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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Notes and Examples from Class:

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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


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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


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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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Examples from Class:

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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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Lesson 11: Orders of Magnitude

Estimate Large or Small Numbers


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unit 1 study guide: expressions - math -...

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