Module 3
直訳表 （Chokuyaku-hyō）
帰国子女・インターナショナルスクール生のための、デジタルSAT 数学の無料教材。独学で進められます。
Word problems are not puzzles. They are sentences written in a code that maps, phrase by phrase, onto symbols. Memorise the table below and most sentences convert mechanically.
One exception, and it matters more than the rule. Translating strictly left to right works for +, × and =, but it is wrong for the subtraction phrases in Module 1 — "six less than 2x" is 2x − 6, not 6 − 2x. Convert in order, then check whether any reversal phrase appeared.
| English | Symbol | 日本語 |
|---|---|---|
| is, are, was, will be, equals | = | 〜は〜である |
| a number, what number | x | ある数 |
| sum, more than, increased by, added to | + | 和・増加 |
| difference, less than, decreased by, fewer than | − | 差・減少 |
| product, times, twice, of (with a fraction or percent) | × | 積・〜倍 |
| quotient, per, divided by, ratio of | ÷ | 商・〜あたり |
Translate in order. "Three more than twice a number is 17."
three more than → + 3 · twice a number → 2x · is → = · 17 → 17
Result: 2x + 3 = 17
日本語は助詞で文法上の役割を示します。「ある数に3を足す」なら、語順を入れ替えても、何に何を足すのかは変わりません。英語にはこれに当たる助詞がなく、語順だけが情報です。語順ではなく意味で読む帰国生は、たいてい違う式を立て、その式には正しく答えてしまいます。文の意味を考える前に、前から順に、機械的に記号へ置き換えてください。
Three more than twice a number is 17. What is the number?
Correct Answer: B
Explanation: 2x + 3 = 17 → 2x = 14 → x = 7.
(17 − 2) ÷ 3 — the 2 and the 3 have swapped roles. "Twice" multiplies; "three more" adds.(17 + 3) ÷ 2. The 3 was added instead of subtracted when undoing the equation.2 × 17 — the operation was applied to the answer rather than undone.Rated Easy: a two-step translation with small integers. It is here to establish the mechanical habit before the word order starts fighting you in Module 1.
The sum of a number and 8 is equal to three times the number. What is the number?
Correct Answer: B
Explanation: x + 8 = 3x → 8 = 2x → x = 4.
8 = 4x — the x on the left was subtracted twice.3 × 4 — the correct value of "three times the number", but the question asked for the number. See Module 8.Rated Easy, but choice D is deliberately the correct answer to a question that was not asked — the single most expensive habit on the SAT.
One-third of a number, increased by 6, is 14. What is the number?
Correct Answer: C
Explanation: "One-third of a number" → x/3. So x/3 + 6 = 14 → x/3 = 8 → x = 24.
x/3, not x — the intermediate value, one step short.(x + 6)/3 = 14... which actually gives 36; 18 comes from 3 × 6. Either way, the comma placement was ignored.(14 − 6) × 3 × 2.5-style over-multiplication, or 14 × 3 + 18. It comes from multiplying before undoing the addition.Rated Medium: the comma after "number" carries the grouping. English uses punctuation where Japanese would use a particle, so this is precisely where a returnee's instinct gives no help.