1.

• Order Of Operations

PEMDAS: P leaseE xcuseM yD earA untS ally #1 Step 4:Add or Subtract in order by reading theproblem from left to right. Step 1:Parenthesis first Step 2:Exponents or powers second Step 3:Multiply or Divide in orderby readingthe problem from left to right._ _ _ _ _ _

2. The rules for order of operations exist so that everyone can perform the same consistent operations and achieve the same results.

Order Of Operations Example

Follow all the rules for order of operations. Remember PEMDAS #2 3. #3 Parenthesis 1 st Exponents 2 nd Mult. / Div. left to right Add / Subt. left to right P E MD AS

PEMDAS

4. An expression isNOT an equationbecause it does not have an equal sign.There are 2 types of expressions.NUMERICAL EXPRESSION :Contains only numbers and symbols.Example: 53 + 4 ALGEBRAIC EXPRESSION : Contains numbers, symbols, and variables.Also known as a variable expression.Example: m + 8 AVARIABLEis a letter or symbol that represents a number.Example:x TYPES OF E X P R E S S I O N S #4 5. #5Substitute & Evaluate when x = 2 and y = 4 Evaluate Show the substitution Show your work down Circle your answer Show your work down, one step at a time, no equal signs! 6. add plus sum increased by total more than added to subtract minus difference decreased by diminished by less than subtracted from less multiply times product of... divide quotient Key Words #6 twice 7. WORD PHRASES Aword phraseis a sentence that can be translated into a variable expression or equation. Aword phraseis like a verbal phrase.It is made up of only words. Example: The difference of 8 and a number. Algebraic Expression: 8 - n #7 8. Write anAlgebraic Expressionfor theWord Phrases. 5.8 more than 4 times a5.8 + 4aor4a + 5.8 The difference of 3a and 2 3a - 2 6 less than the number 58t 58t - 6

Writing Algebraic Expressions

# 8 9. IntegersIntegers - are the set of numbers including positive whole numbers, negative whole numbers and zero. Negative Numbers Positive Numbers * Negative integers are less than zero *Positive integers are greater than zero* The integer zero isneither positive or negative #9 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 10. Opposites Pairs of integers that are thesame distance from zeroon a number line areopposites . Example:3 and -3are opposites because each integer is 3 units away from zeroOther Examples: 2 and 2 5 and -5 #10 11. Absolute Value Absolute valueof an integer is thedistance the number is from zeroon a number line. Examples: |-2| = 2|1| = 1 The absolute value of-5is5 spaces from zero . #11 Two vertical barsaround the number means find theabsolute value . 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 12. Steps To Add Integers 1) Put in the 1 stnumber of+or 2) Add the 2 ndnumber of+ or 3) Balance out what you have5) The leftovers are the final answer Virtual Manipulative: Color Chips - Addition #12 4) One+balances out one When a+andcancel each other out it is called aNEUTRAL FIELDorZERO BANK 13. Integer Addition Rules If the signs are the same Add the numbers.The sign stays the same. 4 + 3 = -4+-3= + + + + + + +7 _ _ _ _ _ _ _ -7 If the signs are different Subtract the numbers. The larger number determines the sign of the answer. -9 + 5 = 9- 5 = 4 Subtract the numbers - 4 #13 _____+++++ ____ Answer-4 because you started with more negatives 14. 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 Integer Elevator GroundFloor -5 +2= -3 -5 + 2 Positive=Up Negative=Down Add Integers With a Number Line #14 15.

A Model to Subtract Integers

1)Put inthe 1 stnumber of+or 2)Subtract , or remove, the 2 ndnumber of+or Show that you remove them bycircling them&attaching anarrowto them.3)IF YOU CANNOT REMOVE THE 2 ndNUMBERADD ENOUGH ZERO PAIRS SO YOU CAN.4)Countyour remaining tiles.(one+ balances out one-) 5)Recordyour answer (the leftovers) #15 16.

Subtract Integers Example 1

3 - 2 1) Put in 3 2) Take away 2 3) You are left with 1 = 1 3 --2 1) Put in 3 2) You cant take away2 so add 2 zeros 3) Take away-2 4) You are left with+ 5 = 5 ++ +++ -- +++#16 17.

Subtract Integers Example 2

-3--2 1) Put in-3 2) Take away-2 3) You are left with-1 = -1 -3- 2 1) Put in-3 2) You cant take away 2 so add 2 zeros 3) Take away +2 4) You are left with-5 = -5 http://www.matti.usu.edu/nlvm/nav/frames_asid_162_g_2_t_1.html _____ ++ _ __#17 18. Subtracting Integer Rules Keep the first number andadd the opposite . 56 5 6 Is the same as = -1 4 ( 2 ) Is the same as 4 ( 2 ) = 6 -3 1 Is the same as -3 (1 ) = -4 #18 *SUBTRACT = PLUS CHANGE! 19. 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 Integer Elevator GroundFloor -4 - 2= -6 -4 - 2 1)Start at 0. Move to the 1 stnumber. 2) Then look at the 2 ndnumber. 3) Subtract aPositive = Down 4) Subtract aNegative=Up Subtract Integers With a Number Line #19 20. To Remember Multiply & Divide Integers #20 When good things, happen to good people, thats good! ++=+ When bad things, happen to bad people, thats good! =+ When good things, happen to bad people, thats bad! += When bad things, happen to good people, thats bad! += ++=+ =+ += += 21. RULES FOR DIVIDING INTEGERS When determining the sign, therulesof multiplying integersare the samefor dividing integers. If thesignsare thesame , the answer ispositive . - 64- 8 = 8If thesignsaredifferent , the answer isnegative . - 84 = -2 #21 22. 08 = 80 = 0 undefined 22Dividing with Zero A calculator might display ERROR when you divide by 0. NoZEROin the denominator! 23. Equations An equation is a mathematical statement thatshows2 quantitiesareequal .An equationcontains an equal sign. #23 12 3 = 9Numerical 3a = 30Algebraic To solve any equation useinverse operations . Your goal is to get the variable all by itself. 24. To solve an addition equation m + 8 = 12Get the variable alone. 88Subtract 8 from both sides. m = 4+8 and -8 cancel each other out. 4 + 8 = 12 Show your check. Subtractthesame numberfrom both sides #24 12 = 12 Finish your check! 25. To solve a subtraction equation a 15= 22 Get the variable alone. +15+15Add 15 to both sides . a = 37+15 and -15 cancel out 37 - 15 = 22 Show your check! Addthesame numberto both sides #25 22 = 22 Finish your check! 26. To Solve a Multiplication Equation 5x = 40Get the variable alone. 55 Divide 5 into both sides. x=85 divided by 5 cancels out to 1. 58= 40 Show your check! Divide the same number into both sides #26 40 = 40 Finish your check! 27. To Solve a Division Equation = 20Get the variable alone. 2 =2 20 Multiply both sides by 2. x =402 divided by 2 cancels out to 1. Show your check! x2 x2 Multiply the same number to both sides #27 20 = 20 Finish your check!