📚 Cambridge KS3 Mathematics: Fractions, Decimals and Percentages | 剑桥KS3数学：分数、小数和百分比
Welcome to this TutorHao revision guide for Cambridge KS3 Mathematics. This article focuses on fractions, decimals and percentages, one of the most important number topics at Key Stage 3. Many learners meet this topic in exercises such as page 226, question 2, and it appears frequently in Cambridge Checkpoint tests. Understanding how these three forms connect will help you solve a wide range of numerical and real-world problems.
欢迎阅读 TutorHao 为剑桥 KS3 数学准备的复习指南。本文聚焦分数、小数和百分比，这是第三学段最重要的数论主题之一。许多学习者在第226页第2题等练习中接触过这一内容，它也经常出现在剑桥 Checkpoint 考试中。理解这三种表达形式之间的联系将帮助你解决各种数值和现实问题。
1. Understanding Fractions, Decimals and Percentages | 理解分数、小数和百分比
A fraction represents part of a whole. The numerator, which is the top number, tells us how many parts are taken. The denominator, which is the bottom number, tells us the total number of equal parts. For example, ¾ means three quarters of a whole, with 3 as the numerator and 4 as the denominator.
分数表示整体的一部分。分子是上面的数，表示取了多少份；分母是下面的数，表示整体被平均分成的份数。例如，¾ 表示整体的四分之三，其中3是分子，4是分母。
A decimal uses place value and a decimal point. The digits after the point show tenths, hundredths, thousandths, and so on. A percentage means 'out of 100', so 25% means 25 out of 100. This is the same as ¼ or 0.25. These three forms are just different ways of describing the same value.
小数使用位值和一个小数点。小数点后的数字分别表示十分位、百分位、千分位等。百分比表示每100份中的部分，所以25%表示100份中的25份。它等同于 ¼ 或 0.25。这三种形式只是描述同一个值的不同方式。
¾ = 0.75 = 75%
2. Converting Between Fractions, Decimals and Percentages | 分数、小数和百分比之间的转换
.75. To convert a decimal to a percentage, multiply the decimal by 100. So 0.75 × 100 = 75%. To convert a percentage to a decimal, divide by 100, giving 75% = 0.75.
要将分数转换为小数，用分子除以分母。例如，¾ = 3 ÷ 4 = 0.75。要将小数转换为百分比，将小数乘以100。因此 0.75 × 100 = 75%。要将百分比转换为小数，除以100，得到75% = 0.75。
o a fraction, write the percentage over 100 and then simplify if possible. For example, 40% e fraction to a decimal, then multiply by 100. For example, ⅝ = 5 ÷ 8 = 0.625, so ⅝ = 62.5%.
要将百分比转换为分数，先将百分比写在100上，然后尽可能化简。例如，40% = 40/100 = 2/5。要将分数转换为百分比，先将分数转换为小数，再乘以100。例如，⅝ = 5 ÷ 8 = 0.625，因此 ⅝ = 62.5%。
Fraction → Decimal → Percentage
| Fraction | Decimal | Percentage |
|---|---|---|
| ½ | 0.5 | 50% |
| ¼ | 0.25 | 25% |
| ¾ | 0.75 | 75% |
| ⅕ | 0.2 | 20% |
| ⅖ | 0.4 | 40% |
3. Ordering and Comparing Values | 数值的大小比较与排序
ntages, the easiest method is to convert all values into decimals. For example, to compare ⅖, 0.3 and 35%, convert each value: ⅖ = 0.4, 35% = 0.35, and 0.3 is already a decimal. Then order the decimals: 0.3 < 0.35 < 0.4.
当你需要排列分数、小数和百分比的大小时，最简单的方法是把所有值都转换为小数。例如，比较 ⅖、0.3和35%，先转换每个值：⅖ = 0.4，35% = 0.35，0.3已经是小数。然后排列小数：0.3 < 0.35 < 0.4。
Another useful idea is that a larger denominator means smaller parts. Therefore ¼ is smaller than ⅓. For example, ½ is larger than ⅓ because halves are larger pieces than thirds. This concept helps you compare fractions without using a calculator.
另一个有用的概念是分母越大表示每一份越小。因此 ¼ 小于 ⅓。例如，½ 大于 ⅓，因为每一份更大。这个概念有助于你在不使用计算器的情况下比较分数。
4. Adding and Subtracting Fractions | 分数的加减法
owest common denominator of 2 and 3, which is 6. Convert: ½ = 3/6 and ⅓ = 2/6. Then add: 3
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