如何讀懂「數學英文」來解答出數學應用題

【大紀元2016年05月19日訊】學生們在解答數學應用題時常常在想：「怎樣才能最好的理解這道題的題意，並把它分解成幾個簡單的問題？」「如何把這個包含數字的句子轉換成我能理解的英文？」本文就來討論如何破除數學應用題的神秘感。

首先我們必須讀懂的是，這道應用題要求解答的是什麼，例如是某個百分比？某個值？兩個答案？一個答案？某個估計值？還是精確值？瞭解這點後，就可以把它設為未知變量，以及建立方程式來求解未知量。得出答案後，再把答案代回方程式來證實答案是正確無誤的。

學生們往往對數學有一種恐懼感，這並非因為他們不會做題，而是因為他們沒有讀懂問題或者沒能把它分解成簡單的問題來解答。INC Tutoring輔導公司把這套技巧教給其學生後，他們就能成功解答出一個又一個難題。最後他們往往會感嘆道：「我真希望學校的老師能這樣教我們」或者說「這套方法比我在學校學的容易多了。」

我們會不斷的和大家分享新的技巧以及更快捷的思考和學習方法，以便大家各取所需。這樣，數學應用題的神秘感就再也不存在了。

下面分析一道數學應用題來作為例子（保留英文原文）。

Solving a mixture problem takes precision, but you can break it down with mathematical English as well. You have to remember these steps. 1) What is being mixed? 2) Organize the information. 3) Set up gallons of the ingredient for each container. 4) Form a mixture equation. 5) Solve and Check.

Q: How many gallons of a 60% solution must be added to 30 gallons of a 10% solution in order to produce a 20% solution?

We know so far that a 60% solution is being mixed with a 10% solution. We do NOT know how much of the 60% solution we have, so that is “x”. We do have 30 gallons of the 10% solution.

The next step is to ORGANIZE the information. One jar contains the 60% solution (x gallons). Another jar contains the 10% solution (30 gallons). There is a 20% solution jar that combines the two as well (x + 30). The last jar is the place where we want to have the 20% solution created. In the first jar, we have a 60% solution that houses 60% of the gallons of one liquid. In the other jar, we have 40% of the container having other ingredients.

Now, it is time to calculate the gallons of the ingredient in each of the containers by multiplying the total gallons of EACH container by the percentage listed for the container.   Next, you have 60% * x, 10% * 30, and 20% * (x+30). The verbal equation is (Ingredient in Jar 1) + (Ingredient in Jar 2) = (Ingredient in Jar 3). The equation using decimals is: .60x + 3 = .20x + 6. You would then subtract .20x from both sides and subtract 3 from both sides to get .40x = 3. Next, you divide both sides by .40 and x = 7.5.

Problem solved and you should check it by plugging the value for x back into the equation.  This is how easy math can be using mathematical English.   Let’s try this again in a different way.

“What is 75% of 300?”

How are we going to break this problem down? When a problem says “What”, that means “x”. The word “is” ALWAYS means “equals”. “Percentage” always means “out of 100 parts”, so the 75% converts to 75/100. “Of” means multiplication and the number 300 remains just that – a number. So, here is the updated version of this: x = (75/100) * 300. Now, 100 goes into 300 three times. So, you have 3 times 75 which equals 225. Problem solved.  This is how easy math can be using mathematical English. Let’s try this again in a different way.

35 is what percent of 80?

We now solve this problem: 80 goes into 100 1.25 times. So, we have 35 = x/1.25. We then cross multiply 35 * 1.25 and get 43.75 which is our answer. X = 43.75%. As you see, this process is again very simple. Visual learners will need to break problems down by drawing pictures or sketching out the process of the problem. Auditory learners just need to hear the correct conversion of the problem. Kinesthetic learners will need to get up and act out the problem or write on the boards themselves. This simple mathematical English process can be used on more advanced problems to provide clarity to the problem solver.

文 | Jay Veal（INC Tutoring輔導公司總裁）

責任編輯：李元