方程式唔使驚:點樣講 x、y、Equals 同 Solve For
喺一個英文備試班入面,有個學英文嘅人畀人叫去大聲讀出 2x + 3 = 11 呢一行,並解釋點樣搵 x。佢呆咗,望住塊板,最後細聲講:「Two x and three is eleven, so x is four。」導師接手講:「Two x plus three equals eleven. Subtract three from both sides, then divide by two. So x equals four。」數學係完美嘅。英文只係需要一條跑道。當你冇啲動詞嚟講方程式嗰陣,佢哋睇落好嚇人,但當你有嗰陣,佢哋就好普通。
點解呢樣嘢重要
代數匿埋喺講課、補習、溫書小組、科學堂,甚至技術崗位嘅見工面試入面。教授可能會講:「If you solve for x, you'll see the relationship between the two variables。」同你一齊溫書嘅朋友可能會問:「Can you plug in five and tell me what you get?」如果你讀得出啲符號但講唔到你用緊佢哋做乜,你聽落就會冇你實際上咁有自信。詞彙好少,而且大部分都同日常英文重疊。
規律
一隻代表未知數嘅字母叫做 variable(變數)。喺英文數學堂入面最常用嘅係 x、y 同 z,讀法用佢哋嘅字母名:「x」(同 necks 押韻)、「y」(同 why 押韻)、「z」(美式英文係 zee;英式英文係 zed)。物理入面嘅多字母變數,每隻字母通常分開讀:F 係 F,m 係 m。
當兩樣嘢由 = 連住嗰陣,你讀做 equals 或者 is。所以 x = 5 係「x equals five」或者「x is five」。
當兩隻字母緊貼住嗰陣,即係 times(乘)。所以 2x 係「two x」(默默表示 two times x),而 xy 係「x y」(表示 x times y)。
當你畀人叫 solve for x 嗰陣,即係 搵出令方程式成立嘅 x 值。動詞 solve 喺你分離一個特定變數嗰陣接介詞 for。「Solve for x」同「solve the equation」兩個都自然;第一個較明確。
當你將一個數字放入原本係變數嗰個位置嗰陣,你講 plug in 或者 substitute。「Plug in five for x」即係 用 5 代替 x。「Substitute five for x」係同一回事,但英文稍為正式啲。
方程式運算嘅四個基本動詞:
- Add(將某樣嘢 to 兩邊):「Add three to both sides。」
- Subtract(將某樣嘢由兩邊 from):「Subtract three from both sides。」
- Multiply(兩邊 by 某樣嘢):「Multiply both sides by two。」
- Divide(兩邊 by 某樣嘢):「Divide both sides by two。」
每一個都將方程式推近答案一步。Both sides 呢個短語好重要 —— 佢話畀聽嘅人知你維持緊方程式平衡。
當你做完嗰陣,你用 so 或者 therefore 嚟公布答案:「So x equals four」或者「Therefore, x is four」。
錯誤 / 自然 / 點解
| 錯誤 | 自然 | 點解 |
|---|---|---|
| Solve x. | Solve for x. | 當你分離一個特定變數嗰陣,動詞 solve 接介詞 for。 |
| Plug five into x. | Plug in five for x. | 固定嘅片語動詞結構係 plug in N for the variable。 |
| Substitute x with five. | Substitute five for x. | 英文 substitute 用 for,方向同 plug in 一樣。 |
| Add three to the equation. | Add three to both sides. | 方程式只有喺你改變兩邊嗰陣先平衡。 |
| Divide the equation by two. | Divide both sides by two. | 同一條平衡規則適用。 |
| X is equal to four, so x equals four. | X equals four. (or: X is four.) | 揀一種形式;唔好將 is equal to 同 equals 疊埋。 |
| Equation equals four. | The solution is four. | 成個方程式唔係一個數;個 solution 先係。 |
| Find out x. | Find x. (or: Find the value of x.) | 喺數學語境,動詞 find 唔接 out。 |
| If we replace x as five | If we replace x with five | 動詞 replace 用 with,唔係 as。 |
常見情境
喺堂上讀塊板。 老師寫 2x + 3 = 11 同講:「Two x plus three equals eleven. Let's solve for x. Subtract three from both sides — that gives us two x equals eight. Now divide both sides by two, and x equals four。」留意個節奏:每個動詞都帶住自己嘅介詞(from both sides、by two)。
同朋友一齊做題。「Can you plug in ten for y and see if the equation holds?」你朋友講:「I get nine on the left and eleven on the right, so no, ten does not work。」隨意、快速、完全自然嘅數學英文。
問教授問題。「I got x equals six, but the textbook says x equals five. Where did I go wrong?」教授望吓你嘅做法講:「You added instead of subtracting in line three. Try again。」對話流暢,因為你喺啱嘅位置用咗啱嘅動詞。
喺公司解釋一條公式。「If we let x be the number of orders and y be the average revenue per order, then total revenue equals x times y。」你忽然聽落似個分析師,而唔係個學英文嘅人。
標準化考試嘅聽力。「Solve the equation for x when y is two。」喺標準化學術考試入面,呢句可能就係成個指示。如果你明每隻字,你就答得到;如果你聽漏咗 solve for 或者 when y is two,成條問題就會溜走。
如果你仲要處理呢啲口語方程式入面嘅運算字眼,Plus、Minus、Times、Divided By:點樣喺英文讀數學符號 講咗啲基本組塊,而 點樣講小數、分數同比例而唔會卡住 處理你 plug in 嘅數字。
常犯嘅錯誤
- 喺 solve 後面漏咗介詞。要講 solve for x,唔好淨係講 solve x。淨講就好似叫你溶解嗰個變數,而唔係搵佢嘅值。
- 混淆 plug in 同 substitute 嘅方向。兩個喺你將一個值放入變數位置嗰陣都用 for。係 plug in five for x —— 永遠唔係 plug x in for five。
- 講咗 replace x as five。動詞 replace 用 with:replace x with five。固定結構係 replace [舊] with [新]。
- 喺描述一個步驟嗰陣唔記得 both sides。Subtract three 可能解做淨係由左邊減;subtract three from both sides 維持方程式平衡同令解釋清晰。
- 將
2x讀做「two x times」或者「two times x times」。並排已經表示乘法,所以淨係講「two x」。加咗 times 會令聽嘅人懷疑係咪漏咗第三個數字。 - 想講 the solution is four 嗰陣講咗 the equation equals four。成個方程式係一個陳述;答案係一個值。
- 喺數學用咗 find out。數學動詞係 find:find x、find the value of y。Find out 屬於發現同八卦(「I want to find out what happened」)。
- 將 is equal to 同 equals 疊埋。佢哋係同一回事。用一個就得。
迷你練習
讀出每一行,並描述你會點樣做嚟解出個變數。
x + 7 = 123y = 212x − 5 = 9(x + 1) ÷ 4 = 3- If
y = 2x + 1, what isywhenx = 4?
總結
要喺英文講方程式,你需要一小套字:variable 名、equals 或者 is、四個平衡動詞(add、subtract、multiply、divide)各自帶住佢嘅介詞同 both sides,加上 solve for、plug in 同 substitute。由左讀到右,用每個動詞帶住佢嘅介詞嚟描述每一步,用 so 或者 therefore 嚟公布答案。數學係點就係點,但英文唔再拖慢你。
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