Fractions: Equal Parts and Sharing | 分数：等分与分配

📚 Fractions: Equal Parts and Sharing | 分数：等分与分配

In this lesson, we will explore what fractions are, how to read and write them, and how to share things equally. Fractions are everywhere in daily life, from cutting a pizza to counting coins.

在本课中，我们将探索什么是分数、如何读写分数，以及如何把物品平均分配。分数在日常生活中无处不在，从切比萨到数硬币都会用到。

1. What Is a Fraction? | 什么是分数？

A fraction is a way to show one or more equal parts of a whole. When we divide something into equal pieces, each piece is a fraction of the whole.

分数是用来表示一个整体的一个或多个相等部分的方式。当我们把一个物体分成相等的几份时，每一份就是整体的一部分，可以用分数来表示。

For example, if a chocolate bar is broken into two equal pieces, each piece is one half of the bar. If a paper strip is cut into four equal parts, each part is one fourth of the strip.

例如，如果一块巧克力被掰成两个相等的小块，那么每小块就是整块巧克力的二分之一（一半）。如果把一条纸带剪成四个相等的部分，那么每个部分就是纸带的四分之一。

A fraction has two numbers separated by a line: the top number and the bottom number.
分数由两个数字组成，中间用一条横线隔开：上面的数字和下面的数字。
The bottom number tells how many equal parts the whole is divided into.
下面的数字表示整体被分成了多少个相等的部分。
The top number tells how many parts we are talking about.
上面的数字表示我们取了其中的多少个部分。

2. Halves | 二分之一（一半）

When a whole is divided into two equal parts, each part is called a half. We write one half using the fraction symbol: ½.

当一个整体被分成两个相等的部分时，每一部分都叫做一半。我们写一半时使用分数符号：½。

Look at a square folded along one straight line. The two pieces are exactly the same size and shape. Each piece is ½ of the square.

观察一个沿直线对折的正方形。折出来的两个部分大小和形状完全相同。每个部分都是正方形的½。

1 ÷ 2 = ½

Two halves make one whole: ½ + ½ = 1
两个二分之一合起来就是一个整体：½ + ½ = 1
If you share 1 apple between 2 friends, each friend gets ½ apple.
如果1个苹果分给2个朋友，每个朋友得到½个苹果。

3. Thirds | 三分之一

When a whole is divided into three equal parts, each part is called a third. We write one third as ⅓.

当一个整体被分成三个相等的部分时，每一部分都叫做三分之一。我们写三分之一为⅓。

Imagine a rectangular cake cut with two straight cuts so that the three pieces are exactly equal. Each piece is ⅓ of the cake.

想象一个长方形蛋糕，用两刀切成大小完全相等的三块。每一块都是蛋糕的⅓。

⅓ + ⅓ + ⅓ = 1 whole

Three thirds make one whole. If you have two thirds, you have ⅔ of the whole.

三个三分之一组成一个整体。如果你有三分之二，那你就有了整体的⅔。

4. Fourths (Quarters) | 四分之一

When a whole is divided into four equal parts, each part is called a fourth or a quarter. We write one fourth as ¼.

当一个整体被分成四个相等的部分时，每一部分都叫做四分之一。我们写四分之一为¼。

A square can be divided into four equal smaller squares, or into four equal triangles. Either way, each piece is ¼ of the big square.

一个正方形可以被分成四个相等的小正方形，也可以分成四个相等的三角形。无论哪种方法，每一块都是大正方形的¼。

Number of parts	Name of each part	Fraction symbol
2	half	½
3	third	⅓
4	fourth / quarter	¼

Four quarters make one whole. If you have three quarters, you have ¾ of the whole.

四个四分之一组成一个整体。如果你有四分之三，那你就有了整体的¾。

5. Numerator and Denominator | 分子和分母

Every fraction has two important parts with special names. The top number is the numerator. The bottom number is the denominator.

每个分数都有两个重要的部分，它们有专门的名称。上面的数字叫分子，下面的数字叫分母。

Fraction = Numerator ÷ Denominator

The denominator tells how many equal parts in the whole. It is the number below the line.
分母表示整体被分成了多少个相等的部分，它写在横线下面。
The numerator tells how many parts we select or have. It is the number above the line.
分子表示我们选取或拥有的部分数量，它写在横线上面。

In the fraction ⅔, the denominator is 3 and the numerator is 2. We read it as “two thirds.”

在分数⅔中，分母是3，分子是2。我们把它读作“三分之二”。

6. Fractions of a Set | 一个集合的分数

Fractions can also describe part of a group or set of objects, not just a single shape.

分数不仅可以描述一个物体的部分，也可以描述一组物品中的一个部分。

Suppose there are 6 apples in a basket, and 2 of them are red. Then ²⁄₆ of the apples are red.

假设篮子里有6个苹果，其中2个是红色的，那么红苹果占苹果总数的²⁄₆。

To find a fraction of a set, divide the objects into equal groups according to the denominator, then count the groups according to the numerator.

要求一个集合的分数，先按分母把物品分成相等的几组，再按分子数出对应的组数。

Example: Find ½ of 8 stars. Divide 8 stars into 2 equal groups: 8 ÷ 2 = 4. So ½ of 8 is 4.

例如：求8颗星的½。把8颗星分成2个相等的组：8 ÷ 2 = 4。所以8的½是4。

7. Comparing Fractions with the Same Denominator | 比较同分母分数

When two fractions have the same denominator, the fraction with the greater numerator is the larger fraction.

当两个分数的分母相同时，分子较大的分数更大。

34 > ¼ because 3 > 1

Think of a circle cut into 4 equal pieces. Three pieces cover more area than one piece. So ¾ is greater than ¼.

想一想一个圆被切成4个相等的扇形。三块扇形比一块扇形占据更大的面积。所以¾大于¼。

When the numerators are the same, compare the denominators. A larger denominator means smaller pieces, so the fraction is smaller.

当分子相同时，就比较分母。分母越大，表示每一份越小，所以分数越小。

¼ is greater than ⅛ because fourths are larger pieces than eighths.
¼大于⅛，因为四分之一比八分之一更大块。
½ is greater than ⅓ because halves are larger than thirds.
½大于⅓，因为一半比三分之一更大。

8. Equivalent Fractions | 相等的分数

Sometimes two different fractions name the same amount. These are called equivalent fractions.

有时两个不同的分数表示相同的数量，这样的分数叫做等值分数。

Look at a strip of paper. Fold it into 2 equal parts, then fold again. You get 4 equal parts. The shaded part that was ½ is now ²⁄₄. So ½ = ²⁄₄.

观察一条纸带。把它折成2个相等部分，再对折一次，就得到4个相等部分。原来涂色的½现在变成了²⁄₄。所以½ = ²⁄₄。

½ = ²⁄₄ = ³⁄₆ = ⁴⁄₈

To make an equivalent fraction, multiply or divide the numerator and denominator by the same number.

要得到一个等值分数，可以把分子和分母同时乘或除以同一个数。

9. Adding and Subtracting Simple Fractions | 简单的分数加减法

When fractions share the same denominator, we simply add or subtract the numerators and keep the denominator unchanged.

当分数具有相同的分母时，我们只需对分子进行加减，分母保持不变。

²⁄₄ + ¼ = ¾

Here, 2 plus 1 equals 3, and the denominator stays 4.

在这里，2加1等于3，分母保持4不变。

For subtraction: ¾ − ²⁄₄ = ¼. Here, 3 minus 2 equals 1.

对于减法：¾ − ²⁄₄ = ¼。在这里，3减2等于1。

If the denominators are different, we first find equivalent fractions with the same denominator.

如果分母不同，我们首先要找到分母相同的等值分数。

Example: ½ + ¼ = ²⁄₄ + ¼ = ¾.

例如：½ + ¼ = ²⁄₄ + ¼ = ¾。

10. Fractions in Real Life | 生活中的分数

Fractions help us every day. When we share food, measure ingredients, or tell time, we use fractions.

分数每天都在帮助我们。当我们分享食物、测量配料或看时间时，都会用到分数。

A clock: half past 3 means 3:30, which is ½ of an hour after 3.
时钟：3点半表示3:30，也就是3点之后过了½小时。
Money: 25 cents is ¼ of a dollar.
钱币：25美分是1美元的¼。
Cooking: ½ cup of flour means fill the cup halfway.
烹饪：½杯面粉表示把杯子装到一半。
Shopping: a “quarter off” means the price is reduced by ¼.
购物：“打四分之一折”表示价格降低了¼。

Whenever you see that something is divided into equal parts and some parts are chosen, you are looking at a fraction.

每当你看到某物被分成相等部分，并且选取了其中几部分时，你看到的就正是一个分数。

11. Common Mistakes and Tips | 常见错误与提示

Many students make the same small mistakes when learning fractions. Here are the most common ones and how to avoid them.

许多同学在学习分数时都会犯一些类似的小错误。下面是常见的错误以及如何避免它们。

Mistake 1: Drawing unequal parts. Always check that every part is exactly the same size.
错误1：画出不相等的部分。务必检查每一部分的大小是否完全相同。
Mistake 2: Confusing numerator and denominator. Remember: denominator is “down,” numerator is “number we have.”
错误2：混淆分子和分母。记住：分母的“母”字有“底部”的含义，分子则是“我们拥有的数量”。
Mistake 3: Adding denominators. When adding like fractions, never add the denominators.
错误3：把分母相加。在计算同分母分数加法时，千万不要把分母加起来。
Tip: Draw a picture or a number line to check your answer.
提示：画图或画数轴来检验你的答案。

12. Practice and Review | 练习与复习

Try these quick problems on your own, then check the answers below.

请自己动手尝试下面的快速练习，然后对照下面的答案。

Question 1: What fraction of a square is shaded if one of four equal parts is shaded?

问题1：如果一个正方形的四个相等部分中有一个被涂色，涂色部分占正方形的几分之几？

Question 2: Which is larger, ¾ or ¼?

问题2：¾和¼哪个更大？

Question 3: Write ½ as an equivalent fraction with denominator 6.

问题3：把½写成以6为分母的等值分数。

Answers: 1) ¼ 2) ¾ 3) ³⁄₆

Review these ideas every day, and fractions will become easy and fun. Keep practicing with shapes, sets, and real objects around you.

每天复习这些概念，分数就会变得简单而有趣。持续用图形、集合和身边的实物进行练习吧。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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Fractions: Equal Parts and Sharing | 分数：等分与分配