Equations and The Order of Operations

Page  2 Section 1: Variables and Expressions  Variables –Are letters or symbols that act as placeholders for numbers. –One letter = One number.  Simplify –To replace a variable with a number.  Expressions: Numerical and Variable –Expressions don’t have an equal sign  Expression –Equations do have an equal sign = 60  Equation  Numerical Expressions –Only have numbers:  No Variables  Variable Expressions –Have at least 1 Variable: 75 + g + 25  At least 1 Variable –3x + y  At least 1 Variable

Page  3 Language of Math: Operations  Addition: Total, Sum, Altogether, Increase, and Combine.  Subtraction: Difference, Less Than, More Than, and Decrease.  Multiplication: Product, Times, and Each.  Division: Quotient, Share, and Each. Operations and their Parts: Addition & Subtraction  Two numbers being added are called ADDENDS.  The answer to an addition problem is called the SUM.  The number being subtracted is the SUBTRAHEND and the number from which we are subtracting is called the MINUEND. (First Number  Minuend) – (Second Number  Subtrahend) = Difference.  The answer to a subtraction problem is called the DIFFERNCE.

Page  4 Operations and their Parts: Multiplication & Division  Two numbers in a multiplication problem are called the FACTORS.  The answer to a multiplication problem is the PRODUCT.  The number being divided is called the DIVIDEND. The number we are dividing by is called the DIVISOR.  The answer to a division problem is the QUOTIENT. (Top Number  Dividend) / (Divisor  Bottom Number) = Quotient

Page  5 Writing Variable Expressions: Example Problems Nine more than number y  y + 9 A number z times three  z x 3, z 3, z3 5 times the quantity 4 plus a number c  5 (4 + c), 5(4 + c) Try These:  The product of x and y, plus 5   The sum of t and u, divided by 4   R divided by 5, minus 3, equals 2.   Y fewer than 27   Daniel has 14 more than Sam.   The total of Tommy’s marbles and 13   55 subtracted from 105, divided by 5 equals 10.  Challenge problems are in purple.

Page  6 Section 2: The Order of Operations  Simplify an Expression –To replace the expression with the simplest name for its value… –or solve as far as possible! –What does ÷ 5 simplify to?  The Order of Operations – ÷ 5 Division first! 25 ÷ 5 = 5 Rewrite Addition second! = is the simplified expression for ÷ 5

Page  7 The Order of Operations: PEMDAS  P : Do operations inside PARENTHESES (or other delimiters/grouping symbols, like [BRACKETS] and division bars). –Work from the inside of the Parentheses/Brackets to the outside. –Division Bars: Simplify the top and bottom first, then divide!  E : Evaluate terms with EXPONENTS. –The exponent ONLY effects the NUMBERS/VARIABLES/PARENTHESES in front of the little number (to the left). Example: 5 10, x 2, (5 + 8) 3.  D M : Do MULTIPLICATION and DIVISION. –In order from LEFT to RIGHT. –5 10 ÷ 2  5 10 = 50, 50 ÷ 2 = 25, 510÷2=25  A S : ADD and SUBTRACT terms. –In order from LEFT to RIGHT. –8 + 7 – 5  = 15, 15 – 5 = 10, 8+7-5=10 PEDMAS is where order REALLY matters!

Page  8 Example Problems: Show each Step of PEMDAS  2[(13 – 4) ÷ 3] =  – 2 = 4  4 – ÷ 3 =  ÷ 3 – 1 = Example of Showing Steps: PEMDAS 1)2[(13 – 4) ÷ 3] = Copy Problem 2)2[(9) ÷ 3] = Simplify Parentheses 3)2[3] = Simplify Brackets 4)2[3] = 6, Multiply 5)6, Answer, Always Boxed!