7日間コース
Master Variables & Expressions in 7 Days
From writing expressions with variables to equations and inequalities — understand the language of algebra and learn to manipulate it with confidence.
対象: Junior High 1-2 / Overseas Japanese students
Concepts & Worked Examples
Understand how to express quantities using variables, perform operations on algebraic expressions, and write equations and inequalities.
文字を使うと、具体的な数字の代わりに一般的なパターンを表せる。
例: 「1個 a 円のりんご。3個の代金は 3a 円。」
文字式の書き方ルール（日本の数学）:
例: 「ボール1個 x グラム。200gの箱に4個入れた重さは 4x + 200 グラム。」
同類項（文字の部分が同じ項）をまとめることができる。
3a + 5a = 8a 7x - 2x = 5x
かけ算: 係数と文字を別々にかける。 3a × 4 = 12a 2x × 5y = 10xy
割り算: 係数を割る。 6a ÷ 3 = 2a
例: 5x - 2 + 3x + 8 = (5x + 3x) + (-2 + 8) = 8x + 6
異なる文字の項や分数を含む式は、それぞれのグループを丁寧に扱う。
例: 2(3a - 4) + 5a を簡単にする = 6a - 8 + 5a = 11a - 8
分数を含む例: (2x + 1)/3 + (x - 2)/2 = 2(2x + 1)/6 + 3(x - 2)/6 = (4x + 2 + 3x - 6)/6 = (7x - 4)/6
等式 は = を使って2つの量が等しいことを表す。 不等式 は <, >, ≤, ≥ を使って量の大小関係を表す。
例: 「プリン(x円)を3個、ゼリー(y円)を6個買うと合計1500円」 → 3x + 6y = 1500
例: 「大人1枚 a 円、子ども半額。大人2人と子ども2人で5000円以下」 → 2a + 2(a/2) ≤ 5000 → 3a ≤ 5000
A pencil costs *a* yen. Express the total cost of 5 pencils and a 300 yen eraser.
解答
5a + 300 (yen)
5 pencils at *a* yen each = 5a. Add the fixed cost of 300 yen for the eraser.
Simplify: 3x + 2y - x + 5y
解答
Group like terms: (3x - x) + (2y + 5y) = 2x + 7y
Combine terms with the same variable. 3x - x = 2x, and 2y + 5y = 7y.
Simplify: 4(2a - 3) - 2(a + 5)
解答
Distribute: = 8a - 12 - 2a - 10 Combine like terms: = (8a - 2a) + (-12 - 10) = 6a - 22
First expand both brackets, then combine like terms. Be careful with signs when distributing the negative.
A number *a* is more than 5 less than another number *b*. Write this as an inequality.
解答
a - 5 > b or equivalently: a > b + 5
"*a* is more than 5 less than *b*" means a exceeds b by more than 5.
Basic Practice (★1-2)
10 problems covering Units 5-8. Practice writing expressions, combining like terms, and setting up equations.
単元5〜8の演習問題。正しい式の立て方と丁寧な計算を身につけよう。
★1 A box of *n* items weighs 250g per item plus a 500g box. Express the total weight.
解答
250n + 500 (grams)
n items × 250g each + 500g box.
★1 Simplify: 7a - 3a + 2
解答
7a - 3a + 2 = 4a + 2
Combine like terms: 7a - 3a = 4a. The +2 stays.
★2 Simplify: 3(2x + 4) - 5x
解答
= 6x + 12 - 5x = x + 12
Distribute 3 first, then combine like terms.
★2 Express as an equation: "x meters of rope cut into 3 equal pieces, each piece is 2m long."
解答
x ÷ 3 = 2 or: x/3 = 2
Total length divided by 3 equals the length of each piece.
Standard Practice (★2-3)
10 problems at standard difficulty covering expression manipulation and equation setup.
Pattern Drills (★2-3)
10 problems focusing on fractions in expressions, multi-variable simplification, and inequality writing.
Applied Problems (★3-4)
10 challenging problems combining word problems with algebraic expression writing and simplification.
Advanced Challenge (★4-5)
10 high-difficulty problems. Complex expressions, proof-style questions, and real-world equation modeling.
Comprehensive Test & Bridge to Equations
Mixed test covering ★1-5. Plus: how algebraic expressions connect to equations — what you learn next.