Chapter 1: Whole Numbers

Place Value & Rounding

Understanding place value is fundamental to working with whole numbers. Rounding is used to approximate numbers to a specified place value for easier computation or estimation.

• Place Value: Each digit in a whole number has a value depending on its position (ones, tens, hundreds, thousands, etc.).

• Rounding Rule: To round to a specific place value, examine the digit immediately to the right:

  • If the digit is 5 or greater, round up.

  • If the digit is less than 5, keep the digit the same and change all digits to the right to zero.

• Example: Round to the nearest thousand:

  • The digit in the thousands place is 7; the digit to the right (hundreds) is 8 (which is greater than 5).

  • So, round up: .

Order of Operations (PEMDAS)

Order of operations ensures that mathematical expressions are evaluated consistently and correctly.

• PEMDAS: The acronym stands for:

  1. Parentheses / Grouping Symbols

  2. Exponents

  3. Multiplication & Division (from left to right)

  4. Addition & Subtraction (from left to right)

• Example: Evaluate :

  • First, multiplication and division: ,

  • Then, addition and subtraction:

Evaluating Expressions

To evaluate algebraic expressions, substitute the given values for variables and simplify using the order of operations.

• Example: Evaluate when and :

  • Substitute:

Chapter 2: Integers

Absolute Value

Absolute value measures the distance of a number from zero on the number line, always resulting in a non-negative value.

• Notation:

• Example:

• Practice: Find the value of :

  • , ,

  • So,

Adding & Subtracting Integers

Adding and subtracting integers depends on the signs of the numbers involved.

• Same Sign: Add the absolute values and keep the original sign.

  • Example:

• Different Signs: Subtract the smaller absolute value from the larger, and keep the sign of the larger absolute value.

  • Example:

• Subtraction: Rewrite as addition of the opposite.

  • Formula:

  • Example:

• Practice: Simplify :

  • Rewrite:

  • Combine: ,

Multiplying & Dividing Integers

The sign of the result depends on whether the numbers have the same or different signs.

• Same Signs: The product or quotient is positive.

  • ,

  • Example:

• Different Signs: The product or quotient is negative.

  • ,

  • Example:

• Practice: Evaluate :

  • ,

  • So,

Evaluating Integer Expressions

Substitute values for variables and apply integer operations.

• Example: Evaluate when and :

Practice Test Summary Table