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1.7 Exponents and Order of Operations. Exponential Notation:. Shorthand for writing repeated multiplication of the same number. 1.7 Exponents and Order of Operations. Order of Operations:. The order in which mathematical operations must be performed. PEMDAS. P → Parenthesis

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slide1

1.7 Exponents and Order of Operations

Exponential Notation:

Shorthand for writing repeated multiplication of the same number.

slide2

1.7 Exponents and Order of Operations

Order of Operations:

The order in which mathematical operations must be performed.

PEMDAS

P → Parenthesis

E → Exponents

M → Multiplication

D → Division

A → Addition

S → Subtraction

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1.7 Exponents and Order of Operations

PEMDAS

Order of Operations:

slide4

1.7 Exponents and Order of Operations

Order of Operations:

PEMDAS

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1.7 Exponents and Order of Operations

Order of Operations:

PEMDAS

slide6

1.8 Variables, Algebraic Expressions and Equations

Definitions:

Variable - A letter that represents a number or a set of numbers.

Algebraic Expression - A combination of operations on variables and numbers.

Equation- Two algebraic expressions that are equal.

Solution- The value or values for the variable that make an equation true.

Evaluate- Substituting a value for the variable of an expression or equation and calculating the result.

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1.8 Variables, Algebraic Expressions and Equations

Determine whether 8 is a solution of the equation

True statement,

8 is a solution.

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1.8 Variables, Algebraic Expressions and Equations

Determine which numbers in the set { 10, 6, 8} are solutions of the equation

False statement,

False statement,

True statement,

10 is not a solution.

6 is a solution.

8 is not a solution.

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1.8 Variables, Algebraic Expressions and Equations

Write an Algebraic Expression. Use x to represent “a number.”

Twice a number

8 increased by a number

10 minus a number

10 subtracted from a number

The quotient of a number and 6

or

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2.1 Introduction to Integers

Definitions:

Positive numbers – All numbers greater than zero. The positive sign states that the number is to the right of zero on a number line.

Negative numbers – All numbers less than zero. The negative sign states that the number is to the left of zero on a number line.

Signed numbers – Positive numbers, negative numbers and zero.

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2.1 Introduction to Integers

Definitions:

Integers – All positive numbers, negative numbers and zero, but no fractions or decimals.

Zero

Negative integers

Positive integers

NOTE: Zero is neither positive or negative!

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2.1 Introduction to Integers

Graphing Integers

Graph -4, -1, 2, and -2 on the number line.

Zero

Negative integers

Positive integers

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2.1 Introduction to Integers

Representing Position with Integers

Use an integer to represent each of the following positions.

1. The wreck of the Titanic was located at 12,460 feet below sea level.

2. The tamarack tree survives at the edge of the arctic tundra at 85 degrees below zero.

3. The bottom of Crater Lake is located at 4,229 feet above sea level.

4. The world’s deepest colony of bats is located in a New York zinc mine at a depth of 3805 feet.

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2.1 Introduction to Integers

Comparing Integers

For any two numbers graphed on a number line, the number to the right is the greater number and the number to the left is the smaller number.

Inequality Symbols

“is greater than”

“is less than”

“is greater than or equal to”

“is less than or equal to”

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2.1 Introduction to Integers

Comparing Integers

Insert or between each pair of numbers to make a true statement.

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2.1 Introduction to Integers

Absolute Value of a Number

The distance a number is from 0 on the number line.

The distance a number is from 0 is always 0 or a positive distance – NEVER a negative value.

The symbol or operator for the Absolute Value is: | |

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2.1 Introduction to Integers

Opposite Numbers

Two numbers that are the same distance from zero but are on opposite sides of zero.

Which of the following represent opposites?

YES

YES

NO

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2.1 Introduction to Integers

Opposite Numbers

Find the opposite values of the following numbers: