Chapter 1: Integers & Expressions

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Absolute value is always non-negative.

• Notation:

• Example:

Adding & Subtracting Integers

• Same Signs: Add the absolute values and keep the common sign. Example:

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

• Subtraction Rule: Subtracting a number is the same as adding its opposite.

  • Formula:

  • Example:

Multiplying & Dividing Integers

• Same Signs: The product or quotient is positive.

  • Example:

• Different Signs: The product or quotient is negative.

  • Example:

Order of Operations (PEMDAS)

To evaluate expressions correctly, follow the order of operations:

1. Parentheses / Grouping

2. Exponents

3. Multiplication & Division (left to right)

4. Addition & Subtraction (left to right)

Example: Evaluate Step 1: Exponents: (if the negative is outside the exponent, ) Step 2: Multiplication/Division: , Step 3: Addition/Subtraction:

Chapter 4: Rational Numbers & Fractions

Rational Numbers

A rational number is any number that can be written as a fraction , where and are integers and .

• Examples: , , (since )

Simplifying Fractions

To simplify a fraction, divide both the numerator and denominator by their Greatest Common Factor (GCF).

• Example: Simplify GCF of 8 and 12 is 4.

Multiplying Fractions

Multiply the numerators together and the denominators together:

• Formula:

• Example:

Dividing Fractions

To divide by a fraction, multiply by its reciprocal ("Keep, Change, Flip"):

• Formula:

• Example:

Adding & Subtracting Fractions

Fractions must have a Least Common Denominator (LCD) to be added or subtracted:

• Formula:

• Example:

Practice Test

Section A: Integers & Order of Operations

1. Evaluate:

2. Calculate:

3. Evaluate:

Section B: Rational Numbers & Fractions

4. Simplify to lowest terms:

5. Multiply:

6. Divide:

7. Solve:

Additional info: The above practice problems reinforce the core concepts of integer operations, order of operations, and fraction arithmetic. Students should show all steps and simplify answers where possible.