unit 1 study guide: expressions - math -...
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Unit 1 Study Guide: Expressions
Lesson 2: Expressions
Mathematical Expression: Numbers and one or more operations (Addition,
Subtraction, Multiplication, Division)
To Solve a Mathematical Expression: you MUST do the operations in the correct
order.
Exponent: the number of times you multiply a number times itself
Example: 32 = 3 ∙ 3 = 9 2 is the exponent
54 = 5 ∙ 5 ∙ 5 ∙ 5 = 625 4 is the exponent
PEMDAS – Please Excuse My Dear Aunt Sally
Step 1: P = Parentheses or other grouping symbol (), {}, []
Step 2: E = Exponents
Step 3: M/D = Multiplication and Division (these are equal – do the one that
comes first, reading left to right)
Step 4: A/S = Addition and Subtraction (these are equal – do the one that comes
first, reading left to right)
Example: 5+ 4 ∙ (6 – 2) Parentheses first (6-2) = 4
5 + 4 ∙ 4 Multiplication is next 4 ∙ 4 = 16
5 + 16 Addition is last
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Helpful Hints: Do 1 step at a time
Underline the step you are working on
If the expression is a fraction, simplify the top, simplify the
bottom, then reduce the fraction to lowest terms
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Lesson 3: Variables
Variable – symbol (usually a letter) that represents a number
Example: x, y, a, n
Variable Expression – a math sentence with one or more variables and one or
more numbers
Examples: 8 – 6 + a
3n ÷ 7
Simplify a Variable Expression: combine the Like Terms (terms with the same
variable and the same exponent, or combine the numbers)
Example: 10 – 2 + 3y + 4y 10 and 2 are numbers, so they can be combined
3y and 4y have the same variable so they can be combined
8 + 7y 8 and 7y are not like terms, so they cannot be combined
Example: 7m2 + 6k – 2m2 + 4k
5m2 + 10k
Distributive Property – the number on the outside of the parentheses is
multiplied by EVERYTHING on the inside (the 4 VISITS everyone at the party!)
Example: 4(c + 5) = 4 * c + 4 * 5
= 4c + 20
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Lesson 5
Positive Exponents
Represent Numbers in different forms:
Standard Form: 81
As a Product: 3 * 3 * 3 * 3
Exponential Form: 34
Word Form: eighty-one
Exponential Form: 34 3 is the base
4 is the exponent (or the power)– it tells how
many times to multiply 3 times ITSELF
34 = 3 * 3 * 3 * 3 = 81 34 DOES NOT EQUAL 3 * 4
(-4)3 = -4 * -4 * -4 = -64 (-4)3 DOES NOT EQUAL -4 * 3
Special Exponents: Any number raised to the 0 power = 1: 170 = 1
Any number raised to 1 is the number: 8761 = 876
Notes and Examples from Class:
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Lesson 6: Negative Exponents
Negative Exponents: rewrite as a positive exponent in order to simplify
Remember: If you see a negative exponent:
If it’s on the bottom, put it on the top and make it positive
If it’s on the top, put it on the bottom and make it positive
Negative exponents make me sad
Make them positive and smile!!
Example:
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Lesson 8: Working with Exponents
Properties of Exponents
Power to a Power Property
Product of Powers Property
Quotient of Powers Property
Notes and Examples from Class:
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Lesson 9: Scientific Notation
1. Move the decimal point between the first 2 numbers that are not 0
2. Count the places you moved the decimal – this is the power of 10
3. If you move the decimal to the left, the exponent is positive
4. If you move the decimal to the right, the exponent is negative
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Adding and Subtracting Numbers in Scientific Notation
If the exponents are the same, use the Distributive Property:
If the exponents are different, you have to change one of the numbers to make
the exponents the same
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Multiplying Numbers in Scientific Notation
Multiply the Numbers
Add the Exponents
Put the answer in Scientific Notation
Example:
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