Summary of "[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:
- If the signs are the same: add magnitudes and keep the sign.
- Example: (+5) + (+3) = +8
- 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
- If the signs are the same: add magnitudes and keep the sign.
- 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:
- Parentheses / brackets
- Exponents
- Multiplication and division (left to right)
- 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
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