Equal Parts and Fractions | 等分与分数

📚 Equal Parts and Fractions | 等分与分数

Welcome to this lesson on equal parts and fractions! In Grade 2, we learn how to split shapes and groups into fair shares, and we give each share a special name using fractions. This skill helps us share food, sort objects, and understand parts of a whole.

欢迎来到”等分与分数”这节课！在二年级，我们学习如何把图形和物体平均分成公平的几份，并用分数给每一份取一个特别的名字。这个本领能帮助我们分食物、分类物体，以及理解整体中的一部分。

1. What Are Equal Parts? | 什么是等分？

Equal parts are pieces that are exactly the same size. When we fold a paper in half, we get two equal rectangles. When we cut a cake into four slices of the same size, we get four equal parts.

等分就是把一个整体分成大小完全相同的几份。当我们将一张纸对折时，我们得到两个大小相同的长方形。当我们把蛋糕切成大小相同的四块时，我们就得到了四个等份。

A whole object can be divided into equal parts in many different ways, but every part must match the others in size. If one piece is bigger and another is smaller, those are NOT equal parts.

一个整体可以用许多不同的方式分成等份，但每一份的大小必须和其他份完全一样。如果一块大、一块小，那么它们就不是等分。

2. Halves | 二分之一

When we divide a whole into two equal parts, each part is called a half. The fraction for one half is written as ½. We say “one half” and read it as “1 out of 2 equal parts.”

当我们把一个整体分成两个相等的部分时，每一部分叫作一半。二分之一的分数写作 ½。我们读作”二分之一”，意思是”两个等份中的一份”。

Whole ÷ 2 = ½ and ½

Cutting a sandwich down the middle creates two halves. If you take one half, you have ½ of the sandwich. Taking both halves gives you the whole sandwich, or 2/2 = 1 whole.

把三明治从中间切开，就得到了两个一半。如果你拿走一个一半，你就有了三明治的 ½。拿走两个一半，你就得到了整个三明治，也就是 2/2 = 1 个整体。

3. Thirds | 三分之一

When we divide a whole into three equal parts, each part is called a third. The fraction for one third is written as ⅓. Three thirds make one whole: ⅓ + ⅓ + ⅓ = 1.

当我们把一个整体分成三个相等的部分时，每一部分叫作三分之一。三分之一的分数写作 ⅓。三个三分之一组成一个整体：⅓ + ⅓ + ⅓ = 1。

For example, if you share one chocolate bar equally among three friends, each friend receives ⅓ of the bar. If two friends put their shares together, they have ⅔, which we call two thirds.

例如，如果一块巧克力平均分给三个朋友，每个朋友得到这块巧克力的 ⅓。如果两个朋友把他们的那份合在一起，他们就有 ⅔，我们把它叫作三分之二。

4. Fourths (Quarters) | 四分之一

When we divide a whole into four equal parts, each part is called a fourth or a quarter. The fraction for one fourth is written as ¼. Four fourths make one whole: ¼ + ¼ + ¼ + ¼ = 1.

当我们把一个整体分成四个相等的部分时，每一部分叫作四分之一。四分之一的分数写作 ¼。四个四分之一组成一个整体：¼ + ¼ + ¼ + ¼ = 1。

A square cut along both the middle lines makes four small squares. Each small square is ¼ of the big square. Two squares are 2/4, which equals ½. Three squares are ¾, which we call three fourths.

一个正方形沿着两条中线切开，得到四个小正方形。每个小正方形是大正方形的 ¼。两个小正方形是 2/4，它等于 ½。三个小正方形是 ¾，我们把它叫作四分之三。

5. Writing Fractions with Numbers | 用数字表示分数

A fraction has two important numbers. The bottom number, called the denominator, tells how many equal parts are in the whole. The top number, called the numerator, tells how many parts we are talking about.

分数有两个重要的数字。下面的数字叫作分母，表示整体被分成多少等份。上面的数字叫作分子，表示我们取了多少份。

Fraction	Words in English	中文读法	Meaning
½	one half	二分之一	1 of 2 equal parts
⅓	one third	三分之一	1 of 3 equal parts
⅔	two thirds	三分之二	2 of 3 equal parts
¼	one fourth / quarter	四分之一	1 of 4 equal parts
¾	three fourths	四分之三	3 of 4 equal parts

Remember the denominator shows the total number of equal parts, not the size of the whole. The numerator counts the parts we choose or color.

请记住，分母表示等份的总数，而不是整体的大小。分子表示我们选择或涂色的份数。

6. Fractions of a Set | 一组物体的分数

We can also find fractions of a group of objects. If there are 6 apples and we take half of them, we take 3 apples. We write this as ½ of 6 = 3.

我们也可以求一组物体的分数。如果有 6 个苹果，我们取其中一半，就是取 3 个苹果。我们把它写作 ½ × 6 = 3。

To find a fraction of a set, first divide the objects into equal groups. Then count how many groups the numerator asks for. For example, ¼ of 8 cookies means 8 ÷ 4 = 2, so ¼ of 8 is 2 cookies.

要求一组物体的几分之几，先把物体分成相等的组，再数出分子需要多少组。例如，8 块饼干的 ¼ 表示 8 ÷ 4 = 2，所以 8 的 ¼ 是 2 块饼干。

½ of 10 = 5 (10 split into 2 groups)
⅓ of 9 = 3 (9 split into 3 groups)
¼ of 12 = 3 (12 split into 4 groups)
½ 的 10 = 5（10 分成 2 组）
⅓ 的 9 = 3（9 分成 3 组）
¼ 的 12 = 3（12 分成 4 组）

7. Comparing Parts of a Whole | 比较部分与整体

The more equal parts we cut a whole into, the smaller each part becomes. A half is bigger than a fourth, so ½ > ¼. A fourth is bigger than a sixth, so ¼ > ⅙.

我们把整体分成的等份越多，每一份就越小。一半比四分之一大，所以 ½ > ¼。四分之一比六分之一大，所以 ¼ > ⅙。

Also, any fraction that uses all the parts of a whole is equal to 1. For example, 2/2 = 1, 3/3 = 1, and 4/4 = 1. Two halves make one whole, and four quarters also make one whole.

同样，任何使用了整体全部份数的分数都等于 1。例如，2/2 = 1，3/3 = 1，4/4 = 1。两个一半组成一个整体，四个四分之一也组成一个整体。

½ > ¼ because fewer parts means bigger parts

8. Equal or Not Equal? | 等分还是不等分？

Sometimes a shape is cut into pieces that are not the same size. These are not equal parts, so they cannot be called halves, thirds, or fourths. We must always compare the sizes carefully.

有时一个图形被切成大小不同的几块，这些就不是等份，不能叫二分之一、三分之一或四分之一。我们一定要仔细比较每块的大小。

For example, a rectangle split into two parts where one part is large and one part is small is NOT divided into halves. Only cutting along the exact middle line gives two equal halves.

例如，一个长方形被切成一大一小两块，就不能叫作分成两半。只有沿着正中间的那条线切，才能得到两个相等的半份。

Always ask yourself: Does every part have the same size and shape? If the answer is yes, the parts are equal. If not, we cannot use a fraction name.

一定要问自己：每一份的大小和形状都一样吗？如果答案是”是”，那么这些就是等份。如果不是，我们就不能使用分数名称。

9. Practice Questions | 练习

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

请先自己尝试完成这些题目，然后再看下面的答案。

Q1: A circle is divided into 4 equal parts and 1 part is colored. What fraction is colored?
Q2: A rectangle is divided into 3 equal parts and 2 parts are shaded. Name the fraction.
Q3: Which is larger, ½ or ¼?
Q4: There are 12 marbles. What is ⅓ of the marbles?
Q5: A square is cut into two pieces of different sizes. Can we call one piece half?
题目1：一个圆被分成 4 等份，涂色 1 份。涂色部分占几分之几？
题目2：一个长方形被分成 3 等份，阴影部分有 2 份。这个分数叫什么？
题目3：½ 和 ¼ 哪个更大？
题目4：有 12 颗弹珠。这些弹珠的 ⅓ 是多少颗？
题目5：一个正方形被切成大小不同的两块。其中一块能叫一半吗？

Answers: Q1 = ¼. Q2 = ⅔, two thirds. Q3 = ½. Q4 = 4 marbles. Q5 = No, because the pieces are not equal.

答案：第1题 = ¼。第2题 = ⅔，三分之二。第3题 = ½。第4题 = 4 颗弹珠。第5题 = 不能，因为两块大小不相同。

10. Common Mistakes and Tips | 常见错误与小技巧

One common mistake is calling any two pieces “halves” even when they are different sizes. Always check equality first. Another mistake is writing the numerator and denominator in the wrong order. The denominator always tells the total number of equal parts.

一个常见错误是：只要有两块就说是”两半”，即使它们大小不同。一定要先检查是否相等。另一个错误是把分子和分母写反。分母总是表示等份的总数。

Here are some helpful tips: count the equal parts first; name the fraction using the total number of parts; use a real pizza or paper to practice cutting; and compare fractions by thinking about the size of each piece.

这里有一些有用的小技巧：先数等份总数；用总份数来写出分数名称；可以拿真的比萨或纸来练习切分；并通过思考每一份的大小来比较分数。

Keep practicing with shapes and sets, and soon fractions will feel easy and fun!

多练习图形和物体的分数，很快你就会觉得分数又简单又有趣！

Published by TutorHao | Mathematics Revision Series | aleveler.com

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Equal Parts and Fractions | 等分与分数