Order of Operations
Aim: To apply the order of operations rule
Standard(s) – 7.N.11
Do Now
Who is right and why?
Timmy
3+4x2
=7x2
= 14
Incorrect!
Suzie
3+4x2
=3+8
= 11
Correct!
Timmy performed the operation of
addition first, then multiplication,whereas
Suzie performed multiplication first, then
addition. Suzie is RIGHT! According to
order of operations
Instructional material
When a numerical expression involves two or more operations, there is a specific order in which these
operations must be performed.
PEMDAS
Parenthesis, Exponents, (Multiplication/Division) then
(Add/Subtract)
Please Excuse (My Dear) (Aunt Sally)
The reason (multiplication & division) and (add & subtract) are grouped is when those operations are next
to each other you do the math from left to right.
Numerical expression – a way of writing a number in symbols. (it can be a single numeral or a collection
of numerals with one or more operation symbols)
Simplify – find its value
Real Life ~ How does order of operations take place in our everyday lives and not just math?
Example(s): Baking a cake, making a peanut, everyday classroom routine…
Peanut butter and Jelly sandwiches ~ Before you make a sandwich you need to take out all your
materials just like when you see a numerical expression you need to write down PEMDAS. There is an
order in which you use to make a PBJ sandwich but, it does not matter whether you put the peanut butter
or the jelly first because the sandwich still tastes the same. You usually would grab what ever is closest to
you and put that on first. This is the same as the order in which we perform multiplication and division
and addition and subtraction (what ever comes first)
Order of Operations is not an isolated skill. This skill applies to almost every topic in Math.
Remember that "Aunt Sally" is used with evaluating formulas, solving equations, evaluating algebraic
expressions, simplifying monomials & polynomials, etc..
Example(s):
a) 6 + 7 x 8 = 6 + 56 = 62
b) (5 - 1) x 3 = 4 x 3 = 12
36 − 6 30
=
=2
d) 20 + 3(5 - 1) = 20 + 3(4) =20 + 12 = 32
12 + 3 15
When there are two or more parenthesis, grouping symbols, you perform the inner most grouping symbol
first.
e) 2 + 3[5 + (4 - 1)] = 2 + 3[5 + 3] = 2 + 3[8] = 2 + 24 = 26
c)
Worksheet~ “Real Life Situations and Using Order of Operations”
Not only do you need to be able to simplify a numerical expression using the order of operations you have
to be ablt to analyze a situation and set up the numerical expression correctly so that wne you simplify it
you get the correct answer.
Practice:
1) 9 + 6 x (8 - 5) = 9 + 6 x 3 = 27
2) 2(3 + 5) - 9 = 2(8) – 9 = 16 – 9 = 7
3) 4 +
4)
2
12 = 4 + 2 2 = 4 + 4 = 8
6
36 - 3 × 4 36 − 12 24
=
=
= 12
15 - 9 ÷ 3 15 − 3 12
5) 0.8 0.1 + 0.5 0.4 = 0.8 + 0.20 = 0.28
6) 3 + 6 x (5 + 4) ÷ 3 - 7 = 3 + 6 x 9 ÷ 3 – 7 = 3 + 54 ÷ 3 – 7 = 3 + 18 – 7 = 21 – 7 = 14
7) 9 - 5 ÷ (8 - 3) x 2 + 6 = 5 ÷ 5 x 2 + 6 = 1 x 2 + 6 = 2 + 6 = 8
8) 150 ÷ (6 + 3 x 8) - 5 = 150 ÷ 6 = 25
9) 2[ 13 - ( 1+ 6)] = 2[13-7] =2[6] =12
10) 3(6+4)(5 - 3) = 3(10)(2) = 30(2) =60
11) 100 + 3[(5 – 2) + (6 + 3)] = 100 + 3[3 + 9] = 100 + 3[12] = 100[36] = 3600
12)
5 x 4 – 10
=
20 – 10
5 + 2[3 – (2-1)] 5 + 2[3 – 1]
=
10
5 + 2[2]
= 10
5+4
= 10
9
13) Insert operational symbols (+, - , ÷, x) & parentheses to make each of the following statements true.
a) 3 + 2 - 1 = 4
b) 1 x 3 + 1 = 4
c) (1+ 2) ÷3 + 4 = 5
d) (4 + 3 – 2) x 1 = 5
e) (6 x 6 – 6) ÷6 = 5
f) 6 + 6 x (6 – 6) = 6
**Thanks to regentsprep.org