📚 Understanding Fractions: Halves, Thirds, and Quarters | 认识分数：一半、三分之一与四分之一
Welcome to Grade 2, Lesson 16-6! In this lesson, we will discover what a fraction is, how to name equal parts of a whole, and how to find fractions of shapes and groups. We will focus on three special fractions: 1/2, 1/3, and 1/4. These simple ideas form the building blocks of many topics in IGCSE Mathematics, from ratios to percentages.
欢迎来到二年级第 16 章第 6 课！在本课中，我们将了解什么是分数、如何命名一个整体的等分部分，以及如何找出形状和物体组的分数。我们将重点学习三个特殊的分数：1/2、1/3 和 1/4。这些简单的概念是 IGCSE 数学中许多主题（从比到百分数）的基石。
1. What Is a Fraction? | 什么是分数？
A fraction is a way to describe part of a whole. When we cut a cake into equal pieces and eat one piece, the piece we eat is a fraction of the whole cake. Fractions help us talk about parts of a shape, parts of a group, or parts of a number.
分数是用来描述”整体中的一部分”的方法。当我们把一块蛋糕切成相等的小块并吃掉一块时，吃掉的那一块就是整个蛋糕的一个分数。分数帮助我们描述一个形状的一部分、一组物体的一部分或一个数的一部分。
Every fraction has two numbers. The number on the top is called the numerator. It tells us how many parts we are talking about. The number on the bottom is called the denominator. It tells us how many equal parts the whole is divided into in total.
每个分数都有两个数字。最上面的数字叫作分子，它告诉我们所讨论的部分有几份。最下面的数字叫作分母，它告诉我们整体总共被分成了多少等份。
- In the fraction 1/2, the numerator is 1 and the denominator is 2.
- 在分数 1/2 中，分子是 1，分母是 2。
2. Equal Parts | 等分
Before we can write a fraction, the parts of the whole must be equal. This means every part must have the same size and the same shape. When we share fairly, we cut the whole into equal parts.
在写出一个分数之前，整体的各部分必须是相等的。也就是说，每一部分的大小和形状都必须相同。当我们公平分享时，就是把整体切成相等的几份。
Look at a rectangle. If we draw one line down the middle, we get two equal parts. But if we draw a line that is not in the middle, the two parts are not equal, so we cannot call them halves.
看一个长方形。如果我们从中间画一条竖线，就得到两个相等的部分。但如果画的线不在正中间，两部分就不相等，我们就不能把它们叫作”一半”。
Equal parts ⇌ same size and same shape
等分 ⇌ 大小相同、形状相同
3. One Half (1/2) | 二分之一
When a whole is divided into 2 equal parts, each part is called one half. We write one half as 1/2 or ½. The denominator 2 tells us there are 2 equal parts, and the numerator 1 tells us we are looking at 1 of those parts.
当一个整体被分成 2 个相等的部分时，每一部分叫作二分之一。我们把二分之一写作 1/2 或 ½。分母 2 表示一共有 2 个等份，分子 1 表示我们取其中的 1 份。
Imagine a round pizza cut into two equal slices. Each slice is one half of the pizza. If you take one slice, you have one half of the whole pizza.
想象一块圆形披萨被切成两个相等的扇形。每一块都是这块披萨的二分之一。如果你拿走一块，你就拥有了整块披萨的一半。
1 ÷ 2 = 1/2 = ½
1 ÷ 2 = 1/2 = ½
- One half of 10 apples is 5 apples, because 10 ÷ 2 = 5.
- 10 个苹果的二分之一是 5 个苹果，因为 10 ÷ 2 = 5。
4. One Third (1/3) | 三分之一
When a whole is divided into 3 equal parts, each part is called one third. We write one third as 1/3. The denominator 3 means three equal parts in total, and the numerator 1 means we take just one part.
当一个整体被分成 3 个相等的部分时，每一部分叫作三分之一。我们把三分之一写作 1/3。分母 3 表示总共有 3 等份，分子 1 表示我们只取其中 1 份。
Suppose we have a chocolate bar and we want to share it equally among three friends. We break it into 3 equal pieces. Each friend receives one third of the bar, which is written as 1/3.
假设我们有一块巧克力，想平均分给三个朋友。我们把它掰成 3 块相等的巧克力。每个朋友得到这块巧克力的三分之一，写作 1/3。
1 ÷ 3 = 1/3
1 ÷ 3 = 1/3
5. One Quarter (1/4) | 四分之一
When a whole is divided into 4 equal parts, each part is called one quarter or one fourth. We write one quarter as 1/4. Sometimes the word “quarter” is used for 1/4 in everyday life, such as a quarter of an hour or a quarter of a dollar.
当一个整体被分成 4 个相等的部分时，每一部分叫作四分之一。我们把四分之一写作 1/4。在日常生活中，我们常用”quarter（夸脱/四分之一）”来表示 1/4，比如一刻钟（一小时的四分之一）或 25 美分（一美元的四分之一）。
If a square is divided into 4 equal smaller squares, each smaller square is one quarter of the large square. If we shade 2 of the 4 parts, we have two quarters, which is written as 2/4. Notice that 2/4 is the same as 1/2, because two quarters make one half.
如果一个正方形被分成 4 个相等的小正方形，每个小正方形都是大正方形的四分之一。如果我们涂色 2 个小正方形，就得到四分之二，写作 2/4。注意，2/4 与 1/2 相同，因为两个四分之一等于一个二分之一。
1 ÷ 4 = 1/4 and 2 ÷ 4 = 2/4 = 1/2
1 ÷ 4 = 1/4，且 2 ÷ 4 = 2/4 = 1/2
6. Comparing Fractions | 比较分数
When the whole is the same size, a fraction with a larger denominator means more equal parts, so each part is smaller. For example, 1/4 is smaller than 1/2, because cutting the same whole into 4 parts gives smaller pieces than cutting it into 2 parts.
当整体大小相同时，分母越大的分数表示等份越多，因此每一份就越小。例如，1/4 小于 1/2，因为把同一个整体切成 4 份时，每一份会比切成 2 份时更小。
We can put our three fractions in order from smallest to largest: 1/4, 1/3, 1/2. The fraction 1/3 is larger than 1/4 but smaller than 1/2.
我们可以把三个分数从小到大排列：1/4、1/3、1/2。分数 1/3 大于 1/4，但又小于 1/2。
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