Understanding Fractions | 认识分数

📚 Understanding Fractions | 认识分数

Fractions are everywhere around us. When we share a pizza, measure time, or split a cake, we are using fractions. In this lesson, we will learn what a fraction is, how to read and write it, and how to use it in everyday life.

分数在我们的生活中无处不在。当我们分披萨、量时间或切蛋糕时，其实就在用分数。这节课我们将学习什么是分数、如何读写分数，以及如何在生活中运用分数。

1. What Is a Fraction? | 什么是分数？

A fraction shows a part of a whole. It tells us how many equal parts we have out of the total number of equal parts.

分数表示整体的一部分。它告诉我们，在总共分成若干等份后，我们取了多少份。

For example, if one whole pizza is cut into 4 equal slices and we eat 1 slice, we have eaten 1/4 of the pizza.

例如，如果一个整披萨被切成4块大小相同的片，我们吃了1片，那么我们就吃了整个披萨的 1/4。

2. Parts of a Fraction: Numerator and Denominator | 分数的组成部分：分子和分母

Every fraction has two numbers separated by a line. The number above the line is called the numerator. The number below the line is called the denominator.

每个分数都由一条分数线隔开的两个数字组成。线上面的数叫做分子，线下面的数叫做分母。

Numerator: tells us how many parts we take or count.
Denominator: tells us how many equal parts the whole is divided into.

分子：表示我们取走或数出的份数。
分母：表示整体被分成了多少等份。

3 / 4 → 3 = numerator, 4 = denominator

3 / 4 → 3 = 分子，4 = 分母

3. Equal Parts | 等分

In a fraction, the parts must be equal. If a shape is split unevenly, we cannot write a proper fraction for it.

在分数中，每一部分必须是相等的。如果一个图形被分成大小不一样的部分，我们就无法用它写出正确的分数。

Look at a rectangle divided into 4 strips. If all strips have the same width, each strip is 1/4 of the rectangle. If one strip is wider than the others, they are not equal parts.

看一个被分成4条的长方形。如果每条宽度相同，那么每条就是长方形的1/4。如果有一条比其他的宽，那它们就不是等分。

Equal parts: ½ + ½ = 1 whole | 等分：½ + ½ = 1 个整体

4. Fractions of a Shape | 图形的分数

We can shade parts of a shape to show a fraction. For example, dividing a circle into 3 equal parts and shading 2 of them gives the fraction 2/3.

我们可以通过给图形的部分涂色来表示分数。例如，把一个圆平均分成3份，并涂上其中2份，就得到分数 2/3。

Shape \| 图形	Fraction Shaded \| 涂色部分
A square cut into 2 equal triangles \| 正方形分成2个三角形	1/2
A circle cut into 4 equal quarters \| 圆分成4个扇形	3/4
A rectangle cut into 6 equal squares \| 长方形分成6个小正方形	5/6

Always count the shaded parts as the numerator and the total parts as the denominator.

永远把涂色的部分数作为分子，把总部分数作为分母。

5. Fractions of a Set | 集合的分数

A fraction can also describe part of a group of objects. For example, if there are 8 balloons and 3 are red, then the fraction of red balloons is 3/8.

分数也可以描述一组物体中的一部分。例如，如果有8个气球，其中3个是红色的，那么红气球所占的分数就是 3/8。

To find a fraction of a set, count the selected objects as the numerator and the total number of objects as the denominator.

求一个集合的分数时，把选中的物体数量作为分子，把物体的总数作为分母。

5 apples, 2 are green → green apples = 2/5

5个苹果，2个是绿色 → 绿苹果 = 2/5

6. Comparing Fractions | 比较分数

When two fractions have the same denominator, the one with the larger numerator is larger. Example: 3/4 > 1/4.

当两个分数的分母相同时，分子大的那个分数更大。例如：3/4 > 1/4。

When two fractions have the same numerator, the one with the smaller denominator is larger. Example: 1/3 > 1/5, because cutting a whole into 3 parts makes larger pieces than cutting it into 5 parts.

当两个分数的分子相同时，分母较小的那个分数更大。例如：1/3 > 1/5，因为把一个整体分成3份，每一份会比分成5份时更大。

Fraction Pair \| 分数对	Comparison \| 比较结果
2/5 and 4/5	2/5 < 4/5
1/2 and 1/4	1/2 > 1/4

7. Equivalent Fractions | 等值分数

Equivalent fractions are different fractions that name the same amount. For example, 1/2 is equal to 2/4 and also 4/8.

等值分数是指名称不同但大小相同的分数。例如，1/2 等于 2/4，也等于 4/8。

You can get an equivalent fraction by multiplying or dividing the numerator and denominator by the same number (not zero).

你可以通过把分子和分母同时乘以或除以同一个数（不是0）来得到等值分数。

1 × 2 / 2 × 2 = 2/4

So, 1/2 and 2/4 are equivalent because they represent the same shaded region.

所以，1/2 和 2/4 是等值的，因为它们表示相同的涂色区域。

8. Adding and Subtracting Fractions with Like Denominators | 同分母分数的加减

When adding or subtracting fractions with the same denominator, keep the denominator unchanged and add or subtract the numerators.

当同分母分数相加或相减时，分母保持不变，只把分子相加或相减。

1/4 + 2/4 = (1 + 2)/4 = 3/4

5/6 − 3/6 = (5 − 3)/6 = 2/6 = 1/3

Remember to simplify your answer if possible.

记住，如果可能的话，要把答案化成最简分数。

9. Fractions in Real Life | 分数在生活中的应用

We use fractions all the time without even noticing. Here are some examples:

我们经常在使用分数，甚至自己都没有注意到。这里有一些例子：

Half an hour = 1/2 of an hour.
A quarter dollar = 1/4 of a dollar.
Sharing 2 chocolates among 3 friends = each gets 2/3 of a chocolate.

半小时 = 1 小时的 1/2。
25美分 = 1美元的 1/4。
把2块巧克力分给3个朋友 = 每人得到一块巧克力的 2/3。

Understanding fractions helps us measure, share, and compare things fairly.

理解分数能帮助我们测量、分享，并公平地比较事物。

10. Practice Problems | 练习题

Try these problems on your own before checking the answers.

请先独立尝试这些题目，再核对答案。

What fraction of a circle is shaded if 1 out of 4 equal parts is shaded?
Compare: 2/3 and 1/3.
Find an equivalent fraction for 1/4 with denominator 8.
Add: 2/5 + 1/5.

如果把一个圆平均分成4份，涂了其中1份，那么涂色部分占几分之几？
比较：2/3 和 1/3。
写出分母为8且与 1/4 等值的分数。
计算：2/5 + 1/5。

Answers: 1) 1/4 2) 2/3 > 1/3 3) 2/8 4) 3/5

答案：1) 1/4 2) 2/3 > 1/3 3) 2/8 4) 3/5

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Understanding Fractions | 认识分数