📚 Mastering Fractions, Decimals and Percentages | 掌握分数、小数与百分数
In KS3 Cambridge Mathematics, fractions, decimals and percentages are connected ways of describing parts of a whole. Many learners find them difficult because the same quantity can be written in three different forms. This article explains the key skills, common pitfalls and exam strategies you need to work confidently with FDP.
在 KS3 剑桥数学中，分数、小数和百分数是描述整体的一部分的三种相互关联的方式。许多学生觉得它们困难，因为同一个量可以用三种不同的形式表示。本文讲解关键技能、常见错误以及考试策略，帮助你自信地处理 FDP。
1. Why FDP Matters | 为什么 FDP 很重要
Fractions, decimals and percentages appear in almost every Cambridge KS3 topic, from probability to ratio, measurement and data handling. Being able to switch between forms allows you to compare quantities easily and solve real-life problems such as discounts, interest and test scores.
分数、小数和百分数几乎出现在剑桥 KS3 的每个主题中，从概率到比、测量和数据处理。能够在不同形式之间切换可以让你轻松比较数量，并解决折扣、利息和考试成绩等实际问题。
In an exam, a percentage might be easier to understand than a fraction, or a decimal may be needed for a calculator method. Building fluency in FDP conversion saves time and reduces mistakes.
在考试中，百分数可能比分数更易理解，或者在计算器方法中需要用到小数。熟练掌握 FDP 的转换可以节省时间并减少错误。
2. Equivalent Fractions | 等值分数
Equivalent fractions have the same value even though they use different numerators and denominators. For example, 1/2, 2/4, 3/6 and 50/100 all represent the same proportion. You can create equivalent fractions by multiplying or dividing the numerator and denominator by the same non-zero number.
等值分数虽然分子和分母不同，但数值相同。例如，1/2、2/4、3/6 和 50/100 都表示相同的比例。你可以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。
This idea is the foundation for simplifying fractions and comparing fractions with different denominators. Always multiply or divide both parts of the fraction, never just the numerator or just the denominator.
这个思想是化简分数和比较不同分母分数的基础。一定要同时乘或除分数的两个部分，绝不能只乘或除分子或只乘或除分母。
1/2 = (1 × 3)/(2 × 3) = 3/6
3. Simplifying Fractions | 化简分数
n factor (HCF). For example, to simplify 18/24, the HCF of 18 and 24 is 6, so 18/24 = 3/4.
化简分数时，用分子和分母的最大公因数（HCF）同时除它们。例如，化简 18/24 时，18 和 24 的最大公因数是 6，所以 18/24 = 3/4。
A fraction is in its simplest form when the numerator and denominator have no common factor other than 1. Always check whether you can divide again before writing your final answer.
当分子和分母除 1 以外没有其他公因数时，分数就是最简形式。在写出最终答案之前，一定要检查是否还能继续约分。
18/24 = (18 ÷ 6)/(24 ÷ 6) = 3/4
4. Converting Between Fractions, Decimals and Percentages | 分数、小数与百分数互化
÷ 8 = 0.375. To convert a decimal to a percentage, multiply by 100. Therefore 0.375 = 37.5%.
将分数转换为小数时，用分子除以分母。例如，3/8 表示 3 ÷ 8 = 0.375。将小数转换为百分数时，乘以 100，因此 0.375 = 37.5%。
rt a percentage to a fraction, write it over 100 and simplify if possible. For example, 65% = 65/100 = 13/20.
将百分数转换为小数时，除以 100。将百分数转换为分数时，把它写在 100 之上并尽可能化简。例如，65% = 65/100 = 13/20。
With recurring decimals such as 1/3 = 0.333..., you can write 0.3̇ uestions often ask for an exact fraction or a decimal to a given number of decimal places.
对于循环小数，如 1/3 = 0.333...，你可以写作 0.3̇ 或四舍五入到合适的精确度。剑桥的题目经常会要求写出精确分数或给定小数位数的小数。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
5. Ordering
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