NUMBER OPERATIONS AND CONCEPTS
PEMDAS, which means Parentheses first, then Exponents, then
Multiplication and Division (left to right), and lastly Addition and
Subtraction (left to right). In the expression 9 − 2 × (5 − 3)^2 + 6 ÷ 3, begin
with the parentheses: (5 − 3) = 2. Then do the exponent: 22 = 4. Now the
expression is: 9 − 2 × 4 + 6 ÷ 3. Next do the multiplication and division to get:
9 − 8 + 2, which equals 3. If you have difficulty remembering PEMDAS, use
this sentence to recall it: Please Excuse My Dear Aunt Sally.
5 . Counting Consecutive Integers
To count consecutive integers, subtract the smallest from the largest and
add 1. To count the number of integers from 13 through 31, subtract: 31 −
13 = 18. Then add 1: 18 + 1 = 19.
6 . Exponential Growth
If r is the ratio between consecutive terms, a 1 is the first term, an is the nth
term, and Sn is the sum of the first n terms, then an = a 1 rn − 1 and
7 . Union and Intersection of Sets
The things in a set are called elements or members. The union of Set A and
Set B, sometimes expressed as A ∪B, is the set of elements that are in either
or both of Set A and Set B. If Set A = {1, 2} and Set B = {3, 4}, then A ∪ B = {1,
2, 3, 4}. The intersection of Set A and Set B, sometimes expressed as A ⋂ B,
is the set of elements common to both Set A and Set B. If Set A = {1, 2, 3} and
Set B = {3, 4, 5}, then A ⋂ B = {3}.
