第三单元

Unit 3

Mathematics in beer production - proportion

三 啤酒生产中的数学——比例

The situation of a truck transporting barley malt in two days is shown in the table on the right.

一辆货车两天运输大麦芽情况如右表。

What questions can you ask?

你能提出什么问题？

Cooperative exploration

合作探索

1. What is the ratio of volume to number of shipments? What are they related to?

1. 运输量和运输次数的比各是多少？它们有什么关系？

The ratio of the first day's traffic to the number of trips: sixteen to two

第一天运输量和运输次数的比是： 16:2

The ratio of the next day's traffic to the number of trips: thirty two to four

第二天运输量和运输次数的比是：32:4

I find that the ratio of the volume of traffic to the number of trips is equal.

我发现运输量和运输次数的比的比值相等。

The two ratios are equal, which can be written as the following equation:

两个比相等，可以写成下面的等式：

Sixteen to two is equal to thirty two to four

16:2＝32:4

An expression that expresses the equality of two ratios is called a proportion.

表示两个比相等的式子叫做比例。

The four numbers that make up the ratio are called the terms of the ratio. The two terms at each end are called the outer terms of the ratio, and the two terms in the middle are called the inner terms of the ratio.

组成比例的四个数，叫做比例的项。两端的两项叫作比例的外项，中间的两项叫作比例的内项。

16:2 = 32:4 could also be written as 16/2 = 32/4

16:2＝32:4也可以写成16/2＝32/4

2. What is the relationship between the two outer terms and the two inner terms in the ratio?

2. 在比例里，两个外项与两个内项之间有什么关系呢？

So let's see

我们算算看

Calculate the sum, difference, product and quotient of two outer terms and two inner terms respectively.

分别算出两个外项与两个内项的和、差、积、商……

I find that the product of two outer terms is equal to the product of two inner terms.

我发现两个外项的积等于两个内项的积。

So let's see if this is a rule.

这是不是一个规律，我们来验证一下。

In proportion, the product of two outer terms is equal to the product of two inner terms. That's the fundamental property of proportion.

在比例里，两个外项的积等于两个内项的积。这是比例的基本性质。

According to the basic property of proportion, we can find the unknown term in proportion.

根据比例的基本性质，可以求比例中的未知项。

3. Can you figure out the unknown term in the following ratio?

3. 你能求出下面比例中的未知项吗？

So just like we did up here, we take the unknown term in the ratio, and that's called the solution ratio.

像上面这样，求比例中的未知项，叫作解比例。

Lesson 2

Beer production record sheet

啤酒生产情况记录表

What questions can you ask?

你能提出什么问题？

Cooperative exploration

合作探索

1. What is the relationship between total amount of work and working hours?

1. 工作总量和工作时间有什么关系呢？

The total amount of work and working hours are two kinds of related quantity, the total amount of work is changed with the change of working hours.

工作总量与工作时间是两种相关联的量，工作总量是随着工作时间的变化而变化的。

The longer the work hours, the more beer they produce; The shorter the working hours...

工作时间越长，生产的啤酒越多；工作时间越短……

I find that the ratio of the total amount of work to the number of hours worked is certain.

我发现工作总量与工作时间的比值一定。