Order of Operations: PEMDAS and FOIL
If you are asked to simplify something like 4 + 2×3, the question that naturally arises is, "How do I do
this?” Because there are two options:
Choice 1: 4 + 2×3 = (4 + 2)×3 = 6×3 = 18
Choice 2: 4 + 2×3 = 4 + (2×3) = 4 + 6 = 10
PEMDAS reminds us that math inside Parentheses
comes first, followed by Exponents, then
Multiplication and Division (equal rank), and finally
Addition and Subtraction (equal rank).
PEMDAS
“Please Excuse My Dear Aunt Sally”
Parentheses
Exponents
Multiplication and Division
Addition and Subtraction
When you have a bunch of operations of the same
rank, you just operate from left to right.
15 ÷ 3 × 4 = 5 × 4
2
Simplify 4 + 3
= 4 + 9 = 13
Simplify 4 + (2 + 1)2
15 ÷ 3 × 4 ≠ 15 ÷ 12
Simplify the term with the exponent
then add in the 4
Simplify inside the parentheses
= 4 + (3)2
Take the exponent
= 4 + 9 = 13
Now I can add the 4
Simplify 4 + [–1(–2 – 1)]2.
I shouldn't try to do these nested parentheses from left to right; that method is simply too errorprone. Instead, I'll try to work from the inside out.
4 + [–1(–2 – 1)]2
First, I'll simplify inside the curved parentheses,
= 4 + [–1(–3)]2
Then simplify inside the square brackets
= 4 + [3]2
Now take care of the exponent
= 4 + 9 = 13
Finally, add the 4
Brackets and curly-braces (the "{" and "}" characters) are used when there are nested parentheses, as an
aid to keeping track of which parentheses go with which.
Simplify
I will simplify inside the parentheses first
FOIL method for expanding polynomials
Like terms have the same base and exponent
x7 and 5x7
are like terms
y3 and x3
are NOT like terms (different bases)
z3 and z4
are NOT like terms (different exponents)
Combine like terms: 2x + x = 3x
Please show your work and draw a box around your answer as you simplify the following problems.
1. 4 – 3[4 –2(6 – 3)] ÷ 2
6.
2. 16 – 3(8 – 3)2 ÷ 5
7.
3. 14x + 5[6 – (2x + 3)]
8.
4. –{2x – [3 – (4 – 3x)] + 6x
5. 16 ÷ 2[8 – 3(4 – 2)] + 1
9.