Mastering Fractions, Decimals and Percentages | 掌握分数、小数和百分数

📚 Mastering Fractions, Decimals and Percentages | 掌握分数、小数和百分数

Fractions, decimals and percentages are three different ways of representing the same idea: a part of a whole. In the Cambridge KS3 Mathematics course, you are expected to move fluently between these forms, compare them, and use them in real-life problems such as discounts, probability and measurement. This revision guide covers the core techniques, common pitfalls and exam-style tips.

分数、小数和百分数是表示同一概念——整体的一部分——的三种不同方式。在剑桥 KS3 数学课程中，你需要在这三种形式之间灵活转换、比较它们，并在折扣、概率和测量等实际问题中运用它们。本复习指南涵盖核心方法、常见误区和考试技巧。

1. Fractions: Parts of a Whole | 分数：整体的部分

A fraction is written in the form a/b, where a is the numerator and b is the denominator. The denominator tells you how many equal parts the whole has been divided into, while the numerator tells you how many of those equal parts are selected. For example, in the fraction 3/8, the whole is divided into 8 equal parts and 3 of them are taken.

分数写作 a/b 的形式，其中 a 是分子，b 是分母。分母表示整体被分成多少等份，分子表示取了多少等份。例如在分数 3/8 中，整体被分成 8 等份，取其中的 3 份。

Fractions can be proper, improper or mixed. A proper fraction has a numerator smaller than its denominator, such as 2/5. An improper fraction has a numerator that is greater than or equal to its denominator, such as 7/4 or 4/4. A mixed number combines a whole number and a proper fraction, such as 2 1/3.

分数可分为真分数、假分数和带分数。真分数的分子小于分母，如 2/5。假分数的分子大于或等于分母，如 7/4 或 4/4。带分数由一个整数和一个真分数组成，如 2 1/3。

Proper: 2/5 | Improper: 7/4 | Mixed: 2 1/3

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

Equivalent fractions represent the same value even though they use different numbers. You can create an equivalent fraction by multiplying or dividing both the numerator and denominator by the same non-zero number. The value does not change because you are essentially multiplying or dividing by 1.

等值分数用不同数字表示相同数值。通过将分子和分母同时乘以或除以同一个非零数，可以得到等值分数。数值不会改变，因为本质上你是在乘以或除以 1。

2/3 = (2 × 4)/(3 × 4) = 8/12

To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). For example, 12/16 simplifies to 3/4 because the HCF of 12 and 16 is 4. Always check whether the fraction can be reduced before giving a final answer.

化简分数时，将分子和分母同时除以它们的最大公因数（HCF）。例如 12/16 化简为 3/4，因为 12 和 16 的最大公因数是 4。在给出最终答案之前，始终检查分数是否可以约分。

3. Decimals and Place Value | 小数与位值

A decimal uses a decimal point to separate the whole number part from the fractional part. The first digit after the point is tenths, the second is hundredths, and the third is thousandths. Understanding place value is essential for reading, writing and comparing decimals.

小数使用小数点将整数部分与小数部分分开。小数点后第一位是十分位，第二位是百分位，第三位是千分位。理解位值对于读、写和比较小数至关重要。

For example, in 0.37, the digit 3 is in the tenths column, so it is worth 3/10, and the digit 7 is in the hundredths column, so it is worth 7/100. In 2.045, the 4 is worth 4/100 and the 5 is worth 5/1000.

例如在 0.37 中，数字 3 在十分位，因此表示 3/10；数字 7 在百分位，因此表示 7/100。在 2.045 中，4 表示 4/100，5 表示 5/1000。

4. Percentages: Out of 100 | 百分数：每一百份

A percentage is a fraction with a denominator of 100. The symbol % means ‘per cent’

Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）