Student's Edition: Grade K Lesson 15-3 | 学生版：第15-3课 分数、小数和百分比

📚 Student's Edition: Grade K Lesson 15-3 | 学生版：第15-3课 分数、小数和百分比

Welcome to this IGCSE Mathematics revision lesson focusing on fractions, decimals and percentages. These three number forms are fundamental tools you will use across algebra, geometry, statistics and real-world problem solving.

欢迎来到这节 IGCSE 数学复习课，重点是分数、小数和百分比。这三种数的表示形式是你在代数、几何、统计和实际问题解决中都会用到的基本工具。

1. Understanding Fractions | 理解分数

A fraction represents a part of a whole or a division of two quantities. It is written as a/b, where a is the numerator and b is the denominator. The denominator shows how many equal parts the whole is divided into, and the numerator shows how many parts we take.

分数表示整体的一部分或两个量的除法。它写作 a/b，其中 a 是分子，b 是分母。分母表示整体被分成多少等份，分子表示我们取了多少份。

For example, 3/4 means 3 out of 4 equal parts. In IGCSE, you must be able to interpret fractions in different contexts, such as shading diagrams, splitting amounts, and comparing sizes.

例如，3/4 表示 4 等份中的 3 份。在 IGCSE 中，你必须能够在不同情境中解释分数，例如涂色图形、分割数量和比较大小。

---

2. Equivalent Fractions and Simplifying | 等值分数与化简

Equivalent fractions have the same value even though they look different. You can find an equivalent fraction by multiplying or dividing both numerator and denominator by the same non-zero number.

等值分数数值相同，但形式不同。你可以通过将分子和分母同时乘以或除以同一个非零数来得到等值分数。

lify a fraction, divide both numerator and denominator by their highest common factor (HCF). The fraction 12/16 simplifies to 3/4 because the HCF of 12 and 16 is 4.

例如，1/2 = 2/4 = 5/10。化简分数时，将分子和分母同时除以它们的最大公因数（HCF）。分数 12/16 化简为 3/4，因为 12 和 16 的 HCF 是 4。

Always express your final answer in its simplest form unless the question states otherwise. This is a common mark in IGCSE exam papers.

除非题目另有说明，否则最终答案都要化为最简形式。这是 IGCSE 试卷中常见的得分点。

---

3. Mixed Numbers and Improper Fractions | 带分数与假分数

A mixed number combines a whole number and a proper fraction, such as 2 1/3. An improper fraction has a numerator larger than or equal to its denominator, such as 7/3.

带分数由一个整数和一个真分数组成，例如 2 1/3。假分数的分子大于或等于分母，例如 7/3。

ginal denominator. For 2 1/3, we calculate 2 × 3 + 1 = 7, so the improper fraction is 7/3.

将带分数化为假分数时，用整数乘以分母，再加上分子。把结果放在原分母上。对于 2 1/3，计算 2 × 3 + 1 = 7，所以假分数是 7/3。

To convert an improper fraction back to a mixed number, divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.

将假分数化回带分数时，用分子除以分母。商是整数部分，余数是新分子，分母保持不变。

---

广告 / Sponsored

4. Adding and Subtracting Fractions | 分数加减法

To add or subtract fractions, they must have the same denominator. If they do not, find the lowest common multiple (LCM) of the denominators to create a common denominator.

分数加减法要求分母相同。如果分母不同，找到分母的最小公倍数（LCM）作为公分母。

ite each fraction: 1/3 = 4/12 and 1/4 = 3/12. Then add the numerators: 4/12 + 3/12 = 7/12.

例如，计算 1/3 + 1/4，3 和 4 的 LCM 是 12。重写每个分数：1/3 = 4/12，1/4 = 3/12。然后分子相加：4/12 + 3/12 = 7/12。

When subtracting, follow the same process. If mixed numbers are involved, you can convert them to improper fractions first or handle the whole number and fraction parts separately.

减法也遵循同样的步骤。如果涉及带分数，可以先化为假分数，或者分别处理整数部分和分数部分。

---

5. Multiplying and Dividing Fractions | 分数乘除法

To multiply fractions, multiply the numerators together and the denominators together. Simplify before multiplying if possible to keep numbers small.

分数相乘时，分子乘以分子，分母乘以分母。如果可能，在相乘前先约分，使数字保持较小。

xample, 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2. Notice that the common factor 3 cancels.

例如，2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2。注意公因数 3 被约掉。

multiply by its reciprocal. The reciprocal of a/b is b/a. So 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.

除以一个分数等于乘以它的倒数。a/b 的倒数是 b/a。所以 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9。

With mixed numbers, convert to improper fractions before multiplying or dividing.

遇到带分数时，先化为假分数再进行乘除。

---

6. Converting Fractions to Decimals | 分数转小数

a decimal by dividing the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375.

Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）