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

2. 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

3. 𝑥 𝑛 means xxx… with n factors

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

5. 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!

6. Try these
100
− 16 81 1

7. 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!

8. Try these
Add parentheses!!!!!
# −5
#2 3(68−20)

9. # −5 36 6
# (68−20)
3(48)
144 12

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

11. 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

12. 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

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

14. #1 6−9 +3∙5
−3 +3∙5
3+15 18

15. #2 −3 2 − (−2) 2
−9−4
−13

16. # − 4 5
−11 20
− =− 11 24

17. # −3∙7.1
20.25−3∙7.1
20.25−21.3
−1.05

18. 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.

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

20. 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!

21. Assignment #4A
Pg 38 #3-60 (x3), (x3)

22. 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

23. Substitute
Take out the letters, plug in the numbers!

24. 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 −
4 4 −
16−30+4
−10

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

26. #1 𝑎−𝑐 4−(−2) 6

27. #2 𝑏+𝑐 2𝑎−𝑏
5+(−2) 2 4 −5
3 8−5
3 3 1

28. # 𝑎𝑏𝑐−10
4 5 −2 −10
−40−10
−50

29. 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!

30. 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!

31. 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.

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