[개념 정리] 중1 수학 (상) 2단원. 정수와 유리수 - [진격의홍쌤]

Unit overview

This lesson (middle-school / 1st grade) covers Unit 2: integers and rational numbers. It organizes basic definitions, key properties, computation rules, and problem-solving tips. The presenter encourages focus and repeated practice.

Key definitions

• Integers: whole numbers without fractional parts — positive integers, 0, and negative integers.
• Rational numbers: any number expressible as a fraction (includes all integers, fractions, and terminating or repeating decimals).

Positive and negative numbers

• A number > 0 is positive; a number < 0 is negative; 0 is neither.
• Plus (+) and minus (−) signs indicate sign.
• Common word cues in problems:
  • Positive: increase, above, gain, deposit
  • Negative: decrease, below, underground, expenditure, loss

Number line and ordering

• Use a number line centered at the origin (0).
• Numbers further to the right are larger.
• The number line helps compare integers and other rational numbers.

Absolute value

• Absolute value is the distance from the origin.
  • Examples: |3| = 3, |-3| = 3, |0| = 0
• Absolute value removes the sign and gives magnitude.

Inequalities

• Symbols and meaning:

  • : greater than

  • < : less than
  • ≥ : greater than or equal to
  • ≤ : less than or equal to
• Read and interpret inequalities using the number line or by comparing magnitudes and signs.

Addition and subtraction of rational numbers

• Sign rules for addition:
  1. If the signs are the same: add magnitudes and keep the sign.
     • Example: (+5) + (+3) = +8
  2. If the signs are different: subtract the smaller magnitude from the larger magnitude; the result takes the sign of the larger magnitude.
     • Example: (+5) + (−8) = −3
• Subtraction can be viewed as adding the opposite:
  • a − b = a + (−b)

Multiplication and division of rational numbers

• Sign rules:
  • Same signs → positive result (e.g., (+)(+) = +, (−)(−) = +)
  • Different signs → negative result (e.g., (+)(−) = −)
• Reciprocal (multiplicative inverse):
  • a × (1/a) = 1 (for a ≠ 0)
  • Example: 4 × 1/4 = 1

Mixed calculations and order of operations

• Order of operations:
  1. Parentheses / brackets
  2. Exponents
  3. Multiplication and division (left to right)
  4. Addition and subtraction (left to right)
• Show step-by-step work and simplify inside parentheses first.
• Carefully track signs when operations cross subtraction or multiplication/division.

Practice advice and closing

• Practice the learned rules repeatedly (teacher suggests about 10 times).
• Write out steps clearly when solving problems.
• Remember how signs change across different operations.
• Next unit preview: letters and equations.

Presenter: 진격의홍쌤