Grade 9 Math Final Exam Review: Rational Numbers and Exponents

Grade 9 Math Final Review

Rational Numbers

A rational number is any positive or negative number that can be written as a fraction. Terminating and repeating decimals are always rational because they can be expressed as fractions.

• Adding and Subtracting: Find a common denominator. (e.g., 2/4 + 3/8 = 4/8 + 3/8 = 7/8)
• Multiplying: Reduce before multiplying if possible. (e.g., 11/8 * 6/22 = 1/4 * 3/2 = 3/8)
• Dividing: Use the Keep, Change, Flip method. Keep the first fraction, change division to multiplication, and flip the second fraction.

Converting Between Forms

• Decimal to Fraction: Write the decimal over 1. Count the digits after the decimal and multiply the numerator and denominator by the corresponding power of 10 (e.g., 100 for two digits). Simplify using the greatest common factor. (e.g., 0.75 = 75/100 = 3/4)
• Fraction to Decimal: Divide the numerator by the denominator. (e.g., 3/4 = 3 ÷ 4 = 0.75)

Order of Operations (BEDMAS)

Follow the order: Brackets, Exponents, Division or Multiplication, Addition or Subtraction. (e.g., (3.7 - 3.8) * (6.4 ÷ 2) = -0.1 * 3.2 = -0.32)

Exponents and Powers

Exponents are a mathematical shorthand indicating how many times a base is multiplied by itself.

Exponent Laws

• Law #1 (Multiplying): Add exponents with the same base. (e.g., 4² * 4³ = 4⁵)
• Law #2 (Dividing): Subtract exponents with the same base. (e.g., 4⁵ ÷ 4³ = 4²)
• Law #3 (Power of a Power): Multiply the exponents. (e.g., (4²)³ = 4⁶)

Evaluating Powers

Apply BEDMAS when evaluating expressions with powers. (e.g., 4(9-12)² = 4(-3)² = 4(9) = 36)

Powers and Variables

All exponent laws apply to variables. Note that the bases must be identical to use these laws.