Evaluate numerical expressions involving rational numbers

Key notes:

Definition of Rational Numbers

• Rational numbers are numbers that can be expressed as a fraction p/q​, where p and q are integers, and q ≠ 0.
• Includes integers, fractions, terminating and repeating decimals.

---

Order of Operations (PEMDAS/BODMAS)

• Parentheses / Brackets
• Exponents / Orders (Squares, Cubes, etc.)
• MD Multiplication and Division (Left to Right)
• AS Addition and Subtraction (Left to Right)

---

Operations with Rational Numbers

• Addition & Subtraction: Convert to a common denominator if necessary.
• Multiplication: Multiply numerators and denominators separately.
• Division: Multiply by the reciprocal of the divisor.

---

Working with Decimals & Fractions

• Convert between fractions and decimals for ease of computation.
• Use long division to convert fractions to decimals.

---

Using Negative Numbers

Follow sign rules:

• Addition/Subtraction: Same signs → Add & keep sign, Different signs → Subtract & use sign of the larger absolute value.

---

Multiplication/Division:

• Positive × Positive = Positive
• Negative × Negative = Positive
• Positive × Negative = Negative

---

Evaluating Expressions with Exponents

• Apply exponent rules (e.g., a^m × aⁿ = a^{m + n}).
• Square and cube rational numbers carefully.

---

Distributive Property

• Use a (b + c) = ab + ac when simplifying expressions.

---

Solving Word Problems

• Identify rational number operations from the problem statement.
• Apply the correct order of operations and check for reasonableness.

Learn with an example

Let’s practice!🖊️