTICE, PRACTICE, PRACTICE! LEARN THE VOCABULARY. LEARN THE SYMBOLS. BE NEAT! BE CLEAR! USE A PENCIL. HEY, SHOW YOUR WORK! CIRCLE YOUR ANSWERS. DIVISION PROBLEMS ARE WRITTEN AS FRACTIONS. 9. USE PARENTHESES TO WRITE MULTIPLICATION PROBLEMS. 10. BE POSITIVE! 11. ASK QUESTIONS! 12. TAKE RESPONSIBILITY FOR YOUR WORK! SA M PL E 1. 2. 3. 4. 5. 6. 7. 8. PRACTICE, PRACTICE, PRACTICE! TRY NOT TO USE A CALCULATOR. Work out your brain. Your math skills need to be exercised to be strong. LEARN THE VOCABULARY. Talk the talk. Words are power! Words are the road map to getting the answers. LEARN THE SYMBOLS. Knowing the symbols gives you power. Symbols are the road signs to the answers! BE NEAT! BE CLEAR! Writing clearly is an important step to success. Write big. Write clearly. You have to be able to read your work! © Copyright 2009 Illegal to copy www.firelightbooks.com 1 UNIT 1 ALGEBRA TIPS TO WIN! USE A PENCIL. Smart people do a lot of erasing, so get out your pencil! HEY, SHOW YOUR WORK! Write each step under the one before it. Do not skip steps. You will save time. It will be easier for people to understand what you are doing. E CIRCLE YOUR ANSWERS. We want to see them! PL DIVISION PROBLEMS ARE WRITTEN AS FRACTIONS. Check it out. p x + 3 5 SA M USE PARENTHESES TO WRITE MULTIPLICATION PROBLEMS. Check it out. p (x)(5)(9) = 90 BE POSITIVE! Even if you hate math, pretend like you love it. Knowledge is power, and you need to know this stuff in real life! ASK QUESTIONS! Many people care about you. They can help. Just ask! TAKE RESPONSIBILITY FOR YOUR WORK! Be proud of your good work. Fix your mistakes. Learn how to do it right. Sometimes math is hard, but remember, you are smarter than those numbers! YOU CAN DO ALGEBRA!!! Which tip will help you the most? © Copyright 2009 Illegal to copy www.firelightbooks.com 2 UNIT 1 FILL IT IN! Look at this place value table. The place tells you the value of the number. The Game: Fill in the blanks. Millions Thousands Ones PL ________________ TEN-THOUSANDS E Hundreds Tens Ones , Hundreds Tens Ones , Hundreds Tens Ones , 6 2 4 9 1 ________________ THOUSANDS ________________ HUNDREDS ________________ TENS SA M ________________ ONES The Game: Fill in the blanks. Millions Thousands Ones Hundreds Tens Ones , Hundreds Tens Ones , Hundreds Tens Ones , 7 1 6 0 ________________ THOUSANDS ________________ HUNDREDS ________________ TENS ________________ ONES Read 62,491 aloud. Read 7,160 aloud. © Copyright 2009 Illegal to copy www.firelightbooks.com 10 MORE OR LESS? Use these two symbols to compare numbers. > means greater than < means less than The arrow points to the smaller number. For example: 2>1 E 2 is greater than 1. The arrow points to the smaller number (1). PL The Game: Compare the numbers. Fill in the blanks. < means less than > means greater than 68 ____ 37 31 ____ 36 360 ____ 370 SA M 9 ____ 6 Remember! The arrow that points LEFT means LESS THAN. Math in Real Life There are two jobs. The job at the pizza restaurant pays $368 per week. The job at the sandwich shop pays $379 per week. Which job do you pick? Here is a way to show which job pays more. 368 ____ 379 Did you pick the job at the pizza restaurant or the job at the sandwich shop? ________________ Why?_________________________________________ © Copyright 2009 Illegal to copy www.firelightbooks.com 11 UNIT 1 LESS OR MORE? The arrow points to the smaller number. For example: 200 > 100 200 is greater than 100. p 100 100 is the smaller number. For example: 100 < 200 100 is less than 200. 100 ____ is the smaller number. For example: 200 = 200 200 equals 200. Is there a smaller number? _______ PL E p SA M < means less than > means greater than = means equal The Game: Compare the numbers. Fill in the blanks. 431 ____ 311 909 ____ 9109 79 ____ 97 664 ____ 646 943 ____ 934 504 ____ 445 141 ____ 411 49 ____ 54 47 ____ 47 97 ____ 79 Which group has more fish? Write < or > in the blank. ________ © Copyright 2009 Illegal to copy www.firelightbooks.com 12 UNIT 1 ROUNDING OFF Rounding is like estimating. We use rounding every day. Gloria went to the movies. She bought popcorn and a drink. The total was $3.75. She didn't have the exact change, so she rounded $3.75 up to the nearest dollar amount. She gave the clerk $4. Bobbie needed a red silk ribbon that was 1½ feet long to make a fancy bow. She wanted to have a little extra, so she rounded the amount up and got 2 feet of ribbon. PL E How to round: 1. First find the place value you want. It’s called the rounding number. 2. Look right! If that number is 0–4, do not change the rounding number! If that number is 5–9, change it! Add one to the rounding number. 3. Change all numbers to the right of the rounding number to zero. SA M Do it! Round 972 to the nearest tens' place. Millions Thousands Ones Hundreds Tens Ones , Hundreds Tens Ones , Hundreds Tens Ones First find the rounding number. p Look right! p The 2 is in the rounding place. Ask, "Is that number 0–4?" p Change all the numbers to the right of the rounding number to zero. p 972 rounded to the nearest tens place 9 7 2 The 7 is in the tens place. The 2 is on the right. Yes! Do not change the 7. 970 is 970. The Game: Answer the questions. 1. What do you do if the number in the rounding place is 0–4? _________________________________________________________ 2. What do you do if the number in the rounding place is 5–9? _________________________________________________________ © Copyright 2009 Illegal to copy www.firelightbooks.com 13 UNIT 1 USE THOSE WORDS! Math is a game! To find the answer to the expression, p p p follow the operation. The expression p Add p The answer is p 9+4 9+4 13 E The value of 9 + 4 is 13. PL The Game: Write the answers (the values) in the blanks. 4 + 5 = ____ 42 + 51 = ____ 14 + 5 = ____ 2 + 2 = ____ 3 + 4 = ____ 23 + 14 = ____ 55 + 4 = ____ 1 + 7 = ____ 5 – 1 = ____ 55 – 13 = ____ 16 – 16 = ____ 30 – 20 = _____ 50 – 50 = ____ 40 – 0 = ____ 70 – 50 = ____ 6 + 9 = ____ 81 + 9 = ____ 68 + 10 = ____ SA M 1 + 2 = ____ 8 + 9 = ____ Write the answers. What is the value of 9 + 4? ____ What is the value of 12 + 4? ____ What is the value of 9 – 4? ____ What is the value of 12 – 4? ____ What are some operation signs? © Copyright 2009 Illegal to copy www.firelightbooks.com 18 UNIT 1 OPERATION DIVISION! This time use a different operation! The expression p 8/2 Divide p 8/2 The answer is p 4 The value of 8/2 is 4. PL E HOT TIPS! Tip: You can also use parentheses and dots to show multiplication: 7(3) = 21 8(2) = 16 9(9) = 81 7 • 7 = 49 5 • 4 = 20 4•1= 4 Tip: Use ÷ or / for division: 12/3 = 4 16 ÷ 4 = 4 81/9 = 9 The Game: Write the answers (the values) in the blanks. 6/2 = ____ 10 ÷ 2 = ____ 12 ÷ 2 = ____ 5 x 5 = ____ 6 x 3 = ____ 4 x 5 = ____ 7 x 3 = ____ 4 ÷ 2 = ____ 10 • 2 = ____ 8 ÷ 2 = ____ 20 • 5 = ____ 20 ÷ 2 = ____ 22 ÷ 2 = ____ 18 ÷ 2 = ____ 14/2 = ____ 100 x 1 = ____ 1 x 1 = ____ 8 x 10 = ____ 100 x 2 = ____ SA M 7 ÷ 7 = ____ Write the answers. What is the value of 2 x 6? ____ What is the value of 12 ÷ 4? ____ What is the value of 5 • 6? ____ What is the value of 8/4? ____ What are some operation signs for multiplication? © Copyright 2009 Illegal to copy www.firelightbooks.com 19 UNIT 1 LET’S EXERCISE THOSE MATH SKILLS! The Rule: DOTS • and PARENTHESES ( ) both mean that you should multiply. E The Game: Write the answers (the values) in the blanks. 8 + 7 = ____ 14 ÷ 2 = ____ 4 + 4 = ____ 5 • 5 = ____ 4 x 6 = ____ 7 x 5 = ____ 8 • 2 = ____ 2 • 3 = ____ 20 ÷ 2 = ____ 20 • 5 = ____ 4(8) = ____ 7 • 2 = ____ 32 ÷ 8 = ____ 14 ÷ 7 = ____ 20 ÷ 4 = ____ 12 ÷ 4 = ____ 8 x 5 = ____ 100 x 3 = ____ SA M PL 9 + 1 = ____ 42 ÷ 6 = ____ Write the answers. What is the value of 8 • 2? ____ What is the value of 20 ÷ 4? ____ What is the value of 4(8)? ____ What is the value of 12 ÷ 4? ____ What do dots and parentheses tell you to do? © Copyright 2009 Illegal to copy www.firelightbooks.com 20 UNIT 1 MEET AUNT SALLY Everyone who works algebra knows Aunt Sally! She is the Queen of Operations. She has just moved in to help you! Aunt Sally says, "If a math problem has more than one sign, do things in the right order." You have to know the ORDER OF OPERATIONS. PL E Here is the trick! To do things in the right order, use this saying: Please Excuse My Dear Aunt Sally. Each capital letter stands for a different operation: P = Parentheses ( ) E = Exponents (2²) M = Multiply (•, x) Multiplication and division rank the same. Work from D = Divide (÷, /) left to right doing any "M" or "D" as you find them. A = Add (+) Addition and subtraction rank the same. Work from S = Subtract (–) left to right doing any "A" or "S" as you find them. SA M Please Excuse My Dear Aunt Sally (PEMDAS). Example: Using PEMDAS, we know that DIVIDE So we divide first! We put our answer into our problem: Now we add to get the final answer! 8 + 10 ÷ 2 comes before ADD. 8 + (10 ÷ 2 = 5) 8 + (5) 8 + 5 = 13 1. P 2. E 3. M or D 4. A or S The Game: 5+8÷2 Using PEMDAS, we know that DIVIDE comes before ADD. So we divide first! 5 + (8 ÷ 2 = ____) We put our answer into our problem: 5 + (____) Now we add to get the final answer! 5 + ____ = ____ FYI: An exponent is a small number written with another big number that tells how many times to multiply the big number by itself. It looks like this: 2 2. © Copyright 2009 Illegal to copy www.firelightbooks.com 21 UNIT 1 HEY, AUNT SALLY! HELP! The Game: Fill in the blanks. E Aunt Sally can put a hurt on math with PEMDAS. Follow the Order of Operations: P = Parentheses ( ) E = Exponents (2²) 1. P 2. E M = Multiply (•, x) 3. M or D D = Divide (÷, /) 4. A or S A = Add (+) S = Subtract (–) PL 10 + 4 ÷ 2 Using PEMDAS, we know to DIVIDE before we ADD. So we divide first! 10 + (4 ÷ 2 = ____) We put our answer into our problem: 10 + (____) Now we add to get the final answer! 10 + ____ = ____ SA M Let Aunt Sally help you follow the order of operations to solve your problem! Write your answers in the blanks. 5÷5+2= _____ 9•7+2= _____ 8x5–1= 10 ÷ 2 + 3 = _____ _____ 22 • 4 + 8 = 11 + 7 = 8x2+3= 100 ÷ 5 + 50 = _____ _____ _____ _____ © Copyright 2009 Illegal to copy www.firelightbooks.com 22 UNIT 1 WHAT'S AN EXPONENT? Exponents help you jump to the answer. 2² Look p The little number next to the 2 is called an exponent. It means that you multiply the big number by itself that many times. 2² means: 2 x 2. E The Game: Circle the exponents in these numbers! 22 10 2 82 63 892 44 32 52 87 31 SA M Example: 43 PL Look p 32 This means 3 x 3, which equals 9. The little 2 is the exponent. It DOES NOT mean to multiply the 3 by 2. It tells how many times to multiply the 3 times itself. 43 = 4 x 4 x 4 = 64. The little 3 tells how many 4s to multiply together. The Game: Fill in the blanks. 53 This means 5 x 5 x 5, which equals ____. The little ____ is the exponent. It means to multiply the 5 by itself ____ times. 24 This means 2 x 2 x 2 x 2, which equals ____. The little ____ is the exponent. It means to multiply the 2 by itself ____ times. Aunt Sally says, "You are hot on the trail!" © Copyright 2009 Illegal to copy www.firelightbooks.com 23 UNIT 1 PUSH IT! Exponents help you get the answer. What does 2 3 mean? Break It Down: 2³ means 2 x 2 x 2, and the answer is 8. What does 3 4 mean? The Game: Fill in the blanks. E 3 4 means 3 x 3 x 3 x 3, and the answer is 81. PL 7 ³ means 7 x 7 x 7. What does it equal? ____ x ____ x ____ = ____ SA M 8 ² means 8 x 8. What does it equal? ____ x ____ = ____ 14 means 1 x 1 x 1 x 1. What does it equal? ____ x ____ x ____ x ____ = ____ 64 This means 6 x 6 x 6 x 6, which equals ____. The little ____ is the exponent. It means to multiply the 6 by itself ____ times. Tell Aunt Sally what 2 4 is. © Copyright 2009 Illegal to copy www.firelightbooks.com 24 DISTRIBUTING NUMBERS Distributive means working with each number in the parentheses. The distributive property uses two operations. Here is how it works: UNIT 2 2(4 + 5) 2(4 + 5) PL Break It Down: The problem p Multiply. Then add. Then simplify. E When a number is next to an addition or subtraction problem in parentheses, we distribute that number to both numbers inside the parentheses. 2•4+2•5 8 + 10 8 + 10 = 18 SA M The Game: Fill in the blanks. Multiply. Then add. Then simplify. 6(8 + 9) 6 • 8 + 6 • ____ 48 ____ 54 48 + ____ = 102 The Game: Fill in the blanks. 2(3 + 5) 2 • ____ + 2 • 5 6 + ____ 6 + 10 = ____ 5(4 + 2) 5 • ____ + 5 • ____ 20 ____ 10 ____ + 10 = 30 What does distributive mean? © Copyright 2009 Illegal to copy www.firelightbooks.com 41 USE THE RIGHT STEPS Distribute more numbers using the right steps. Break It Down: The problem p 2(3 + 7) Second step: Multiply. 2 • 3 = 6 and 2 • 7 = 14 Third step: Add. 6 + 14 = 20 E The answer is 20! SA M PL Examples: 8(4 + 5) = 8 • 4 + 8 • 5 (4 – 2)2 = 2 • 4 – 2 • 2 6(6 – 5) = 6 • 6 – 6 • 5 (8 – 7)9 = 9 • 8 – 9 • 7 3(2 + 20) = 3 • 2 + 3 • 20 UNIT 2 First step: Distribute the number. 2 • 3 + 2 • 7 The Game: Distribute these numbers, just like the examples above. Fill in the blanks. 2(4 –1) = ______ – ______ 3(2 + 1) = ______ + ______ 4(2 + 2) = ______ + ______ 5(3 + 1) = ______ + ______ What do you do first in distribution? © Copyright 2009 Illegal to copy www.firelightbooks.com 42 DISTRIBUTION TRAINING Following the right steps is important. Break It Down: The problem p 4(3 + 5) First step: Distribute the number. 4 • 3 + 4 • 5 4 • 3 = 12 and 4 • 5 = 20 UNIT 2 Second step: Multiply. Third step: Add (Make it simple.) 12 + 20 = 32 E The answer is 32! PL The Game: Show the steps for the problems: Hint: Distribute, Multiply, Make it simple. 7(1 + 2) = ____ ______________________ ______________________ ______________________ SA M The problem p 1. ______________________ 2. ______________________ 3. ______________________ The problem p 1. ______________________ 2. ______________________ 3. ______________________ 3(9 + 2) = ____ ______________________ ______________________ ______________________ The Game: Fill in the blanks. 7(4 + 3) = 7 • 4 + 7 • ____ (____ + 5)2 = 2 • 7 + 2 • 5 6(0 + 3) = 6 • 0 + ____• 3 9(8 + 9) = ____ • 8 + 9 • 9 What is the second step of distribution? © Copyright 2009 Illegal to copy www.firelightbooks.com 43 USE A LETTER Think about football players wearing letters instead of numbers on their jerseys. In math we can use a letter instead of a number! A variable is a letter that represents a number. E UNIT 2 A variable expression is a group of variables, numbers, and operations. These are variable expressions: x + 2x 7ab – 3ab 10 + x 2 PL The Game: Circle the variables in each expression. SA M 2+x 7xA 8(A + C) 89 + d T+T RA + 564 200 + ZEB y+3•x Z + 555 B – 3(acd) Smart tip: Expressions can be written in different ways. Examples: 3 times b can be written these ways: 3b or 3xb or 3(b) or 3•b 3 divided by b can be written in these ways: 3÷b or 3/b What is a letter that represents a number called? © Copyright 2009 Illegal to copy www.firelightbooks.com 44 HOW DO WE USE VARIABLES? 2ab = 2 • a • b Example p 4x = 4 • x Example p 3z = 3z ÷ 9 9 E Example p UNIT 2 You know that variables are letters that represent numbers. How are they used? The Game: Fill in the blanks. 8 + t = ____ + t 7x = ____ • x 99z + 14n + 3z = 99z + 14n + ____ 6q + 2 = 6 •____ + 2 PL 5a = 5 • ____ k – 1 = ____ – 1 54g – 56k = 54g – 56____ m + 2 = 2 + ____ 3x + 2 + 1 = 3 • ____ + ____ + 1 SA M 7ad = 7 • ____ • ____ Fractions tell you to divide. This is true with letters (variables) also! Example p x=x÷4 4 Example p 5y = 5y ÷ 10 10 Example p 20n = 20n ÷ 2 2 The Game: Fill in the blanks. 4 = ____ ÷ ____ n n = ____ ÷ ____ 8 4 = ____ ÷ ____ 2g 56J ÷ 4 = ____ 4 © Copyright 2009 Illegal to copy 25n = ____ ÷ ____ 5 50x = ____ ÷ ____ 10 100c = ____ ÷ ____ 20 y ÷ 7 = ____ www.firelightbooks.com 45 TO THE TOP! Here are some more substitution problems, already done for you! Remember PEMDAS. t=5 UNIT 2 Examples: 10t + t – 10 10(5) + 5 – 10 50 + 5 = 55 – 10 = 45 PL E 5t + 5 + 5t 5(5) + 5 + 5(5) 25 + 5 + 25 = 55 100t + 100 + 200t 100(5) + 100 + 200(5) 500 + 100 + 1000 = 1600 SA M t 2 + 2t + 2 (5 • 5) + 2(5) + 2 25 + 10 + 2 = 37 The Game: Substitute or plug in to find the answers. Show your work. t=5 4t + 3t + 5 _____ © Copyright 2009 Illegal to copy t+t+t 7t + t 2 – 0 _____ _____ www.firelightbooks.com t÷5+5 _____ 60 WHERE DO THEY GO? It is important to put your terms and answers in order. The Order: First: terms with exponents Second: numbers with variables and coefficients Last: numbers by themselves 6x 2 + 3x + 2 Example p 6x 2 Numbers with variables and coefficients p Numbers by themselves p 3x 2 E Terms with exponents p SA M UNIT 3 PL The Game: Fill in the blanks. 5x – 8 Terms with exponents p (There aren't any!) Numbers with variables and coefficients p _____ Numbers by themselves p _____ 4x 6 + 90x – 1 Terms with exponents p _____ Numbers with variables and coefficients p _____ Numbers by themselves p _____ The Game: Add the like terms together. First put them in the right order! 2x + 3x + 7x 2 – 2 ______ + _______ – _______ 8n – 2n + 9n 9 + 4 ______ + _______ + _______ 9 + 4 + 7x + 3x ______ + _______ 7x 4 + 5x + 3x + 3 ______ + _______ + _______ © Copyright 2009 Illegal to copy www.firelightbooks.com 61 MORE THAN ONE LETTER Some problems have more than one variable. Don’t worry! Solve these problems the same way as the other ones. Example p 6a + 6b a=2 b=3 SA M You know a = 2, so plug it in! You know b = 3, so plug it in! 10a – 5b a=2 b=3 10(2) 5(3) 10(2) – 5(3) 10(2) = _____ 5(3) = _____ 20 – 15 = _____ UNIT 3 Example p PL E You know a = 2, so plug it in! 6(2) You know b = 3, so plug it in! 6(3) 6(2) + 6(3) Do the math! p 12 + 18 = 30 The answer is 30! Do the math! p Do the math! p Do the math! p The answer is _____. The Game: Substitute or plug in to find the answers. Fill in the blanks. 5z + 1x z = 2, x = 3 What does z equal? _____ What does x equal? _____ Plug it in! 5•2+1•3 Do the math! p 5 • 2 = _____ Do the math! p 1 • 3 = _____ Do the math! p 10 + ___ = _____ The answer is _____. © Copyright 2009 Illegal to copy www.firelightbooks.com 62 UNDO WITH MULTIPLICATION Use multiplication to undo division. Break It Down: (9 x 3) ÷ 3 = 9 27 ÷ 3 = 9 9=9 UNIT 3 PL E You are doing inverse operations with multiplication. The Game: Fill in the missing numbers in these inverse operations. (102 x 4) ÷ ____ = 102 (15 x 4) ÷ ____ = 15 (8 x 2) ÷ ____ = 8 SA M (42 x 7) ÷ ____ = 42 (____ x 3) ÷ 3 = 900 (16 x ____) ÷ 8 = 16 (76 x 1) ÷ ____ = 76 (____ x 4) ÷ ____ = 32 (____ x 10) ÷ 10 = 89 (24 x ____) ÷ 7 = 24 © Copyright 2009 Illegal to copy www.firelightbooks.com 85 UNDOING If you play basketball, you know that you can get a rebound by standing at the opposite angle of a bank shot. E Getting a rebound is like doing inverse operations. (29 + 4) – ____ = 29 SA M (45 x ____) ÷ 5 = 45 UNIT 3 PL The Game: Fill in the missing numbers in these inverse operations. (50 ÷ ____) x 4 = 50 (35 – 5) + ____ = 35 (100 x ____) ÷ 25 = 100 (69 ÷ 3) x ____ = 69 (____ x 2) ÷ 2 = 86 (82 ÷ 41) x ____ = 82 (200 ÷ ____) x 4 = 200 (5 + 5) – ____ = 5 © Copyright 2009 Illegal to copy www.firelightbooks.com 86 SOLVING EQUATIONS BY SUBTRACTION Some equations are easy to work in your mind. Some equations like x + 5 = 8 are harder. Use subtraction to undo addition. Break It Down: The problem p Undo with subtraction (subtract 5 from both sides of the equation). p x+5=8 Simplify both sides. p The solution p x+0=3 x=3 E UNIT 3 PL x+5=8 3+5=8 8=8 SA M Check your answer. p Plug in 3 for x. p Simplify. p x+5–5=8–5 Yes! 3 is the solution. The Game: Fill in the blanks. The problem p Undo with subtraction (subtract 12 from both sides of the equation). p Simplify both sides. p The solution p Check your answer. p Plug in 3 for m. p Simplify. p © Copyright 2009 Illegal to copy m + 12 = 15 m + 12 – 12 = 15 – 12 m+0=3 m = ____ m + 12 = 15 3 + 12 = 15 ____ = 15 Yes! ____ is the solution. www.firelightbooks.com 87 PRACTICE Inverse operations undo each other. Use subtraction to undo addition. x + 15 = 20 PL The Game: Fill in the blanks. The problem p Undo with subtraction (subtract 15 from both sides of the equation). p Simplify both sides. p The solution p E The Game: Fill in the missing numbers in these inverse operations. Use subtraction to undo addition in these problems. Check your answers. UNIT 3 x + 15 = 20 5 + 15 = 20 ____ = 20 Yes! ____ is the solution. SA M Check your answer. p Plug in 5 for x. p Simplify. p x + 15 – 15 = 20 – 15 x+0=5 x = ____ The problem p Undo with subtraction (subtract 30 from both sides of the equation). p Simplify both sides. p The solution p Check your answer. p Plug in 30 for k. p Simplify. p © Copyright 2009 Illegal to copy k + 30 = 60 k + 30 – 30 = 60 – 30 k + 0 = ____ k = ____ k + 30 = 60 30 + 30 = 60 ____ = 60 Yes! ____ is the solution. www.firelightbooks.com 88 UNDO SUBTRACTION WITH ADDITION You know that you can add to undo subtraction. n–2+2=7+2 n=7+2 n=9 n–2=7 9–2=7 7=7 Yes! 9 is the answer. UNIT 3 PL Check your answer. p Plug in 9 for n. p Simplify. p n–2=7 E Break It Down: The problem p Use addition to undo subtraction. p Simplify. p The solution p SA M The Game: Fill in the blanks. The problem p Use addition to undo subtraction. p Simplify. p The solution p n – 25 = 50 Check your answer. p Plug in 75 for n. p Simplify. p Yes! n – 25 = 50 ____ – 25 = 50 ____ = 50 ____ is the solution. © Copyright 2009 Illegal to copy n – 25 + 25 = 50 + 25 n = 50 + 25 n = ____ www.firelightbooks.com 89 ORDER OF OPERATIONS Break It Down: The problem p 15 – 5 • 2 5•2 15 – 10 15 – 10 = 5 5 Multiply first. p Subtract. p Work the problem. p Answer. p UNIT 4 SA M Follow the order! PL E Remember PEMDAS. When you have more than one operation to do, you must follow the order of operations. Here is the order: P = Parentheses ( ) E = Exponents (2²) M = Multiply (•, x) Multiplication and division rank the same. Work from left to right doing any "M" or "D" as you find them. D = Divide (÷, /) A = Add (+) Addition and subtraction rank the same. Go from left to right doing any "A" or "S" as you find them. S = Subtract (–) The value of 15 – 5 • 2 is 5! The Game: Fill in the blanks. 20 – 3 • 2 The problem p Follow the order! 3 • 2 = ______ Multiply first. p 20 – ______ Subtract. p Work the problem. p 20 – ______ = ______ ______ Answer. p The value of 20 – 3 • 2 is ______! © Copyright 2009 Illegal to copy www.firelightbooks.com 106 KEEP THE ORDER! Operations must be performed in order to get the right answer. If you have more than one operation, it can be tricky! Don’t be tricked. Break It Down: The problem p Follow the order! 5 + 25 ÷ 5 – 10 25 ÷ 5 = 5 5 + 5 – 10 10 – 10 = 0 0 Add. Then subtract. p Work the problem. p Answer. p UNIT 4 SA M Divide first. p PL E Follow the order: P = Parentheses ( ) E = Exponents (2²) M = Multiply (•, x) Multiplication and division rank the same. Work from D = Divide (÷, /) left to right doing any "M" or "D" as you find them. A = Add (+) Addition and subtraction rank the same. Work from S = Subtract (–) left to right doing any "A" or "S" as you find them. The value of 5 + 25 ÷ 5 – 10 is 0! The Game: Fill in the blanks. The problem p Follow the order! Multiply first. p Divide. p Add the two answers. p Answer. p The value of 3 • 5 + 20 ÷ 2 © Copyright 2009 Illegal to copy 3 • 5 + 20 ÷ 2 3 • 5 = ______ 20 ÷ 2 = ______ ______ + ______ = ______ ______ is ______! www.firelightbooks.com 107 MEASURE TWICE, CUT ONCE Carpenters have this wise rule: MEASURE TWICE, CUT ONCE. Carpenters measure their board two times before they cut the board. They check their measurements so they don't make a bad cut. Measure twice, cut once means to always check your work. E The Game: Fill in the blanks. Show your work. ¯9 + ¯8 = _____ ¯14 + ¯7 = _____ 7 – ¯3 = _____ 8 – ¯8 = _____ 5 – ¯9 = _____ 8 – 8 = _____ © Copyright 2009 Illegal to copy www.firelightbooks.com UNIT 5 27 + 3 = _____ SA M 14 + 6 = _____ ¯6 + ¯12 = _____ PL 25 + ¯13 = _____ 130 MULTIPLYING INTEGERS The answer to a multiplication problem is called a product. You can use addition over and over to multiply numbers (integers). Break It Down: This number line shows how you can use repeated addition on a number line to solve a multiplication problem. ¯2 + ¯2 + ¯2 PL Repeated addition p ¯2 x 3 E The problem p SA M | | | | | | | | | | | | | | | | | | | | | - 10 - 9 - 8 - 7 - 6 - 5 - 4 -3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 The answer p ¯2 x 3 = ¯6 UNIT 5 The Game: Fill in the blanks. Draw arrows to show the repeated addition on the number line. 1x4 The problem p Repeated addition p 1 + 1 + 1 + 1 or 1 x 4 | | | | | | | | | | | | | | | | | | | | | - 10 - 9 - 8 - 7 - 6 - 5 - 4 -3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 1 x 4 = _____ The number line shows how you can use _______________ addition on a number line to solve a _______________ problem. © Copyright 2009 Illegal to copy www.firelightbooks.com 131 MULTIPLYING INTEGER RULES Look! Use these rules when multiplying integers: • If both factors are positive, the product will be positive. • If both factors are negative, the product will be positive. • If only one factor is negative, the product will be negative. E If the signs are the same, the product will be positive. If they are different, the product will be negative. PL RULE # 1: MULTIPLYING POSITIVE INTEGERS Positive x positive = positive The problem p 4x2 SA M | | | | | | | | | | | | | | | | | | | | | - 10 - 9 - 8 - 7 - 6 - 5 - 4 -3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 The answer p 4x2=8 5(2) = _____ 10 x 2 = _____ 4 • 4 = _____ 9 x 0 = _____ 3 x 1 = _____ 20 • 3 = _____ 11 • 2 = _____ 12(4) = ______ 9 x 6 = ______ 8 • 7 = ______ © Copyright 2009 Illegal to copy www.firelightbooks.com UNIT 5 The Game: Fill in the blanks. 132 RULE #2: MULTIPLYING NEGATIVE INTEGERS Look at the second rule: The product of two negative numbers is positive. The two "neighbor negatives" make friends to form a positive number! ¯5 x ¯2 Negative x negative = positive ¯5 x ¯2 = 10 PL The answer p E The problem p SA M Negative x negative = positive Example: (¯2)(¯4) = 8 ¯2 x ¯2 = _____ ¯2 x ¯50 = _____ ¯2 • ¯30 = _____ ¯19 • ¯1 = _____ ¯1(¯5) = _____ ¯30 x ¯3 = _____ ¯1 x ¯4 = _____ (¯90) ¯1= ______ ¯9 • ¯6 = ______ (¯8)(¯10) = ______ UNIT 5 The Game: Fill in the blanks. What does a negative times a negative equal? © Copyright 2009 Illegal to copy www.firelightbooks.com 133 RULE #3: MULTIPLYING INTEGERS Look at the third rule: A positive number times a negative number makes a negative number. 2 x ¯3 The problem p E | | | | | | | | | | | | | | | | | | | | | - 10 - 9 - 8 - 7 - 6 - 5 - 4 -3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 10 This number line shows that 2 x ¯3 = ¯6 2 x ¯3 = ¯6 PL The answer p SA M Positive x negative = negative Example: (15)( ¯5) = ¯75 ¯3 • 4 = _____ ¯2 • 7 = _____ 20(¯2) = _____ ¯3 x 20 = _____ ¯4(4) = _____ ¯5 • 5 = _____ (3)¯10 = _____ (2)¯2 = ______ UNIT 5 The Game: Fill in the blanks. What does a positive times a negative equal? © Copyright 2009 Illegal to copy www.firelightbooks.com 134 SUBTRACTING NEGATIVE INTEGERS You know that when you see two negatives next to each other, you can change them to a positive! 2 – ¯1 = 2 + +1 2+1=3 The Game: Subtract. Change all the negatives to positives! Show your work. Write the answers in the blanks. 9 – ¯4 = ______ 95 – ¯5 = ______ 2 – ¯8 = ______ 8 – ¯9 = ______ 12 – ¯3 = ______ 20 – ¯3 = ______ UNIT 5 SA M 36 – ¯4 = ______ PL 29 – ¯1 = ______ 3 – ¯7 = ______ E 4 – ¯10 = ______ When you see two negatives together, what do you do? © Copyright 2009 Illegal to copy www.firelightbooks.com 148 SIMPLIFYING PROBLEMS Some equations will have addition and subtraction of positive and negative numbers. Guess what? You already know how to do these! Break It Down: 5 – (7 – ¯3) = x The problem p Group numbers together; two negatives become positive. p The answer p ¯5 = x PL E Plug in. p 5 – (7 + +3) 5 – 10 SA M The Game: Fill in the blanks The problem p 8 – 7 – (5 – ¯1) = x Group numbers together; two negatives become positive. p8 – 7 – (5 + +1) Plug in. p 1–6 The answer p ______ = x © Copyright 2009 Illegal to copy www.firelightbooks.com UNIT 5 The problem p 10 – 2 – (4 – ¯1) = x Group numbers together; two negatives become positive. p10 – 2 – (4 ______ ______) Plug in. p 8 – ______ The answer p ______ = x 149 SUBTRACTING NEGATIVES AGAIN! Remember to change two "neighboring negatives" to positives. The Game: Subtract. Show your work. Write the answers in the blanks. PL 100 – ¯50 = ______ 8 – ¯4 = ______ 35 – ¯5 = ______ 21 – ¯4 = ______ 10 – ¯4 = ______ ¯20 – ¯20 = ______ UNIT 5 5 – 7 – 3 = ______ SA M 6 – (7 – ¯1) = ______ 5 – ¯4 = ______ E 10 – ¯2 = ______ When you see two "neighboring negatives," what do you do? © Copyright 2009 Illegal to copy www.firelightbooks.com 150 GROUPING You know the order of operations (PEMDAS). Use grouping to solve equations. Break It Down: Multiply first. p Subtract. p PL The answer p 15 – 5 • 2 15 – (5 • 2) 5 • 2 = 10 15 – 10 15 – 10 = 5 5 E The problem p Some problems will have subtraction of negative numbers in them. SA M The Game: Fill in the blanks. The problem p Exponents first p Add. p Subtract. p (6 + 9) – 2 (6 + 9) – 2 15 – 2 15 – 2 = ______ ______ UNIT 6 The answer p 6 + (¯3)2 – 2 ¯32 = 9 © Copyright 2009 Illegal to copy www.firelightbooks.com 151 GROUPING PRACTICE Grouping numbers together helps solve equations. Remember to use the order of operations when you work! Add.p The answer p 2+ 2+ 2+ 2+ 18 8x2 (8 x 2) 16 16 = 18 E The problem p Simplify by grouping. Multiply first. p PL Break It Down: The Game: Use grouping to simplify. Show your work. Write the answers in the blanks. 2 + 8 • 2 = ______ 5 + 7 – 3 = ______ 9 • 2 + 4 = ______ 7 • 5 + 3 = ______ UNIT 6 10 • 5 + 4 = ______ SA M 5 • 1 + 9 = ______ What does PEMDAS mean? © Copyright 2009 Illegal to copy www.firelightbooks.com 152 PRACTICE SUBTRACTION Grouping gets you the correct answer. Practice grouping. These equations will have different operations and subtraction. Break It Down: The problem p The answer p PL Add.p E Simplify by grouping. p 42 – ¯9 (16) – ¯9 (16) + +9 (16) + +9 = 25 25 The Game: Use grouping to simplify. Show your work. Write the answers in the blanks. SA M 15 • 2 – ¯6 = ______ 12 – 9 = ______ 42 – ¯3 = ______ 35 – 5 • 2 = ______ 3 • 4 – ¯7 = ______ UNIT 6 5 • 2 – ¯3 = ______ © Copyright 2009 Illegal to copy www.firelightbooks.com 153 WHICH NUMBER TO DISTRIBUTE? The Distributive Property uses the parentheses. Remember! When a number is directly outside the parentheses ( ), you may distribute. The Game: Circle the numbers in these problems that need to be distributed. 5(3 – 1) (8 – 4)2 20(3 + 3) (21 – 7)3 (2 – 2)17 80(2 – 1) 45(9 + 7) (7 – 5)6 PL E 7(9 + 9) SA M DON'T BE TRICKED! Many students mess up when they ignore the parentheses. This is wrong! 2(3 + 6) 2•3+6 6 + 6 = 12 It is wrong to remove the parentheses and multiply 2 and 3, then add 6. The wrong answer is 12. This is correct! Do it this way: 2(3 + 6) (2 • 3) + (2 • 6) 6 + 12 = 18 The correct answer is 18. © Copyright 2009 Illegal to copy www.firelightbooks.com UNIT 6 The Game: Circle the correct problem. Put an X on the incorrect problem. 4(3 + 6) 4(3 + 6) 4•3+6 (4 • 3) + (4 • 6) 12 + 6 = 18 12 + 24 = 36 173 DISTRIBUTION WITH SUBTRACTION Some distribution problems have subtraction in them. We do these the same way as the addition problems. Break It Down: Distribute the 3. p Group. p The answer p PL Multiply and subtract. p 3(4 – 2) 3(4 – 2) (3 • 4) – (3 • 2) (12) – (6) 6 E The problem p SA M The Game: Fill in the blanks. The problem p 6(9 – 1) Distribute the 6. p 6(9 – 1) Separate into groups. p (6 • 9) – (_____ • 1) Multiply and subtract. p 54 – _____ The answer p _____ Which number is distributed? _____ © Copyright 2009 Illegal to copy www.firelightbooks.com UNIT 6 The problem p 3(5 – 4) Distribute the 3. p 3(5 – 4) Separate into groups. p (3 • 5) – (_____ • 4) Multiply and subtract. p 15 – _____ The answer p _____ Which number is distributed? _____ 174 MOVING WITH DISTRIBUTION You know how to distribute. Distribute first. p Multiply. p Group. p Add. p PL The answer p 5(1 + 2) + 7 (5 • 1) + (5 • 2) + 7 5 + 10 + 7 (5 + 10) + 7 15 + 7 22 E Break It Down: The Problem p SA M The Game: Fill in the blanks. 4(2 + 2) + 10 Distribute first. p (4 • 2) + (_____ • 2) + 10 Multiply. p 8 + _____ + 10 Add. p 16 + 10 The answer p _____ UNIT 6 The Problem p © Copyright 2009 Illegal to copy www.firelightbooks.com 175 MULTIPLY AND DIVIDE INTEGERS! Look at the rules for multiplying integers: Positive x positive = positive Negative x negative = positive Positive x negative = negative Negative x positive = negative The Game: Fill in the blanks. ¯8 • ¯4 = _____ 6(¯8) = _____ ¯7 x 7 = _____ ¯6 • ¯5 = ______ (¯4)(¯9) = ______ (¯2)(¯9) = ______ 2 x 8 = ______ PL (3)(¯5) = ______ E ¯3 • 7 = _____ 8 x 8 = ______ SA M Look at the rules for dividing integers: • Positive ÷ positive = positive • Negative ÷ negative = positive • Positive ÷ negative = negative • Negative ÷ positive = negative 20 ÷ 5 = _____ 16 ÷ ¯4 = _____ 14 ÷ ¯2 = _____ 18 ÷ ¯3 = _____ ¯30 ÷ 3 = _____ 12 ÷ ¯1 = _____ 30 ÷ ¯3 = ______ 33 ÷ ¯3 = ______ 24 ÷ 4 = ______ ¯21 ÷ ¯3 = ______ © Copyright 2009 Illegal to copy www.firelightbooks.com UNIT 6 The Game: Fill in the blanks 176 MORE POWER! Read the tricks about exponents. • If the exponent is an even number next to a negative base, the answer is positive. • If the exponent is an odd number next to a negative base, the answer is negative. What does 63 mean? 6 x 6 x 6 What does 102 mean? 10 x 2 6x3 10 x 10 PL What does 24 mean? 4 x 2 E The Game: Underline the correct answer. 2x2x2x2 SA M The Game: Answer the questions. 83 What is the base number? ______ What is the exponent? ______ What does 83 mean? ____________ What is 83? ______ (¯4) 2 = ______ (¯3) 2 = ______ 5 3 = ______ (¯9) 2 = ______ © Copyright 2009 Illegal to copy www.firelightbooks.com UNIT 6 The Game: Find the power in these expressions. Write the answers in the blanks. Show your work! 177 ADDITION PROPERTIES PRACTICE E Read the rules about the Properties of Addition. • The Commutative Property of Addition says that you can add numbers in any order. • The Associative Property of Addition says that you can group numbers in any order when adding. • The Identity Property of Addition says that any number plus zero equals that same number. • The Addition Property of Opposites says that any number plus its opposite equals zero. The Game: Fill in the blanks. Work the problems. 14 + (10 + 18) = (____ + ____) + 18 SA M PL (27 + 5) + 10 = 27 + (____ + ____) (8 + 0) + 10 = 8 + (____ + ____) 35 + 0 = _____ 15 + ¯15 = _____ 126 + ¯126 = _____ 0 + 51 = _____ UNIT 6 (5 + 7) + 10 = 5 + (____ + ____) © Copyright 2009 Illegal to copy www.firelightbooks.com 178