📚 Understanding Equal Parts: Halves, Thirds, and Fourths | 理解等分：一半、三分之一与四分之一
Welcome to Lesson 16-2 of our Grade 2 mathematics series. In this lesson, we will explore one of the most important ideas in math: equal parts. When we share a pizza, a cake, or a chocolate bar fairly, we need to divide it into equal parts. This idea is called fractions in mathematics. Let us learn together how to identify halves, thirds, and fourths and how to use them in our daily lives.
欢迎来到二年级数学系列的第16-2课。在这节课中，我们将探索数学中最重要的概念之一：等分。当我们公平地分享一块披萨、一个蛋糕或一块巧克力时，我们需要把它分成相等的部分。在数学中，这个概念叫做分数。让我们一起学习如何辨认一半、三分之一和四分之一，并在日常生活中运用它们。
1. What Are Equal Parts? | 什么是等分？
Equal parts mean that every part is exactly the same size and shape. When we cut a pizza into 4 slices, all of the slices should be the same size. If one slice is bigger than the others, then the parts are not equal. Equal parts are the foundation of fractions, because a fraction always describes a part of a whole that has been split fairly.
等分意味着每一部分的大小和形状完全相同。当我们把一块披萨切成4片时，所有的片都应该一样大。如果有一片比其他片大，那么这些部分就不相等了。等分是分数的基础，因为分数描述的始终是一个整体被公平分割后的某一部分。
To check whether parts are equal, we can fold paper, cut shapes, or look carefully with our eyes. Imagine a square divided by one straight line down the middle. The two sides are exactly the same size, so they are equal parts. A rectangle divided by a line that is not in the middle will give two unequal parts, so we cannot call those parts halves.
要判断各部分是否相等，我们可以通过折纸、剪裁或仔细观察来判断。想象一个正方形被一条直线从正中间分开，两边的面积完全相同，所以它们是相等的部分。如果一条线不在正中间，一个长方形就会被分成两个不相等的部分，那样我们就不能称它们为”一半”。
- Equal parts have the same size and shape. | 等分的每一部分大小和形状都相同。
- A whole object can be divided into 2, 3, 4, or more equal parts. | 一个整体可以被分成2份、3份、4份或更多相等的部分。
- Each equal part has a special name based on how many parts there are. | 每一部分都会根据总份数拥有一个特殊的名称。
2. Halves: One Out of Two | 一半：两份中的一份
When a whole shape is divided into 2 equal parts, each part is called a half. The symbol for one half is ½. We read it as “one half.” Two halves make one whole, so we can write ½ + ½ = 1. The word “half” is special because we do not say “second” for this fraction.
当一个整体被分成2个相等的部分时，每一部分都叫做一半。二分之一的符号是½，我们读作”二分之一”或”一半”。两个一半合起来就是一个整体，所以我们可以写作½ + ½ = 1。”half”这个词很特殊，因为我们不把这一份叫作”第二份”。
Think about a sandwich cut diagonally into two triangles. Each triangle is a half of the sandwich. The two triangles have exactly the same size and shape. If you put them back together, they form the original whole sandwich. This shows that two halves always make one whole.
想一想把一个三明治沿对角线切成两个三角形。每个三角形都是三明治的一半。这两个三角形的大小和形状完全相同。如果你把它们拼回去，就能得到原来那个完整的三明治。这说明两个一半合起来总是一个整体。
Here is a quick summary of how we write halves:
下面是一个快速总结，看看我们如何书写”一半”：
| Words | 文字 | Symbol | 符号 | Meaning | 含义 |
| one half | 二分之一 | ½ | 1 out of 2 equal parts | 2个等份中的1份 |
| two halves | 两个一半 | ½ + ½ | 2 out of 2 equals 1 whole | 2个等份中的2份等于1个整体 |
A good way to practice halves is to fold a paper circle in half. Open it up and you will see a crease that divides the circle into two equal parts. Color one part. The colored part is ½ of the circle.
练习”一半”的好方法是将一张圆形纸对折。打开后你会看到一条折痕把圆分成两个相等的部分。给其中一部分涂色，涂色的部分就是圆的½。
3. Thirds: One Out of Three | 三分之一：三份中的一份
When a whole shape is divided into 3 equal parts, each part is called a third. The symbol for one third is ⅓. Three thirds make one whole, so we can write ⅓ + ⅓ + ⅓ = 1. If we take two of the three parts, we have two thirds, written as ⅔.
当一个整体被分成3个相等的部分时，每一部分都叫做三分之一。三分之一的符号是⅓。三个三分之一合起来是一个整体，所以我们可以写作⅓ + ⅓ + ⅓ = 1。如果三个部分中取两个，我们就得到了三分之二，写作⅔。
Imagine a chocolate bar broken into 3 equal rectangles. Each rectangle is one third of the whole bar. If you eat one piece, you have eaten ⅓ of the chocolate. If you eat two pieces, you have eaten ⅔, and only ⅓ remains for your friend.
想象一块巧克力被掰成3个相等的小长方形。每个小长方形都是整块巧克力的三分之一。如果你吃了一块，你就吃掉了这块巧克力的⅓。如果你吃了两块，你就吃掉了⅔，只剩下⅓留给你的朋友。
Dividing a shape into thirds can be tricky. A circle divided into three equal parts looks like a peace sign or a three-blade fan. Each angle at the center is 120 degrees, and together the three parts make 360 degrees, which is the whole circle.
把一个图形分成三份可能有点难。一个圆分成三等份后看起来像一个”奔驰标志”或三叶风扇。每一份在圆心处的夹角是120度，三个部分合起来是360度，也就是整个圆。
Can you fold a rectangular piece of paper into thirds? Try it. Fold one end to meet the middle and then fold the other end over it. Unfold the paper and you should see three equal rectangles.
你能把一张长方形纸折成三份吗？试试看。把一边折到中间，再把另一边叠上去。打开纸后，你应该会看到三个相等的长方形。
4. Fourths: One Out of Four | 四分之一：四份中的一份
When a whole shape is divided into 4 equal parts, each part is called a fourth or a quarter. The symbol for one fourth is ¼. Four fourths make one whole, so we can write ¼ + ¼ + ¼ + ¼ = 1. Two fourths equal one half, and three fourths are written as ¾.
当一个整体被分成4个相等的部分时，每一部分都叫做四分之一。四分之一的符号是¼。四个四分之一合起来是一个整体，所以我们可以写作¼ + ¼ + ¼ + ¼ = 1。两个四分之一等于一个一半，三个四分之一写作¾。
A square pizza cut into 4 equal smaller squares is a perfect example. Each small square is one fourth of the whole pizza. If you eat one piece, you have eaten ¼. If you share with your brother and sister, the four of you can each have exactly one piece.
一个方形披萨被切成4个相等的小正方形就是一个完美的例子。每个小正方形都是整个披萨的四分之一。如果你吃一块，你就吃掉了¼。如果你和兄弟姐妹一起分享，你们四个人正好每人一块。
There are many ways to divide a square into fourths. One way is to draw two straight lines through the center, one vertical and one horizontal. Another way is to draw two diagonal lines from corner to corner. Both ways give 4 equal parts, even though the shapes look different.
把一个正方形分成四份有很多方法。一种方法是通过中心画两条直线，一条竖线一条横线。另一种方法是从角到角画两条对角线。两种方法都能得到4个相等的部分，尽管每部分的形状看起来不一样。
We also use the word “quarter” for time. A quarter of an hour is 15 minutes, because 60 minutes ÷ 4 = 15 minutes. A quarter past 3 means 15 minutes after 3 o’clock, so the time is 3:15.
我们也用”quarter”这个词来表示时间。一小时的四分之一是15分钟，因为60分钟 ÷ 4 = 15分钟。3点过一刻（a quarter past 3）表示3点过了15分钟，也就是3:15。
5. Comparing the Size of Parts | 比较各部分的大小
Here is a fun question: which is bigger, one half of a pizza or one fourth of the same pizza? The answer is one half! This idea surprises many students at first. Why is a half bigger than a fourth, even though the number 4 is bigger than the number 2?
这里有一个有趣的问题：同一块披萨的二分之一和四分之一，哪个更大？答案是二分之一！很多学生一开始都会感到惊讶。为什么½比¼大，尽管数字4比2大呢？
The secret is that the bottom number of a fraction tells us how many parts we divide the whole into. The bigger the bottom number, the more parts there are, so each part becomes smaller. Think of sharing a cake with more friends: more friends means smaller pieces for everyone.
秘密就在于分数的下面那个数字告诉我们整体被分成了多少份。下面的数字越大，份数就越多，每一份也就越小。想一想和更多朋友分享一块蛋糕：朋友越多，每个人分到的就越小。
We can compare fractions with the same whole easily:
我们可以轻松地比较同一个整体下的不同分数：
| Number of Parts | 份数 | Name of One Part | 一份的名称 | Size of One Part | 一份的大小 |
| 2 | 2份 | half | 一半 | biggest | 最大 |
| 3 | 3份 | third | 三分之一 | 更多咨询请联系16621398022（同微信）
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