Download Algebra One Review

Algebra One Review
Positive/Negative Integers
On a number line, numbers to the right of 0 are positive; numbers to the left of 0 are
negative. Given any two numbers on a number line, the one on the right will always be
larger—regardless of its sign. [3 is larger than 1; -2 is larger than -9]
Order of Operations (AKA: PEMDAS)
1. Evaluate expressions within grouping symbols; aka: parentheses ( ), brackets [ ],
and sometimes set notation { } is used
2. Evaluate all powers; aka: exponents and radicals
3. Do all multiplication and/or division from left to right (in order of appearance)
4. Do all addition and/or subtraction from left to right (in order of appearance)
Example:
Correct
3 2 4 6
38 6
11  6
17
Incorrect
3 2 4 6
6 46
24  6
30
You would get an incorrect answer if the Order of Operations was not followed (example
on the right). It is very important that the rules are followed.
Addition/subtraction of signed numbers
When two (or more) numbers have the same sign (numbers are either negative or
positive), add the numbers together and keep the same sign.
Examples:
22  4
3  5  8
3  5  7  15
6  2  8  16
If numbers have different signs, you need to subtract the numbers and keep the larger
sign.
Examples: 8  3  5
8  (3)  5
You can turn subtraction problems into additional problems by placing an addition sign in
front of the second number.
Example:
8  3  8  (3)  differentsigns  5
5  4  5  (4)  samesigns  9
Reality √: The reason addition and subtraction are taken in order (left to right) in following
the Order of Operations is most consider them as one; subtraction is just “adding the
opposite”.
Multiplication/division of signed numbers
To multiply or divide signed numbers, treat them like regular numbers but remember the
rule: an odd number of negative numbersthe answer is negative; an even number of
negative numbersthe answer is positive.
Example: (2)(6)  12
(3)(5)(4)  60
Reality √: When two or more letters or a number and a letter are written next to each other
they are understood to be multiplied.
Evaluating Expressions
To evaluate an expression you need to replace the unknown value (variable) with the
value (or values) given and using the Order of Operations to find the resulting value.
Example: If x=4, y=-2, and z=3; evaluate the following.
(1)
(4)(3) 12
xz

 6

2
2
y
(2) x  z  3 y  (4)  (3)  3(2)  4  3  6  13
Adding Like Terms (Simplifying)
A term is a number, a variable, or a product or quotient of numbers and variables. For
example: y, p 4 , 4a,5m3n 2 , and 6b are all terms. Like terms are terms that contain the
same variables, with corresponding variables having the same power.
Three terms having no common variable: 2 x 2  3x  6
Three terms with common variable (so they can be added): 4x  5x  6x or 15x
Mixed: 5 x 3  6 x 2  3 x 3 (the x-cubed terms can be added)  (5  3) x3  6 x 2  2 x3  6 x 2
The Distributive Property
When there is a leading coefficient in front of terms within parentheses you can create an
equivalent expression by multiplying the leading term by each of the terms within—in a
way, distributing the leading term to each individual term.
5(2 x  3 y  4)
Example: (5)(2 x)  (5)(3 y )  (5)( 4)
10 x  15 y  20
Since the terms are all unique, it is simplified.
(9r  3t  4)
(1)(9r )  ( 1)( 3t)  ( 1)(4)
9r  3t  4
Notice, the leading negative sign changes all the signs that follow.
F.O.I.L (First, Outside, Inside, Last) is a process to help us distribute correctly two
binomials (numbers with two terms).
(2 x  3)(6 y  7)
Example: (2 x)(6 y )  (2 x)( 7)  (3)(6 y )  (3)(7)
12 xy  14 x  18 y  21
Another way to look at distribution of binomials (or greater) is by using a generic
rectangle. The terms are written on the outside of the rectangle; their product within the
rectangle.
The terms from within the rectangle result in the following 12 xy  14 x  18 y  21 , which is
the same answer as we obtain when we used FOIL.