Section 1.4 Evaluating Expressions and Order of Operations Integrated Math Section 1.4 Evaluating Expressions and Order of Operations

Definitions Variable-a letter used to represent a number or a set of numbers Expression-a combination of variables, operations, and numbers to represent something Evaluate- replace variables with numbers if necessary and simplify using order of operations

𝑥 𝑛 means xxx… with n factors

Try these #1 5 2 − 2 3 #2 (−4) 2 #3 1 5 #4 (−2) 4

Square Roots 𝑥 = n means 𝑛 2 =x 25 = 5 because 5 2 = 25 We say the square root of 25 𝑥 is the principal square root of x “Squaring” and “square rooting” are opposites!

Try these 100 − 16 81 1

If there is any work to do under the radical, put in parentheses If there is any work to do under the radical, put in parentheses. The parentheses are invisible but it’s ME FIRST time!

Try these Add parentheses!!!!! #1 41−5 #2 3(68−20)

#1 41−5 36 6 #2 3(68−20) 3(48) 144 12

Simplify- replace an expression with the simplest version of the expression using order of operations.

Order of Operations- Parentheses, Exponents, Multiply and Divide (left to right), Add and Subtract (left to right) Remember PEMDAS or Please Excuse My Dear Aunt Sally

Invisible parentheses You must add in parentheses for the following: Numerator or denominator with an operation Work under the radical sign Work inside absolute value sign Taking the absolute value

Simplify or Evaluate Do one operation on each line #1 6−9 +3∙5 #1 6−9 +3∙5 #2 −3 2 − (−2) 2 #3 1 2 + 1 3 1 4 − 4 5 #4 4.5 2 −3∙7.1

#1 6−9 +3∙5 −3 +3∙5 3+15 18

#2 −3 2 − (−2) 2 −9−4 −13

#3 1 2 + 1 3 1 4 − 4 5 5 6 −11 20 −55 120 =− 11 24

#4 4.5 2 −3∙7.1 20.25−3∙7.1 20.25−21.3 −1.05

Fractions are different Before you start to work with an expression that is a fraction, put the numerator and denominator in parentheses! 6(2)+8 7−2 Use order of operations for the denominator and numerator simultaneously! Your last step is to simplify the fraction.

Try these! #1 4+2∙7 3∙2−9 #2 − 2 4 −5 3 2 − 2 4

Homework Only one of the following per line (P,E,MD,AS). Write the letter(s) at the end of the line. Don’t forget to add invisible parentheses. Work down your paper. If letters don’t follow the order- P, then E, then MD, then AS you have a mistake!

Assignment #4A Pg 38 #3-60 (x3), 81-99 (x3)

3 steps minimum! Evaluate the expression 4 𝑎 2 −10𝑏+𝑐 when a = 2, b = 3 and c = 4 #1 Write the expression #2 Substitute the numbers in for the variables #3 Simplify using order of operations

Substitute Take out the letters, plug in the numbers!

Evaluate the expression 4 𝑎 2 −10𝑏+𝑐 when a = 2, b = 3 and c = 4 STEP #1 WRITE THE PROBLEM!!!!!! 4 𝑎 2 −10𝑏+𝑐 when a = 2, b = 3 and c = 4 4 (2) 2 −10 3 +4 4 4 −10 3 +4 16−30+4 −10

Evaluate each expression for a=4, b=5 and c=-2 #1 𝑎−𝑐 #2 𝑏+𝑐 2𝑎−𝑏 #3 𝑎𝑏𝑐−10

#1 𝑎−𝑐 4−(−2) 6

#2 𝑏+𝑐 2𝑎−𝑏 5+(−2) 2 4 −5 3 8−5 3 3 1

#3 𝑎𝑏𝑐−10 4 5 −2 −10 −40−10 −50

Scary variables! Your book has problems with variables named 𝑦 1 , 𝑦 2 , 𝑥 1 , 𝑥 2 These are read as y sub 1, y sub 2, x sub 1 and x sub 2 Don’t be scared of these!! They are just names for variables!

Find the value of 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 when 𝑦 1 =4, 𝑦 2 =−3, 𝑥 1 =2, 𝑥 2 =9 Plug in carefully!

Word problems are not monsters. Each word problem has a formula Word problems are not monsters! Each word problem has a formula. Look for the numbers to plug in! This is like a puzzle.

Assignment #4B Pg. 38 #61-77 odds, 101,103