7日間コース
Master Positive & Negative Numbers in 7 Days
Build unshakable foundations in positive and negative numbers. From addition and subtraction to complex mixed operations — master every pattern through understanding and practice.
対象: Junior High 1 / Overseas Japanese students
Concepts & Worked Examples
Understand positive and negative numbers, absolute value, addition, subtraction, multiplication, division, and mixed operations through clear explanations and worked examples.
基本ルール: 同じ符号の数を足すときは、絶対値を足して符号をそのまま付ける。違う符号の数を足すときは、絶対値の大きい方から小さい方を引いて、大きい方の符号を付ける。
例: (+5) + (-3) → |5| > |3| → 答えは正。5 - 3 = +2
例: (-8) + (+2) → |8| > |2| → 答えは負。8 - 2 = -6
引き算: ある数を引くことは、その数の符号を変えて足すこと。
(+3) - (+7) = (+3) + (-7) = -4
(-5) - (-2) = (-5) + (+2) = -3
符号のルール:
(+) × (+) = (+) (-) × (-) = (+) (+) × (-) = (-) (-) × (+) = (-)
例: (-3) × (-7) → 同符号 → +21 例: (+4) × (-5) → 異符号 → -20 例: (-12) ÷ (+4) → 異符号 → -3
ポイント: 複数のかけ算では、負の数の個数を数える。偶数個なら正、奇数個なら負。
(-2) × (-3) × (-4) = -(2 × 3 × 4) = -24（負が3つ = 奇数 = 負）
計算の優先順位: ① 累乗 → ② 乗法・除法 → ③ 加法・減法
カッコの中は最優先で計算する。
例: 3 × (-2)² - 4 = 3 × 4 - 4 = 12 - 4 = 8
注意: (-2)² = 4 だが、-2² = -4。カッコの有無で結果が変わる！
例: -5 + 3 × (-4) = -5 + (-12) = -17
分数・入れ子のカッコ・複数の演算を含むより複雑な計算。
例: 9 ÷ 3² × (-5) = 9 ÷ 9 × (-5) = 1 × (-5) = -5
例: (-3) × 8 + (-42) ÷ (-6) = -24 + 7 = -17
大事なスキル: 途中計算を全部書くこと。省略するとミスの原因になる。
Calculate: (-8) + (+3)
解答
Different signs, so subtract the smaller absolute value from the larger: |8| - |3| = 5 |8| > |3|, so the answer takes the negative sign. (-8) + (+3) = -5
When signs differ, subtract absolute values and keep the sign of the number with the larger absolute value.
Calculate: (-4) × (-9)
解答
Same signs (both negative), so the result is positive. 4 × 9 = 36 (-4) × (-9) = +36
Negative × negative = positive. Just multiply the absolute values.
Calculate: (-3)² × 2 - 4 × (-5)
解答
Step 1: Exponent first → (-3)² = 9 Step 2: Multiplications → 9 × 2 = 18, 4 × (-5) = -20 Step 3: Subtraction → 18 - (-20) = 18 + 20 = 38
Follow order of operations: exponents → multiplication → subtraction. Subtracting a negative = adding a positive.
Calculate: -2³ + (-6) ÷ 2 × 3
解答
Step 1: Exponent → -2³ = -8 (note: no parentheses around -2) Step 2: Division/Multiplication left to right → (-6) ÷ 2 = -3, then -3 × 3 = -9 Step 3: Addition → -8 + (-9) = -17
Be careful: -2³ means -(2³) = -8, not (-2)³. Then multiply and divide from left to right before adding.
Basic Practice (★1-2)
10 problems covering all four units. Solidify the fundamentals before moving to harder exercises.
単元1〜4の演習問題。正確さを重視して、途中計算を全部書こう。
★1 Calculate: (+7) + (-12)
解答
Different signs: |12| - |7| = 5 |12| > |7|, so the result is negative. (+7) + (-12) = -5
Subtract absolute values, take the sign of the larger.
★1 Calculate: (-3) - (-8)
解答
Change subtraction to addition of opposite: (-3) - (-8) = (-3) + (+8) Different signs: |8| - |3| = 5 = +5
Subtracting a negative = adding a positive. Then apply addition rules.
★1 Calculate: (+6) × (-7)
解答
Different signs → negative 6 × 7 = 42 (+6) × (-7) = -42
Different signs always give a negative product.
★2 Calculate: (-2) × (-3) × (-5)
解答
Count negatives: 3 (odd) → result is negative 2 × 3 × 5 = 30 (-2) × (-3) × (-5) = -30
Three negative factors = odd count = negative result.
★2 Calculate: 4 - 6 × 3 + 10 ÷ (-5)
解答
Step 1: Multiply/divide first 6 × 3 = 18 10 ÷ (-5) = -2 Step 2: 4 - 18 + (-2) = 4 - 18 - 2 = -16
Always do multiplication and division before addition and subtraction.
Standard Practice (★2-3)
10 problems at standard difficulty. Textbook-level patterns that build fluency in all four operations.
Pattern Drills (★2-3)
10 more problems focusing on common exam patterns: fractions, exponents, and mixed expressions.
Applied Problems (★3-4)
10 challenging problems that combine multiple concepts. Multi-step calculations with fractions and exponents.
Advanced Challenge (★4-5)
10 high-difficulty problems at entrance exam level. Test your true understanding of number operations.
Comprehensive Test & Bridge to Variables
Mixed test covering ★1-5 from all four units. Plus: how positive/negative numbers connect to algebraic expressions — what you learn next.