📚 Fractions, Decimals and Percentages | 分数、小数与百分数
Fractions, decimals and percentages are three different ways of representing parts of a whole. In IGCSE Mathematics, you must be able to convert between them, compare their sizes, and use them in real-life calculations such as discounts, interest and data comparisons. This article builds these skills step by step for Year 7 and IGCSE foundation learners.
分数、小数和百分数是表示整体中部分的三种不同方式。在 IGCSE 数学中，你必须能在它们之间进行转换、比较大小，并将它们用于折扣、利息和数据比较等实际计算。本文将为 7 年级和 IGCSE 基础阶段学生逐步构建这些技能。
1. Understanding Fractions | 理解分数
A fraction has a numerator (top number) and a denominator (bottom number). The denominator tells you how many equal parts the whole is divided into, and the numerator tells you how many of those parts are taken. For example, in 3/4, the whole is split into 4 equal parts and we consider 3 of them.
分数由分子（上面的数）和分母（下面的数）组成。分母表示整体被分成多少等份，分子表示取了多少份。例如，在 3/4 中，整体被分成 4 等份，我们考虑其中的 3 份。
A proper fraction has a numerator smaller than the denominator, such as 2/5. An improper fraction has a numerator larger than or equal to the denominator, such as 7/4. A mixed number combines a whole number and a proper fraction, such as 1 3/4.
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。带分数由一个整数和一个真分数组成，如 1 3/4。
2. Equivalent Fractions and Simplifying | 等值分数与化简
the numerator and denominator by the same non-zero number. For example, 1/2 = 2/4 = 5/10.
等值分数虽然形式不同，但值相同。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。例如，1/2 = 2/4 = 5/10。
To simplify a fraction, divide the numerator and denominator by their highest common factor (HCF). For instance, 12/16 simplifies to 3/4 because the HCF of 12 and 16 is 4. A fraction is in simplest form when the only common factor of the numerator and denominator is 1.
化简分数时，用分子和分母的最大公因数（HCF）去除它们。例如，12/16 化简为 3/4，因为 12 和 16 的最大公因数是 4。当分子和分母的唯一公因数是 1 时，分数就是最简形式。
3. Fractions to Decimals | 分数转小数
minator. You can use short division or a calculator. For example, 3/8 means 3 ÷ 8 = 0.375.
要将分数转换为小数，用分子除以分母。你可以使用短除法或计算器。例如，3/8 表示 3 ÷ 8 = 0.375。
ng, put a dot over the repeating digit, such as 1/3 = 0.333... = 0.3 with a repeating dot.
常见转换值得记住：1/2 = 0.5、1/4 = 0.25、3/4 = 0.75、1/5 = 0.2、1/10 = 0.1。如果除法无限循环，在循环数字上方加点，如 1/3 = 0.333... = 0.3（3 上面加循环点）。
4. Decimals to Fractions | 小数转分数
over a power of 10, then simplify. For example, 0.65 = 65/100 = 13/20 after dividing by 5.
要将有限小数转换为分数，把小数数字作为分子，分母写成 10 的幂，然后化简。例如，0.65 = 65/100 = 13/20（除以 5 后）。
but foundation learners should recognise simple recurring decimals such as 0.333... = 1/3.
对于循环小数，可以通过设方程并用减法消去循环部分来转换。这在扩展层级更常见，但基础阶段学生应认识简单的循环小数，如 0.333... = 1/3。
5. Percentages Basics | 百分数基础
A percentage is a fraction with denominator 100. The symbol % means "out of 100". For example, 45% means 45 out of 100, which can be written as 45/100 or 0.45.
百分数是分母为 100 的分数。符号 % 表示“每一百”。例如，45% 表示每 100 份中的 45 份，可以写成 45/100 或 0.45。
Percentages do not have to be whole numbers. You can have 12.5% Percentages greater than 100 represent amounts larger than the original whole, such as 150% = 1.5.
百分数不一定是整数。可以有 12.5%，表示每 100 份中的 12.5 份。大于 100 的百分数表示比原始整体更大的量，如 150% = 1.5。
6. Converting Fractions, Decimals and Percentages | 分数、小数和百分数的互化
100 as a bridge. To change a percentage to a fraction, write it over 100 and simplify: 25% = 25/100 = 1/4. To change a percentage to a decimal, divide by 100: 25% = 0.25.
以 100 为桥梁。将百分数转换为分数时，把它写在 100 上面并化简：25% = 25/100 = 1/4。将百分数转换为小数时，除以 100：25% = 0.25。
To change a decimal to a percentage, multiply by 100: 0.07 = 7% ercentage, first convert it to a decimal by division, then multiply by 100: 3/5 = 0.6 = 60%.
将小数转换为百分数时，乘以 100：0.07 = 7%。将分数转换为百分数时，先用除法把它转换为小数，再乘以 100：3/5 = 0.6 = 60%。
Percentage → Decimal: ÷ 100 | Decimal → Percentage: × 100
Keep the same numerical value when converting. The representation changes but the amount does not.
转换时保持数值不变。表示形式改变，但数量不变。
7. Comparing and Ordering | 比较与排序
iest common form is often a decimal or a percentage. For example, compare 3/5, 0.55 and 58%. As decimals: 3/5 = 0.6, 0.55 = 0.55, 58% = 0.58. Order from smallest to largest: 0.55, 0.58, 0.6.
比较分数、小数和百分数时，将它们改写成同一种形式。最简单的共同形式通常是小数或百分数。例如，比较 3/5、0.55 和 58%。写成小数：3/5 = 0.6，0.55 = 0.55，58% = 0.58。从小到大排序为：0.55、0.58、0.6。
For fractions with the same denominator, compare numerators directly. For fractions with different denominators, use equivalent fractions or convert to decimals.
对于分母相同的分数，直接比较分子。对于分母不同的分数，使用等值分数或转换为小数。
8. Percentage of a Quantity | 求一个数量的百分数
of a quantity, write the percentage as a decimal or fraction and multiply. For example, 30% of 80 = 0.30 × 80 = 24.
要求一个数量的百分数，把百分数写成小数或分数，然后相乘。例如，80 的 30% = 0.30 × 80 = 24。
Non-calculator methods often use 10% as a starting point. To find 15% of 60, find 10% = 6 and 5% = 3, then add to get 9.
非计算器方法通常以 10% 为起点。求 60 的 15%，先求 10% = 6 和 5% = 3，然后相加得到 9。
9. Fraction of a Quantity | 求一个数量的几分之几
divide by the denominator and multiply by the numerator. For example, 3/4 of 20 = (20 ÷ 4
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