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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
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CHAPTER 4 NUMBER EXPRESSIONS
EATING OUT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
IMPORTANT WORDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
USE THOSE WORDS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
OPERATION DIVISION! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
LET'S EXERCISE THOSE MATH SKILLS! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
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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
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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
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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
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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
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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
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CHAPTER 21 IDENTIFYING AND WRITING EXPONENTS
SHORTCUT! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
FIND THE POWER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
EXPONENTS IN ACTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .103
WHAT TIMES WHAT? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .104
EXPONENTS FOR REAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
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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
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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
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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
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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!
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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?
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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.
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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?_________________________________________
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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.
________
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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?
_________________________________________________________
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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?
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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?
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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?
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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.
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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 =
_____
_____
_____
_____
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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!"
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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.
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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?
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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?
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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?
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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?
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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
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25n = ____ ÷ ____
5
50x = ____ ÷ ____
10
100c = ____ ÷ ____
20
y ÷ 7 = ____
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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
_____
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t+t+t
7t + t 2 – 0
_____
_____
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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
______ + _______ + _______
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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 _____.
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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
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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
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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
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m + 12 = 15
m + 12 – 12 = 15 – 12
m+0=3
m = ____
m + 12 = 15
3 + 12 = 15
____ = 15
Yes! ____ is the solution.
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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
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k + 30 = 60
k + 30 – 30 = 60 – 30
k + 0 = ____
k = ____
k + 30 = 60
30 + 30 = 60
____ = 60
Yes! ____ is the solution.
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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.
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n – 25 + 25 = 50 + 25
n = 50 + 25
n = ____
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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 ______!
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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
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3 • 5 + 20 ÷ 2
3 • 5 = ______
20 ÷ 2 = ______
______ + ______ = ______
______
is ______!
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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 = _____
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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.
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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 = ______
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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?
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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?
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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?
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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
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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?
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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
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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?
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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 = ______
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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.
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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? _____
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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
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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 = ______
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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 = ______
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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 + (____ + ____)
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178