Module 6
Rates, Per, and Each.
単位あたりの英語 （Tan'i Atari no Eigo）
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。
Rate questions are decided by which quantity goes on the bottom. The English word that tells you is almost always per, each, or for every — and the unit named after it is the denominator.
Read the unit aloud. "Kilometres per litre" is literally km ÷ L. "Bottles per minute" is bottles ÷ minutes. If you can say the unit, you have the formula — the word "per" is the division sign.
日本人がハマる理由
日本語では同じ関係を 「〜あたり」 で表し、「1リットルあたり」 のように単位の後ろに付きます。英語は per を単位の前に置きます。順序が逆なので、日本語の語順のままリットルを先に置いて式にすると、分数の上下が逆になり、L ÷ km を計算してしまいます。出てきた数字は小さいだけで、いかにも間違いという見た目ではないため、直感では気づけません。答えには必ず単位を付けてください。「0.067」だけでは何の値か分かりませんが、「0.067 litres per kilometre」と書けば、上下を逆にしたことがその場で分かります。
練習問題
難易度は出題者による目安です。College Board の判定ではありません。
A machine fills 240 bottles every 8 minutes. At this rate, how many minutes does it take to fill 900 bottles?
Correct Answer: B
Explanation: The rate is 240 ÷ 8 = 30 bottles per minute. Time = 900 ÷ 30 = 30 minutes.
- (A) 3.75: From
900 ÷ 240— the 8 minutes never entered the calculation. The units would be "bottles per bottle", which is meaningless. - (C) 112.5: From
900 ÷ 8— divided by the time instead of by the rate. - (D) 240: A number copied from the problem.
Difficulty Justification
Rated Medium: two numbers and two plausible ways to combine them. Computing the rate as an explicit intermediate step, with its unit written down, removes the ambiguity.
A car travels 240 kilometres using 16 litres of fuel. How many kilometres does the car travel per litre?
Correct Answer: B
Explanation: "Kilometres per litre" → 240 ÷ 16 = 15.
- (A) 0.067: From
16 ÷ 240— the inverted fraction. This is litres per kilometre, the rate the question did not ask for. - (C) 224: From
240 − 16. Subtraction between two different units is never meaningful. - (D) 3,840: From
240 × 16.
Difficulty Justification
Rated Easy, and it exists purely to train the habit in choice A: the phrase "per litre" tells you litres is the denominator.
Tickets cost $12 each. A group has $150 to spend. What is the greatest number of tickets the group can buy?
Correct Answer: A
Explanation: 150 ÷ 12 = 12.5. You cannot buy half a ticket, and 13 tickets would cost $156 — more than the group has. So 12.
- (B) 12.5: The raw division. A count of physical objects must be a whole number; the context, not the arithmetic, tells you this.
- (C) 13: From rounding 12.5 up by habit. Ordinary rounding rules do not apply when money runs out —
13 × 12 = 156 > 150. - (D) 138: From
150 − 12.
Difficulty Justification
Rated Medium. The mathematics finishes at 12.5; the question is then decided by "greatest number the group can buy", which forces rounding down regardless of the decimal.