📚 Number Skills: Fractions, Decimals and Percentages | 数字技能：分数、小数与百分比
Fractions, decimals and percentages are three connected ways of representing parts of a whole. In IGCSE Mathematics, this topic forms the foundation for many later areas, including ratio, proportion, algebra and probability. Building strong number skills at Year 7 level will make future problem solving much easier and more accurate.
分数、小数和百分比是表示整体中某一部分的三种相互关联的形式。在 IGCSE 数学中，这一主题为许多后续内容打下基础，包括比、比例、代数和概率。在 7 年级阶段建立扎实的数字技能，会让今后的解题更加容易和准确。
1. Understanding Fractions | 理解分数
A fraction represents a part of a whole or a part of a set. It is written as a/b, where a is the numerator and b is the denominator. The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts are taken.
分数表示一个整体或一组对象的一部分。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，分子表示取了多少份。
For example, in the fraction 3/4, the denominator 4 means the whole is split into 4 equal parts, and the numerator 3 means we have 3 of those parts. Fractions can also represent division, so 3/4 is the same as 3 ÷ 4.
例如，在分数 3/4 中，分母 4 表示整体被分成 4 等份，分子 3 表示我们取其中的 3 份。分数也可以表示除法，所以 3/4 等同于 3 ÷ 4。
2. Equivalent Fractions and Simplifying | 等值分数与化简
Equivalent fractions are fractions that look different but represent the same value. You can create equivalent fractions by multiplying or dividing both the numerator and the denominator by the same non-zero number.
等值分数是看起来不同但数值相同的分数。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。
To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). A fraction is in its simplest form when the numerator and denominator have no common factor other than 1. For example, 8/12 simplifies to 2/3 because both 8 and 12 can be divided by 4.
化简分数时，用分子和分母的最大公因数（HCF）同时除以它们。当分子和分母除了 1 以外没有其他公因数时，分数就是最简形式。例如，8/12 化简为 2/3，因为 8 和 12 都能被 4 整除。
3. Improper Fractions and Mixed Numbers | 假分数与带分数
An improper fraction has a numerator that is greater than or equal to its denominator, such as 7/4 or 9/3. A mixed number combines a whole number and a proper fraction, such as 1 3/4.
假分数的分子大于或等于分母，例如 7/4 或 9/3。带分数由一个整数和一个真分数组成，例如 1 3/4。
ver the original denominator. For example, 7/4 = 1 3/4 because 7 ÷ 4 = 1 with remainder 3.
将假分数转换为带分数时，用分子除以分母。商是整数部分，余数作为分数部分的分子，分母保持不变。例如，7/4 = 1 3/4，因为 7 ÷ 4 = 1 余 3。
4. Adding and Subtracting Fractions | 分数的加减
and keep the denominator unchanged. For example, 2/9 + 4/9 = 6/9, which simplifies to 2/3.
同分母分数相加减时，只需将分子相加或相减，分母保持不变。例如，2/9 + 4/9 = 6/9，化简后为 2/3。
minator, then add or subtract the numerators. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
如果分母不同，先求出最小公分母（LCD），把每个分数改写为以该分母为分母的等值分数，然后再加减分子。例如，1/3 + 1/4 = 4/12 + 3/12 = 7/12。
5. Multiplying and Dividing Fractions | 分数的乘除
ominators together. Simplify the result if possible. For example, 2/5 × 3/4 = 6/20 = 3/10.
分数相乘时，分子乘以分子，分母乘以分母。如果可能，再化简结果。例如，2/5 × 3/4 = 6/20 = 3/10。
multiply by its reciprocal. The reciprocal of a/b is b/a. This rule is often remembered as 'keep, change, flip'. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
除以一个分数等于乘以它的倒数。a/b 的倒数是 b/a。这个规则常被记作 'keep, change, flip'。例如，2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6。
6. Introduction to Decimals | 小数入门
A decimal is another way of writing a fraction whose denominator is a power of 10, such as 10, 100 or 1000. The digits after the decimal point represent tenths, hundredths, thousandths, and so on.
小数是分母为 10、100 或 1000 等 10 的幂的分数的另一种写法。小数点后的数字依次表示十分位、百分位、千分位等。
hs place, and the 5 is in the thousandths place. This means 0.375 = 3/10 + 7/100 + 5/1000.
读写小数时，数位非常重要。例如，在小数 0.375 中，3 在十分位，7 在百分位，5 在千分位。这意味着 0.375 = 3/10 + 7/100 + 5/1000。
7. Converting Between Fractions and Decimals | 分数与小数互化
/8 = 3 ÷ 8 = 0.375. This method works for any fraction, even if the division does not end.
将分数转换为小数时，用分子除以分母。例如，3/8 = 3 ÷ 8 = 0.375。这个方法适用于任何分数，即使除法不能除尽。
10 based on the number of decimal places, then simplify. For example, 0.75 = 75/100 = 3/4.
将有限小数转换为分数时，根据小数位数把小数写成分母为 10 的幂的分数，再化简。例如，0.75 = 75/100 = 3/4。
ing decimals is useful for IGCSE questions. For example, 2/3 = 0.666... and 1/9 = 0.111...
有些分数会得到循环小数，例如 1/3 = 0.333...，也可在循环数字上加点表示。识别常见循环小数对 IGCSE 题目很有帮助。例如，2/3 = 0.666...，1/9 = 0.111...
8. Percentages and Their Meaning | 百分比及其意义
A percentage is a fraction with denominator 100. The symbol % means 'out of 100'. For example, 25% means 25 out of 100, or 25/100.
百分比是分母为 100 的分数。符号 % 表示 '每一百'。例如，25% 表示 100 份中的 25 份，即 25/100。
Percentages are used to compare proportions in a standardised way. They appear in discounts, interest rates, test scores and statistics. Understanding percentages is therefore a key life skill as well as an exam requirement.
百分比用于以标准化方式比较比例。它们出现在折扣、利率、考试成绩和统计数据中。因此，理解百分比既是一项重要的生活技能，也是考试要求。
ultiply the quantity by the percentage expressed as a decimal or fraction. For example, 15% of 60 = 0.15 × 60 = 9.
求一个数量的百分之几时，用该数量乘以表示成小数或分数的百分比。例如，60 的 15% = 0.15 × 60 = 9。
9. Converting Between Fractions, Decimals and Percentages | 分数、小数和百分比互化
The three forms of a rational number can be converted easily if you remember the key equivalents. Fractions to percentages: first convert to a decimal or directly make denominator 100. Decimals to percentages: multiply by 100 and add the % sign. Percentages to decimals: divide by 100.
有理数的三种形式可以轻松互化，只要记住关键等值关系。分数转百分比：先转换为小数，或直接把分母变成 100。小数转百分比：乘以 100 并加上 % 号。百分比转小数：除以 100。
It is also useful to memorise common conversions so that you can spot them quickly in exam questions.
记住常见的转换也很有用，这样你就能在考试题目中快速识别它们。
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| 1/3 | 0.333... | 33⅓% |
10. Comparing and Ordering Quantities | 数量比较与排序
To compare fractions, decimals and percentages, convert them all to the same form. Decimals are often the easiest for comparison because you can align place values.
要比较分数、小数和百分比，先把它们化为同一种形式。小数通常最容易比较，因为可以对齐数位。
For example, arrange 2/5, 0.45 and 38% in ascending order. Convert: 2/5 = 0.4, 0.45 = 0.45, 38% = 0.38. The order from smallest to largest is 38%, 2/5, 0.45.
例如，将 2/5、0.45 和 38% 按从小到大排列。转换后：2/5 = 0.4，0.45 = 0.45，38% = 0.38。从最小到最大的顺序为 38%、2/5、0.45。
Always double-check whether the question asks for ascending or descending order, and give your answer in the original forms. This is a common place to lose easy marks.
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